Psychological Review
2005, Vol. 112, No. 4, 951–978
Copyright 2005 by the American Psychological Association
0033-295X/05/$12.00 DOI: 10.1037/0033-295X.112.4.951
Why Most People Disapprove of Me: Experience Sampling
in Impression Formation
Jerker Denrell
Stanford University
Individuals are typically more likely to continue to interact with people if they have a positive impression of
them. This article shows how this sequential sampling feature of impression formation can explain several
biases in impression formation. The underlying mechanism is the sample bias generated when the probability
of interaction depends on current impressions. Because negative experiences decrease the probability of
interaction, negative initial impressions are more stable than positive impressions. Negative initial impressions, however, are more likely to change for individuals who are frequently exposed to others. As a result,
systematic differences in interaction patterns, due to social similarity or proximity, will produce systematic
differences in impressions. This mechanism suggests an alternative explanation of several regularities in
impression formation, including a negativity bias in impressions of outgroup members, systematic differences
in performance evaluations, and more positive evaluations of proximate others.
Keywords: impression formation, sampling, judgment bias, stereotypes
Suppose, for example, that a colleague in your field asks about
the social skills of a faculty member at your school. Approaching
life systematically, you begin by listing all your interactions with
this individual and evaluating his or her social skills during these
interactions. Being statistically trained, you take the average and
report this as your best estimate. Although this procedure seems
fair, it will often result in systematically biased estimates. Moreover, the estimate will also vary systematically depending on the
type of individual that you are evaluating. In particular, even if you
accurately register and recollect all your interactions, there is a risk
of reporting systematically lower estimates for members of minority groups to which you do not belong.
The reason is that the above procedure ignores a major feature
of experience sampling (Denrell & March, 2001; Eiser, Fazio,
Stafford, & Prescott, 2003; Gilovich, 1991; T. M. Newcomb,
1947). The experience of interacting with an individual with seemingly low social skills decreases the likelihood of future interactions, whereas the experience of interacting with an individual with
seemingly high social skills increases the likelihood of future
interactions. As a result of such experience sampling, false negative initial impressions are unlikely to be corrected. A false positive initial impression, however, will lead to further sampling,
which might disconfirm the initial belief. This asymmetry implies
that even if impressions are based on all available observations,
and each observation is accurately interpreted and remembered,
impressions may nevertheless be biased (Denrell & March, 2001;
Eiser et al., 2003; Fazio, Eiser, & Shook, 2004). In fact, even if
each experience is equally likely to be positive or negative, a
majority of individuals, when asked about their impression, will
report that their impression is negative.
This article shows how this sequential sampling feature of
impression formation can explain a variety of biases in impression
formation. I demonstrate that experience sampling implies that
individuals with similar characteristics and skill levels may be
evaluated differently as a result of differences in social ties and
Why do evaluations and impressions depend systematically on
gender, ethnicity, proximity, and attractiveness? Much research in
impression formation has attributed such systematic biases to flaws in
information processing and hypothesis testing and to motivational
influences. Prior expectations, including stereotypes, confirmation
bias and self-fulfilling prophecies, as well as the desire to maintain a
positive social identity have been argued to distort the perception,
interpretation, and recall of behavior of individuals and groups (Allport, 1954; Asch, 1946; Fiske & Taylor, 1991; Hilton & von Hippel,
1996; Rosenthal & Jacobsen, 1968; Snyder & Stukas, 1999; Snyder &
Swann, 1978; Tajfel, Flament, Billig, & Bundy, 1971; Word, Zanna,
& Cooper, 1974).
This article argues that there is an important alternative source
of bias in impression formation. Even if impressions would be
based on all available evidence, and the evidence would be accurately interpreted, impressions might nevertheless be biased. The
reason is the sample selection bias introduced by experience
sampling.
This article has benefited from prior joint work with James March. I
thank Chip Heath, James March, and Dale Miller for their extensive
comments and help. I am also grateful for comments and help from Bill
Barnett, Marilynn Brewer, Lawrence Brown, Glenn Carroll, Christian
Czernich, Hillary Elfenbein, Christina Fang, Deborah Gruenfeld, Mike
Hannan, Richard Harrison, Rod Kramer, Dan Levinthal, Steve Lippman,
Anders Martin-Löf, Maggie Neal, Jeffrey Pfeffer, Patrick Regnér, Lee
Ross, Zur Shapira, Udo Zander, and participants in seminars at the Haas
School of Business at the University of California, Berkeley, Harvard Business
School Scandinavian Consortium for Organizational Research, Stanford
Graduate School of Business, the Department of Psychology at Stanford
University, Stockholm School of Economics, and the Wharton School of
Management. Erica Carranza, Deborah Prentice, Jeff Larsen, Noah Gans,
George Knox, Rachel Croson, James Shah, Paige Brazy, and Tory Higgins
generously allowed me to use their data. All errors are my own.
Correspondence concerning this article should be addressed to Jerker
Denrell, Graduate School of Business, Stanford University, 518 Memorial
Way, Stanford, CA 94305-5015. E-mail: [email protected]
951
DENRELL
952
interactions. The implication is that experience sampling can provide an alternative explanation for several systematic biases in
impression formation. In this explanation, biased evaluations do
not result from the influence of prior expectations on the interpretation of subsequent observations, biased hypothesis testing and
self-fulfilling prophecies, or motivational influences. Rather, biased evaluations are the result of systematic differences in social
interactions, which determine the information to which evaluators
have access. Individuals whom evaluators are likely to meet,
irrespective of their opinions of them, will have more chances to
correct a false negative impression. In contrast, individuals whom
evaluators are less likely to meet are less likely to get a second
chance. For such individuals, false-negative first impressions are
more likely to be stable.
Such a model of experience sampling cannot, and does not try
to, provide an alternative explanation of the findings of experiments in which the information available to subjects is fixed and
exogenous. A long line of work has established that cognitive and
perceptual biases can influence impression formation in such situations. This article suggests a complementary explanation of
systematic biases in impression formation in many real-life contexts in which information is not automatically provided but has to
be actively sampled. In particular, I demonstrate that pragmatic
constraints in sampling (Einhorn & Hogarth, 1978; Friedrich,
1993) may contribute to what researchers typically interpret as
cognitive–perceptual biases. In line with recent work on sampling
(Fiedler, 1996, 2000; Kashima, Woolcock, & Kashima, 2000; Van
Rooy et al., 2003), this article suggests that cognitive and perceptual biases are not necessary to explain systematic biases in impression formation and judgment.
Sampling in Impression Formation
Much research in impression formation has examined how
impressions are influenced by cognitive heuristics in information
processing and perceptual biases. By manipulating the order of
observation or by inducing different expectations before the information is presented, studies have demonstrated how information
order and expectations influence the interpretation, recall, and
integration of information (Asch, 1946; Jussim & Eccles, 1995;
Lord, Ross, & Lepper, 1979; Rosenthal & Jacobsen, 1968; Snyder,
Campbell, & Preston, 1982; Snyder & Stukas, 1999; Snyder &
Swann, 1978). By manipulating group membership, other studies
have demonstrated how group identification influences information integration and evaluation (Cadinu & Rothbart, 1996; Hewstone, Rubin, & Willis, 2002; Krueger, 1996; Mullen, Brown, &
Smith, 1992; Tajfel, 1982; Tajfel et al., 1971).
However, impressions do not only depend on how observations
are interpreted and processed but also on the observations that are
sampled. In many settings observations vary widely, and impressions may depend more on decisions about sampling than on
information integration. Any systematic biases in sampling will
thus lead to systematic biases in impression formation (Fiedler,
2000). Such systematic sample biases have of course been explored in the literature. They have been prominent in discussions
of confirmation bias (Klayman & Ha, 1987; Snyder & Swann,
1978), selective exposure (Kunda, 1990), and availability and
salience (Nisbett & Ross, 1980; S. E. Taylor, 1982; Tversky &
Kahneman, 1973), in which sample bias has been attributed to
heuristics or motivational influences. Sample bias may also be due
to unrepresentative samples, based on the available information
(Combs & Slovic, 1979; Dawes, 1993; Denrell, 2003; Fiedler,
2000) or based on the self (Krueger, 1996; Krueger & Zeiger,
1993; Ross, Greene, & House, 1977). Mere differences in sample
sizes can also produce systematic differences in evaluations of
groups in situations in which information aggregation has a systematic effect on judgments (Fiedler, 1996, 2000; Kashima et al.,
2000; Van Rooy et al., 2003). Finally, how much and what type of
information people search for and how they process it has been
shown to depend on the valence of their current impression
(Ybarra, 2002). Positive impressions lead to more testing and more
critical information processing than negative impressions do, because negative behaviors are assumed to be more diagnostic.
In social interactions, however, there is an important source of
sample bias that has remained largely unexplored. In many impression formation contexts, the information available depends on
decisions about social interactions. Unless an individual decides to
interact with another individual, no additional information may be
available (T. M. Newcomb, 1947; Towles-Schwen & Fazio, 2003).
Decisions about interactions, however, are influenced by the valence of impressions formed on the basis of previous interactions.
In particular, one of the more common ideas about social interactions is that future interactions are more likely if previous interactions suggest that future interactions will be rewarding or pleasurable (Altman & Taylor, 1973; Berscheid, 1985; Homans, 1961;
Lott & Lott, 1972; Montoya & Horton, 2004; T. M. Newcomb,
1953; Sunnafrank, 1986; Thibaut & Kelley, 1959). “If good outcomes are experienced in initial contacts or if these contacts lead
the persons to anticipate good outcomes in the future, the interaction is likely to be repeated” (Thibaut & Kelley, 1959, p. 20).
Such a tendency has been demonstrated in a variety of experimental and field studies. Experiments manipulating rewards during interactions have shown that willingness to continue the interaction is
higher for individuals who have experienced rewarding interactions
(Chambliss, 1966; D. A. Taylor, Altman, & Sorrentino, 1969, p. 333).
Ratings of attraction, based on initial information about a future
interaction partner, also predict willingness to continue the interaction
(Carranza, Prentice, & Larsen, 2004; Montoya & Horton, 2004, p.
700; M. S. Schwartz, 1966, cited in Byrne, 1971, p. 231). For
example, in the study by Carranza et al. (2004), 66 subjects each
listened to statements by 60 individuals. Subjects were asked to rate
how much they liked each individual and how likely they would be,
on a scale from 1 to 5, to be friends with him or her, to hang out with
him or her, to enjoy spending time with him or her, to stay away from
him or her, and so forth. The correlations with ratings of liking were
⫹.76 (be friends), ⫹.71 (hang out with), ⫹.74 (enjoy spending time),
and ⫺.70 (stay away).1 Experiments and field studies have also
shown that negative impressions and outcome expectancies predict
avoidance (S. Levin, van Laar, & Sidanius, 2003; Plant, 2004; Plant
& Devine, 2003; Towles-Schwen & Fazio, 2003). In particular, Plant
and Devine (2003, Study 2; see also Plant, 2004) showed that subjects
with negative expectations about future interactions were less likely to
return for an additional session in which they would continue the
interaction. Finally, several experimental studies have shown that the
N ⫽ 3,960. I calculated these correlations on the basis of data provided
by Carranza et al. (2004).
1
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
frequency of communication is higher for individuals who have
experienced rewarding interactions (D. A. Taylor et al., 1969), have
positive impressions of others (Kelley, 1950, pp. 437– 438; Thibaut &
Coules, 1952, pp. 774 –775), and for groups that have more favorable
attitudes to each other (Lott & Lott, 1961; Moran, 1966).
The general tendency that attraction breeds interaction is also
consistent with sociometric data. Sociometric studies have typically shown that similarity, an important determinant of attraction
(Byrne, 1971), is a good predictor of affiliation (for a review, see
McPherson, Smith-Lovin, & Cook, 2001). More generally, sociometric studies have shown that ratings of attraction and liking are
positively correlated with sociometric nomination measures
(Bukowski, Sippola, Hoza, & Newcomb, 2000; Hoffman, 1962;
Maassen, van der Linden, Goossens, & Bokhorst, 2000) and that
popular individuals tend to have more likable characteristics (Bonney, 1947; French, 1956; French & Mensh, 1948; Jennings, 1950;
Leman & Solomon, 1952; A. F. Newcomb, Bukowski, & Pattee,
1993). There is also some evidence that sociometric rank (i.e.,
popularity) is positively correlated with the number of actual
interactions and conversations (Homans, 1954, Table 1).
However, attraction does not always lead to interaction (Berscheid, 1985). Highly attractive individuals may be difficult to
access. Attractive and competent individuals are also less likely to
be chosen as interaction partners if one fears that the choice will
not be reciprocated (Berscheid, 1985; Huston & Levinger, 1978;
Shaw & Gilchrist, 1955). Highly attractive and competent individuals may also be avoided for fear of low evaluations (Berscheid,
1985; Montoya & Horton, 2004) or due to intimidation (Aronson,
Willerman, & Floyd, 1966; Helmreich, Aronson, & LeFan, 1970).
Notwithstanding these caveats, positive impressions do seem to be
an important determinant of the probability of future interaction.
Such a tendency, however, implies that the sample of information available will be biased. In particular, if decisions about social
interactions depend on impressions based on the available information, and decisions about social interactions determine the available information, the sample of information available will depend
on the outcomes of past observations. As a result, the available
sample will not be exogenous but endogenous. Although not
universal, such endogenous sampling is likely in social settings
satisfying the following conditions.
First, impressions are mainly based on, or at least influenced by,
impressions formed by personal observations. For example, assessments of social skills can mainly be based on impressions obtained
through personal interactions. Impressions of several other personal
attributes are also influenced by personal observations, even if information from tests and from other individuals may be available. In
these situations, future interaction, and thus the available sample, will
be influenced by impressions based on previous interactions. In other
situations, such as in exams, the set of observations available is
exogenously determined.
Second, individuals can choose with whom they want to interact. If individuals cannot voluntarily choose their future interaction
partners, such as when interaction patterns are circumscribed by
the division of labor, status hierarchies, or roles, impressions based
on previous interactions cannot influence the probability of future
interactions.
Third, impressions based on observations from previous interactions are relevant for expectations about how rewarding or
productive future interactions will be. For example, impressions of
953
social skills are relevant for expectations of how pleasurable future
interactions will be. Impressions of many other personal attributes,
such as skills, creativity, or reasoning ability, may also influence
expectations about how rewarding or productive future interactions will be. Nevertheless, this does not hold for all personal
attributes and interactions. For example, your impressions of the
bowling skills of others may be irrelevant to your expectation of
the pleasures of future social interactions.
In social situations satisfying these conditions, the available
information will not be a random sample of fixed size as in
experiments. Rather, the composition and size of the sample will
depend on past observations. To illustrate this, consider a schematic representation of the sampling process depicted in Figure 1.
As shown, the information available depends on decisions about
interactions, which depend on current impressions. Current impressions, however, depend on observations obtained through previous interactions. It follows that the set of observations available
will depend on the outcome of past interactions. In particular, a
positive impression implies that the probability of further observations is high and the sample size will expand. A negative
impression, in contrast, implies that the probability of further
observations is low and the sample size will be constrained (Gilovich, 1991; T. M. Newcomb, 1947; Towles-Schwen & Fazio,
2003; Ybarra, 2002, p. 437). Thus, the valence of current impressions will determine not only how much and what type of information people search for and how they process it (Ybarra, 2002),
but also whether new information will be available at all.
Because historical outcomes influence sampling, experience sampling produces a sample bias (Denrell & March, 2001; Eiser et al.,
2003; Fazio et al., 2004; Heckman, 1979; March, 1996). Despite such
bias, experience sampling is often the only practical way of sampling.
If productive interactions are important and impressions are relevant
for expectations about future interactions, it may not be sensible to
continue sampling if the impression is sufficiently negative. Few
people continue to interact with people they disapprove of just to see
if their initial impressions were false. Similarly, few people actively
seek out professional colleagues (who may not be working in the
same organization) if their initial impressions suggest they cannot
gain, professionally or socially, by future interactions.
Such behavior is not unintelligent. People may recognize that
taking more observations will increase the accuracy of evaluations,
but accuracy is seldom the only objective of social interactions
(Friedrich, 1993). The goal of accuracy has to be balanced against the
goal of engaging in productive interactions (Einhorn, 1986; Einhorn
& Hogarth, 1978; Friedrich, 1993; Klayman & Ha, 1987; Peeters,
1971; B. Schwartz, 1982). The basic trade-off is the same as in the
classical one-armed bandit problem (e.g., DeGroot, 1970), in which a
Figure 1. The relation between the current impression, decisions about
interactions, and the information available under experience sampling.
DENRELL
954
decision maker can repeatedly choose between a certain alternative
with a known payoff and an unknown alternative with an uncertain
payoff. In this situation, more information about the uncertain alternative is valuable because it makes possible more informed choices in
the future. Nevertheless, if the uncertain alternative is perceived to be
inferior, obtaining such information is costly because information can
only be obtained by choosing a seemingly inferior alternative. As a
result, it may be optimal to stop sampling in order to exploit the
alternative that is believed to be better. For a similar reason, limited
sampling in impression formation may be optimal when individuals
care about the outcome of interactions as well as the accuracy of their
evaluations. Such limited sampling has also been observed in experiments on rule learning when payoffs depend on outcomes. Subjects
who were instructed to maximize their outcomes were much less
likely to experiment with alternative rules if they had found a rule that
generated a satisfactory outcome than were subjects who were told
that they would be assessed on whether they found the correct rule (B.
Schwartz, 1982).
This implies that in many situations in which information gathering is not the only priority, impressions have to be based on
limited and biased samples. Some of the complications introduced
by this type of sample bias have been noted in the statistical
literature (Duflo, 1997, chap. 9; Lee, 1989, chap. 7; Melfi & Page,
2000; Wetherill, 1966, chap. 8), and some of its behavioral consequences have been noted in psychology, economics, and organization theory (Cohen & Levinthal, 1994, Proposition 1; Denrell
& March, 2001; Eiser et al., 2003; Gilovich, 1991, pp. 46 – 48;
March, 1996; Rabin, 2002, p. 807). Here, I examine how this bias
may explain systematic differences in impression formation.
A Simple Example of the Effect of Experience Sampling
Model
To illustrate the implications of experience sampling, consider
the process by which an individual, A, forms an impression of
another individual, B. Because B’s behavior may vary, any single
observation of B’s behavior may be regarded as a sample from a
random variable, X. For the purposes of this illustration, assume
that X is a normally distributed random variable with a mean of 0
and a standard deviation of 1.
A’s belief about B is assumed to evolve over time as a function of
new observations of the behavior of B. I assume that this process of
belief formation can be modeled as a sequential revision of current
beliefs in view of new evidence (Anderson, 1981; Hogarth & Einhorn, 1992; Kashima & Kerekes, 1994). Specifically, A’s current
belief is assumed to provide an anchor that is adjusted on the basis of
new evidence. The revised belief then becomes the anchor for the next
adjustment, and the process continues sequentially.
A simple way to model such a sequential process of belief
revision is to assume that the revised belief is some weighted
combination of the previous belief and the new evidence, if any. If
the belief, or estimate, in period t is denoted x̂t, one way to
represent such a process is as follows:
x̂t⫹1 ⫽
冦
共1 ⫺ b兲x̂t ⫹ bxt⫹1
if an observation is made in period t ⫹ 1
.
x̂t
if no observation is made in period t ⫹ 1
(1)
It is also assumed that the impression in the first period is equal
to bx1. Here, b is a positive fraction regulating the weight of the
most recent observation. This specific process implies that A’s
current estimate is an exponentially weighted average of all observations of B. Such a weighted-average model is in the spirit of
the models suggested in the literature on information integration
and belief adjustment (Anderson, 1959, 1981; Hogarth & Einhorn,
1992; Kashima & Kerekes, 1994). The specific model above is
also consistent with a recency effect, in which late observations are
given more weight than early observations. A recency effect has
been consistently observed in experimental studies of impression
formation if subjects are required to formulate an impression after
each piece of information is presented (i.e., serial responding; for
reviews, see Hogarth & Einhorn, 1992; Kashima & Kerekes,
1994). Such serial responding seems representative of situations in
which individuals have to decide, after each impression, whether
to continue the interaction.
In contrast to more elaborate models in the literature (e.g.,
Hogarth & Einhorn, 1992; Kashima & Kerekes, 1994; Van Overwalle & Labiouse, 2004), the above model assumes that the weight
of the most recent observation is constant and independent of the
value of the observation and of the distance between the observation and the existing impression, which may not hold (Hogarth &
Einhorn, 1992; Kashima & Kerekes, 1994; Skowronski & Carlston, 1989; Stangor & McMillan, 1992; Van Overwalle & Labiouse, 2004). Moreover, in contrast to theories of impression formation as driven by schemata and categorizations (Fiske & Taylor,
1991), the above model assumes that all observations are correctly
registered and interpreted and, thus, does not capture the significance of schemata, the effect of first impressions, or differential
memory for consistent or inconsistent information (Stangor &
McMillan, 1992). Also, the model does not allow for confirmation
bias or self-fulfilling prophecies, which can contribute to a primacy effect. These omissions, however, also imply that any bias in
evaluations resulting from the above belief-formation process cannot be due to such errors of information processing or to the effects
of attention. I also demonstrate that the general results hold for
more general assumptions about how impressions are formed.
Assume, for simplicity, that A always interacts with B in the first
period. In later periods, however, A’s current impression, x̂t, forms the
basis for whether A will choose to interact with B. In particular,
assume that A is more likely to interact with B in period t ⫹ 1 if the
current impression, x̂t, is high than if it is low. The reason is that a low
estimate implies a low expectation of the benefits of future interactions. A low expectation of the benefits of future interactions, in turn,
implies a low probability of future interactions (Altman & Taylor,
1973; Homans, 1961; Lott & Lott, 1972; Thibaut & Kelley, 1959).2
2
The problem of sequentially choosing whether to interact with B can be
seen as a version of the one-armed bandit problem. The optimal solution to
this problem implies that the sampling probability is either 0 or 1 (e.g.,
DeGroot, 1970). In experiments, however, individuals do not behave in this
way but switch quite often (Gans, Knox, & Croson, 2004; Meyer & Shi,
1995). Moreover, on the basis of a comparison of several models, Gans et
al. (2004) concluded that the model presented in this section (assuming a
weighted average and an exponential-choice model) provided the best
overall fit to the behavior of subjects in an experiment on bandit problems.
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
955
Figure 2. The distribution of A’s estimate at the end of the 10th period compared with a standard normal
distribution. The probability of sampling is e3x̂t/(1⫹e3x̂t), and b ⫽ 0.5 (based on 5 million simulations).
A simple model of such a choice process, which also can handle
negative impressions, is the exponential version of the Luce choice
model (Luce, 1959). In this model, the probability that A will
interact with B in period t ⫹ 1 is
ec⫹Sx̂t
.
1 ⫹ ec⫹Sx̂t
(2)
Here, S is a parameter regulating how sensitive the choice probability is to the value of the estimate, and c determines the baseline
probability of sampling. Although several alternative specifications are possible, this model has the advantage that it can be given
an axiomatic foundation as a choice model (Luce, 1959; McFadden, 1981). The exponential version of the Luce choice model also
has some empirical support as a choice model (e.g., Guadagni &
Little, 1983; Yechiam & Busemeyer, 2005) and is often used in
models of adaptive learning (e.g., Camerer & Ho, 1999). As
demonstrated below, the above choice model also provides a good
fit to data on how the probability of future interactions varies with
the current impression.
Implications
Given the above assumptions, what will be the distribution of
A’s estimate at the end of the 10th period, for example? Figure 2
shows this distribution when b ⫽ 0.5, S ⫽ 3, and c ⫽ 0.3 A
majority of the estimates are negative (75%), and the mean is also
negative (⫺0.33). These results also hold if one examines the
distribution of A’s estimate in later periods. In fact, as t 3 ⬁, the
distribution of A’s estimate quickly converges to a stationary
distribution, which can be solved analytically (see Appendix A).
For example, in the above case, the expected estimate can be
shown to converge to ⫺0.82 and the probability of a negative
estimate to 0.87.
The reason for these results is the tendency to avoid sampling
when the estimate is low. To illustrate this, consider the development of A’s estimate over time in one simulation run, plotted in
Figure 3. Here, A’s estimate is initially positive. However, after
some random negative observations, the estimate turns negative.
Because the probability of taking another sample is low if the
estimate is negative, the estimate then remains at a low level for
the rest of this simulation run. More generally, because the probability of sampling is lower if the estimate is low than if it is high,
low estimates are more stable than high estimates (Gilovich, 1991;
T. M. Newcomb, 1947).4
This stability of negative impressions was illustrated in an early
experiment by Kelley on impression formation (Kelley, 1948;
cited in Kelley, 1950, p. 438), which showed that individuals with
a negative initial impression of another person interacted less with
that person. Individuals who interacted less also had more stable
impressions. As noted by Nisbett and Smith (1989, p. 72), another
illustrative example of the stability of negative estimates can be
found in T. M. Newcomb’s (1961) longitudinal study of attitudes
and attraction among undergraduates living in the same dorm.
Although attraction ratings were relatively unstable for most individuals, 4 out of 17 individuals had stable ratings (T. M. Newcomb, 1961, p. 225). Of these 4, 3 were individuals who were
ranked among the least attractive (14, 15, and 16 on a scale where
17 is the least attractive) during the 1st week (T. M. Newcomb,
1961, p. 226, Table 12.2). Such persistence of negative ratings has
also been found in later studies of sociometric ranks (Cillessen,
Bukowski & Haselager, 2000; A. F. Newcomb & Bukowski,
1984).5
An experiment on attitude formation (Fazio et al., 2004) provides an illustration of how the stability of negative estimates can
3
This was based on 5 million simulations. All simulations were programmed in both C⫹⫹ and Crystal Ball, an add-on to Excel.
4
The stability of negative evaluations does not imply that all estimates
will eventually become negative. Even in the long term, some estimates
will be positive. In addition, if the average observation were positive rather
than 0, the average estimate would be positive but below the average
observation.
5
Table 5.1 in Cillessen et al. (2000) summarized stability ratings for
different sociometric status groups in studies of children. Computation of
the average and the median of Cohen’s kappa shows that the rejected group
was the most stable.
DENRELL
956
Figure 3.
The development of A’s estimate during one simulation run.
lead to a negativity bias. Subjects in this experiment engaged in a
survival game, in which they had to eat beans with positive energy
levels and avoid beans with negative energy levels in order to
survive. Subjects were initially uninformed about the energy value
of beans with different shapes, and they could only obtain information about the energy values of different beans by eating them.
In each period of the game, subjects were presented with a bean of
a particular shape. Because subjects were less likely to eat beans
they believed had negative energy levels, false negative beliefs
about the energy levels of beans were more likely to persist than
false positive beliefs. As a result, at the end of the game, subjects
were more likely to have false negative than false positive beliefs,
consistent with the experience sampling model.
Figure 3 also suggests one way in which false negative impressions may change. Namely, suppose that A does interact with B
again even if A’s estimate is negative. For example, A may be
forced to interact with B if they work in the same department.
Alternatively, A may have a low estimate of the ability of B, but
interact with B for noninstrumental and social reasons (Blau, 1962,
1963). In this case, A will obtain another sample of X. Because A’s
estimate is below 0 and because the mean of X is 0, it follows that
the effect of taking another sample is most likely that A’s estimate
will be adjusted upward, toward 0. This reasoning suggests that
evaluations based on experience sampling may be sensitive to
exogenous differences in the probability of interactions. To include
this in the model, suppose that the probability that A will interact
with B in period t ⫹ 1 is given by
r ⫹ (1 ⫺ r)
ec⫹Sx̂t
.
1 ⫹ ec⫹Sx̂t
(3)
Here, r can be interpreted as the probability of nonvoluntary
(Thibaut & Kelley, 1959) or noninstrumental (Blau, 1962) interactions, which both imply that A may interact with B for reasons
unrelated to A’s estimate of B’s ability, for example. Such interactions may nevertheless provide further observations of the behavior of B relevant for evaluating the ability of B.
As the above reasoning suggests, a higher probability of nonvoluntary or noninstrumental interactions implies a higher average
evaluation.6 This is illustrated in Figure 4, which shows A’s
average estimate at the end of the 10th period as a function of r.
Figure 4 also shows that A’s average estimate will only be free
from any bias (i.e., 0) if r ⫽ 1. In this case, A will sample in every
period and, thus, always obtain new information about B. This
theoretical result is consistent with the finding that no bias
emerged in the experiment on attitude formation (Fazio et al.,
2004) if subjects were always informed about the value of beans
with which they were presented, regardless of whether they ate
them.
The effect of r also implies that evaluations can differ systematically between people with whom one tends to interact socially
and people one is less likely to meet socially. By meeting people
often, one will obtain further information about their abilities and
correct any false negative initial impressions. Often this process
implies that evaluations will be systematically lower for individuals of minority groups to which one does not belong. The reason
is that individuals are most likely to interact with socially similar
others (Fischer, 1982; Marsden, 1987; McPherson & Smith-Lovin,
1987; McPherson et al., 2001). Because one is less likely to meet
individuals of minority groups to which one does not belong to, a
low estimate of such individuals will be more stable.
This effect also implies that social contacts may compensate for
ability in evaluations. Consider, for example, two individuals: The
first has an average ability equal to 0, whereas the second has an
average ability equal to 0.3. Suppose that the first is likely to
interact socially with evaluators (i.e., r ⫽ 0.8). The second individual, however, never interacts socially with evaluators (i.e., r ⫽
0). In this case, the average evaluation of the first and the second
individual, at the end of the 10th period, is roughly equal—that is,
⫺0.04 (when b ⫽ 0.5, c ⫽ 0, and S ⫽ 3, based on 500,000
simulations). Thus, despite having a higher average ability, the
second individual will typically be rated as equal to the wellconnected first individual. Moreover, if the difference in abilities
were smaller, the well-connected first individual would, on average, be rated higher than the more able second individual.
6
Cross and Parker (2004) found several examples of this effect of
involuntary interactions in a study of networks in organizations: “One of
the most surprising discoveries in our interviews was that many productive
relationships begin with poor first impressions that change over time when
people have no choice but to work together” (p. 105).
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
957
Figure 4. A’s average estimate at the end of the 10th period as a function of r. The probability of sampling is
r ⫹ (1 ⫺ r)[e3x̂t/(1 ⫹ e3x̂t)], and b ⫽ 0.5. Each entry is based on averages from 500,000 simulations.
Relation to Existing Literature
As the above example illustrates, experience sampling suggests
an alternative explanation of systematic differences in impressions.
In contrast to theories emphasizing the influence of prior expectations (Fiske & Taylor, 1991) or behavioral confirmation and
self-fulfilling prophecies (Klein & Snyder, 2003; Snyder & Stukas,
1999), experience sampling does not assume that prior expectations influence the interpretation of subsequent observations or
change future behavior. In contrast to theories emphasizing motivational influences on attitude formation (Kunda, 1990; Tajfel &
Turner, 1979) or how impressions about members of the ingroup
are anchored on the self (Cadinu & Rothbart, 1996; Krueger,
1996), experience sampling does not assume that impressions are
influenced by motivations or are anchored on the self. The implication is not that cognitive and motivational influences are not
important. Rather, experience sampling suggests an additional
mechanism that can lead to persistence of negative impressions
and to systematic differences in impressions.
The underlying mechanism also differs from recent models of
impression formation and sampling (Fiedler, 1996; Kashima et al.,
2000; Van Rooy et al., 2003), which also have shown how differences in sample sizes can give rise to systematic differences in
impressions of groups or individuals. Sampling in these models is
assumed to be independent of the current impression, although the
probability of sampling may differ among groups. Fiedler’s (1996)
BIAS exemplar model, as well as Kashima et al.’s (2000) tensor
product model and Van Rooy et al.’s (2003) connectionist model,
instead rely on information aggregation to explain the effect of
sample size. The basic intuition behind their results is that larger
sample sizes will reduce noise and better reveal systematic tendencies. As a result, if members of two groups have primarily
positive traits, the impression will be higher for the most frequently sampled group. Thus, in these models the effect of sample
size is akin to the set-size effect (Anderson, 1981, p. 131).
In contrast to the model of experience sampling, these models
only predict an effect of the sample size if the proportion of
positive versus negative observations is unequal or differs from
initial beliefs (Fiedler, 1996, p. 199; Kashima et al., 2000, p. 923).
These models would not predict a bias in the above example, in
which X was symmetrically distributed, and the mean and initial
belief were both equal to 0. Models relying on information aggregation also imply that differences in impressions will eventually
disappear as sample sizes increase (Van Rooy et al., 2003, p. 540).
Experience sampling, however, suggests that the bias can be
permanent if individuals stop sampling. Nevertheless, whereas the
models differ in their mechanisms and in some of their predictions,
they are best viewed as complementary mechanisms by which
sampling, rather than cognitive–perceptual biases, may contribute
to biases in impression formation. Moreover, experience sampling
is likely to reinforce the bias produced by information aggregation.
A negative impression of an individual or a group, due perhaps to
a small sample size and information aggregation, may not be
revised because future sampling might be avoided.
Of course, a negativity bias in impressions would also occur if
negative observations had a larger impact on impressions than
positive observations, as several studies have shown (for a review,
see Skowronski & Carlston, 1989). The reason may be that undesirable behaviors are more diagnostic than desirable behaviors
(Reeder & Brewer, 1979; Skowronski & Carlston, 1989; Ybarra,
2002). If so, negative observations will have a larger weight in
domains in which such behavior is unusual, such as in the morality
domain, whereas positive observations can have a larger weight in
other domains, such as in the competence domain (Reeder &
Brewer, 1979; Skowronski & Carlston, 1989; Wojciszke, Brycz, &
Borkenau, 1993). As a complement to theories relying on diagnosticity, the model of experience sampling suggests that a negativity bias can emerge when information has to be actively sampled even if all observations are given equal weight. This was also
illustrated in the experiment on attitude formation discussed above
(Fazio et al., 2004), in which a negativity bias emerged in the
absence of differential diagnosticity. In particular, there was no
negativity bias if subjects were always told about the energy values
of the beans presented to them regardless of whether they ate them.
If negative observations also have a larger impact, this will
strengthen the bias from experience sampling. However, in cases
in which positive observations have a larger weight, the bias from
experience sampling will be reduced. Even if negative observations have a larger weight, however, such a tendency would not, by
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958
Table 1
Estimates of Models of Belief Updating
Estimate of constant weight
Experiment
Stewart (1965)
Stewart (1965)
Stewart (1965)
Anderson (1968)
Anderson and Farkas (1973)
Levin and Schmidt (1969)
Levin and Schmidt (1970)
Average
Pieces of
information
8
6
4
6
4
6
3
Estimates of declining weight
b
% deviation
␭
␪
% deviation
0.19
0.24
0.24
0.53
0.36
0.45
0.38
0.34
0.05
0.04
0.03
0.03
0.04
0.12a
0.05a
0.45
0.49
0.63
0.58
0.61
0.86
0.48
0.59
0.47
0.53
0.50
0.37
0.45
0.38
0.10
0.40
0.01
0.01
0.01
0.03
0.02
0.11a
0.05a
Note. Values are based on minimizing the absolute deviation. Percentage of deviation is the average of the absolute difference between the actual and
the estimated impressions divided by the range of the scale used.
a
Average absolute difference between the estimated probability and the actual proportions.
itself, lead to systematic differences in impressions as a result of
systematic differences in interaction patterns.
Finally, experience sampling is related to Ybarra’s (2002) theory of how the valence of impressions influences subsequent
information processing. As reviewed by Ybarra (2002; see also
Ybarra, Schaberg, & Keiper, 1999), positive impressions elicit
more testing and critical information processing than negative
impressions, because people are more likely to think that negative
traits are diagnostic. Ybarra (2002, p. 437) also notes that negative
impressions may imply that no additional information is sampled.
As illustrated above, this may be sufficient to produce biases in
impression formation. This implies that negative impressions may
be more stable even if negative behaviors are not (and are not
perceived to be) more diagnostic. More generally, experience
sampling is likely to reinforce a negativity bias produced by more
stringent testing of positive impressions.
Examining the Influence of Experience Sampling
A General Model
The above illustration relied on specific assumptions about
belief updating and sampling. The weight of the most recent
observation was assumed to be constant, and sampling was assumed to follow the exponential-choice rule. However, the results
hold for a wide range of alternative assumptions. Instead of being
constant, the weight of the most recent observation may shift over
time. For example, it may decline as suggested by several experimental studies of impression formation (Anderson & Farkas,
1973; Dreben, Fiske, & Hastie, 1979; Kashima & Kerekes, 1994).
The estimate can also simply be the average of all observations, or
it may even follow Bayes’s rule. As discussed in Appendix B, the
only assumption required is that the new estimate can be written as
some weighted combination of the old estimate and the new
observation, x̂t⫹1 ⫽ (1 ⫺ bt⫹1)x̂t ⫹ bt⫹1xt⫹1, where bt⫹1 can differ
between periods. Similarly, one does not have to assume that
sampling follows the exponential-choice rule. One has to assume
only that sampling is more likely if the impression is high. For all
processes satisfying these assumptions, Appendix B shows that for
all t ⬎ 1, the expected estimate, E(X̂t), will be below the average
observation E(X).
The Magnitude of the Bias
Whereas the above result holds under very general assumptions,
the magnitude of the bias depends on the specific assumptions
made. In particular, a large bias requires that sampling is unlikely
when the estimate is negative (i.e., that S is large), so that negative
estimates are unlikely to be corrected. Moreover, a large bias
requires that the weight of the most recent observation is large (i.e.,
that b is large), so that a positive estimate can turn negative even
after one or two negative observations. To evaluate the practical
significance of experience sampling, one thus needs information
about how strongly people avoid others if their impression is
negative and information about the weight of the most recent
observation.
Consider first the weight of the most recent observation, b. A
large number of studies have shown that if individuals have to
formulate an impression after each piece of information is presented, there is a recency effect in the sense that the most recent
observation has the largest weight (for reviews, see Hogarth &
Einhorn, 1992; Kashima & Kerekes, 1994). Most studies, however, have focused on qualitative properties of the data (i.e., the
existence of a recency effect), and few studies have estimated the
weight of the most recent observation. However, data from some
studies on impression formation can be used to obtain tentative
estimates.
Table 1 shows estimates from seven experiments on personimpression formation that provide data on the development of
impressions over time.7 In each experiment, subjects were presented with a sequence of descriptions (typically adjectives) of a
hypothetical individual, and they stated their impression after each
piece of information was presented. In the experiments of I. P.
Levin and Schmidt (1969, 1970), however, subjects only stated
7
Dreben et al. (1979) also estimated the impact of serial position on
impression formation. No data on the development of impressions over
time are available, however. Nevertheless, their method of estimating the
relative influence implies that the weight of the fourth observation must be
at least 71/200 ⫽ 0.36 to 0.23.
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
whether they liked the individual.8 Both a model with a constant
weight (as in the above illustration) and a model with a declining
weight were estimated. In the model of a declining weight, I
assumed that the weight of the most recent observation could be
modeled as bn ⫽ ␭(1/n)␪ (cf. Hertwig, Barron, Weber, & Erev, in
press), where ␭ is the weight of the first impression, n is the
number of observations made so far, and ␪ is the rate at which the
weight declines. As mentioned above, several studies of impression formation have found that the weight of the most recent
observation tends to decline. Details of the estimation procedure
are given in Appendix D.9
Although the estimates in Table 1 show great variation, they
also illustrate that there are situations in which the weight of the
most recent observation can be large even after several pieces of
information have been presented. For example, estimates from the
model of a declining weight, based on the experiment of Anderson
(1968), imply that the weight of the sixth piece of information is
0.30. Thus, a negative observation after five previous observations
could substantially change the impression. This is also consistent
with the findings of I. P. Levin and Schmidt (1969), who found
that the proportion of subjects who said that they liked the individual about whom they obtained information almost always
dropped below 50% whenever the most recently presented adjective was negative, even if several positive adjectives had been
presented earlier.10 Also, Dreben et al. (1979, p. 1765) found that
there was a stronger recency effect in experiments with a filler task
between each observation. This suggests that the weight of the
most recent observation might be larger when individuals are
involved in several tasks between successive encounters, as in
many real-life situations.
These estimates can be compared with estimates from experiments of repeated choices between uncertain alternatives with
unknown payoffs, a task similar to choosing between interaction
partners. Using data from an experiment of about 100 choices
between two alternatives, Gans et al. (2004) estimated a model
identical to the basic model described in the previous section (A
Simple Example of the Effect of Experience Sampling), with a
constant weight and an exponential-choice rule. The median estimate of the weight of the most recent observation was 0.25 and the
average was 0.40. Using data from an experiment of repeated
choices between four alternatives, Yechiam and Busemeyer (2005)
estimated the same model. Their estimate of the weight of the most
recent observation was 0.31.
Consider next the parameters regulating how the probability of
sampling varies with the impression—that is, S and c. As mentioned above, several studies have examined the effect of attraction
on interaction and communication. Some of these studies provide
data about the effect of initial impressions on the willingness to
continue the interaction. In particular, M. S. Schwartz (1966; cited
in Byrne, 1971, p. 231), Montoya & Horton (2004, p. 700), and
Carranza et al. (2004) showed that ratings of attraction, based on
questions of how much subjects like their future interaction partner, are positively and significantly correlated with the willingness
to continue to the interaction, on the basis of questions such as (a)
if they were willing to “sit next to this person in a class or meeting”
(M. S. Schwartz, 1966), (b) if they “would like to meet my future
interaction partner” (Montoya & Horton, 2004), and (c) if they
959
were likely “to enjoy spending time with him or her” (Carranza et
al., 2004). These studies, however, do not provide any direct
information about how the probability of future interactions varies
with the initial impression. To obtain some tentative information
about this function, I distributed a questionnaire to 109 undergraduates as a part of a larger package of questions, completed for
payment. The questions were variations of the following:
Before the first lecture of one of your courses, you briefly talk to
another student taking the same course. Based on your first impression, you believe that 84% of all students you have met at campus are
friendlier than this student.
In this case, would you choose to:
1. Initiate a brief hallway conversation with this student?
YES___
NO___
2. Sit next to this student when you arrive to class 10 minutes early?
YES___
NO___
YES___
NO___
3. Invite this individual out for a coffee?
Subjects answered five questions in which the percentage (84% in
the example) varied across five levels: 84, 69, 50, 34, and 16%,
corresponding to an impression 1.0 or 0.5 standard deviations
below the mean, at the mean, and 0.5 or 1.0 standard deviations
above the mean (assuming a normal distribution). The order of the
percentages (starting with 84 or 16%) and the order of the alternatives (beginning with yes or no) were counterbalanced.
The results, summarized in Figure 5, show that subjects were
more likely to initiate another interaction if their initial impression
was positive. Estimates of the above exponential-choice model
(Equation 2), based on minimizing the absolute deviation, also
show a very good fit for the data; the average absolute difference
8
To estimate the weight of the most recent observation, I assumed that
the probability of a like response followed the exponential-choice model.
In particular, the probability of a like response was assumed to be
1/共兵1 ⫹ exp[⫺S(x̂t ⫺ 3)]}, where 3 is the middle point of the scale used in
these experiments. I used the data from individuals in I. P. Levin and
Schmidt (1969) and the data from Experiment 1 in I. P. Levin and Schmidt
(1970).
9
There are also data available from experiments that have examined
belief updating in evaluation tasks (Hogarth & Einhorn, 1992)—that is,
when subjects have to decide whether the data support a hypothesis.
Estimates based on Furnham’s (1986) data on formation of guilt and
innocence judgments gives b ⫽ 0.22, assuming a constant weight, and ␭ ⫽
0.25 and ␪ ⫽ 0.08, assuming a declining weight. Pennington and Hastie
(1992, p. 200) reported that the best fitting model, based on data from a
similar experiment, gives b ⫽ 0.55. Estimates based on Hogarth and
Einhorn’s (1992) experiment on hypothesis evaluation (Experiment 4) give
b ⫽ 0.21, assuming a constant weight, and ␭ ⫽ 0.29 and ␪ ⫽ 0.08,
assuming a declining weight. Finally, Busemeyer and Myung (1988, p. 7),
in an experiment on prototype learning, reported that their findings can be
approximated with a model with a constant weight of 0.5.
10
I. P. Levin and Schmidt (1969) also estimated a linear learning model
(Bush & Mosteller, 1955), assuming that the change in the probability of
a like response after a negative adjective was Pn ⫹ 1 ⫽ (1 ⫺ W)Pn. The
estimated value of W for a negative adjective presented at the sixth position
was 0.76 (p. 286), implying that the probability of a like response would be
reduced from 1 to 0.24 after a single piece of negative information.
960
DENRELL
Figure 5. The probability of continued interaction as a function of the first impression. Each entry is based on
responses from 109 subjects.
between the estimated probabilities and the actual proportions was
0.01. The estimates obtained were S ⫽ 1.74 and c ⫽ 1.06 for
“Initiate a brief hallway conversation,” S ⫽ 1.94 and c ⫽ 0.24 for
“Sit next to this student,” and S ⫽ 2.51 and c ⫽ ⫺2.75 for “Invite
this individual out for a coffee.”11 Although these estimates are
based on responses to a hypothetical situation and only provide
information about the effect of the first impression, they provide
some indication of possible parameter values. In particular, they
suggest that when interactions require some investment in time (as
in “Invite this individual out for a coffee”), the probability of
sampling can be relatively sensitive to the impression (cf. Einhorn
& Hogarth, 1978; Friedrich, 1993). Such time consuming interactions probably also provide more opportunities for information
exchange and revision of the impression than do brief
conversations.
Whereas the above estimates of the weight of the most recent
observation and the sensitivity of sampling to the impression must
be regarded as tentative, they provide some indication of reasonable values. These values can then be used as inputs to a simulation, to estimate the possible effect size of the bias produced by
experience sampling. Table 2 shows the effect size for three
different assumptions about belief updating and sampling. As
illustrated, when both the weight of the most recent observation
and the sensitivity of sampling to the impression are small, the
effect size is small. However, when the weight of the most recent
observation is set to the average value in Table 1, and the sensitivity of sampling is set at the median value, the effect size is
noticeable. For example, the probability of a negative impression
is 0.62 after the 10th period, and the average impression is ⫺0.16.
However, the effect size is much stronger when both the weight of
the most recent observation and the sensitivity of sampling to the
impression are large.12 For example, the probability of a negative
estimate is 0.82. It can also be noted that the probability of a
negative estimate will be high whenever sampling is sensitive to
the impression. For example, even if b is only 0.19, the probability
of a negative estimate is still 0.61 when S ⫽ 2.51 and c ⫽ ⫺2.75.13
Overall, these simulations suggest that the bias can be expected to
be significant whenever interactions require some investment and
sampling is sensitive to the impression.
Obviously, these simulations are based on a number of simplifying assumptions. Nevertheless, the main result holds and is
sometimes even stronger if these assumptions are changed. For
example, suppose that negative observations have a larger impact
on impressions than positive observations (Dreben et al., 1979;
Skowronski & Carlston, 1989), as reported in three studies (Anderson, 1968; I. P. Levin & Schmidt, 1969, 1970). In such cases, the
bias will be stronger. However, if positive observations have
greater weight, as reported in Anderson & Farkas (1973, p. 91), the
bias will be reduced. An observation that deviates substantially
from the current estimate may also be more weighted.14 Simulations show that such a contrast effect would generally increase the
11
Estimates based on maximizing the likelihood give very similar
values. Such estimates, however, assume independence within subjects,
which may not hold.
12
The effect size is larger after 50 periods because the probability of
sampling under these assumptions is low, and few people have sampled
more than once after 10 periods.
13
This was after 50 periods, based on 500,000 simulations.
14
A contrast effect can also be modeled in at least two other ways. First,
the weight of the most recent observation may be a function of the absolute
value of the observation. For example, more extreme observations may be
given more weight (e.g., Fiske, 1981). In this case, simulations suggest that
the bias will be stronger than if the weight were constant and equal to the
average weight. The weight of the most recent observation may also
depend on the value of the estimate. For example, the weight may be
greater for more extreme estimates (Hogarth & Einhorn, 1992). This will
typically reduce the bias.
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
Table 2
Simulation of the Effect Size
After 10 periods
After 50 periods
Assumptions
Probability
negative
Average
impression
Probability
negative
Average
impression
Small
Medium
Large
0.54
0.62
0.68
⫺0.05
⫺0.16
⫺0.33
0.54
0.61
0.82
⫺0.02
⫺0.10
⫺0.50
Note. Small: ␭ ⫽ 0.45, ␪ ⫽ 0.47, S ⫽ 1.74, and c ⫽ 1.06. Medium: ␭ ⫽
0.59, ␪ ⫽ 0.40, S ⫽ 1.94, and c ⫽ 0.24. Large: ␭ ⫽ 0.86, ␪ ⫽ 0.38, S ⫽
2.51, and c ⫽ ⫺2.75. Each entry is based on 500,000 simulations.
bias, although the difference is not large.15 The size of the bias is
also essentially unchanged if one assumes that impression formation follows a different model, suggested by Anderson (1959) and
Anderson and Farkas (1973), in which impressions can be decomposed into two components: a surface component, which is sensitive to the most recent observations, and a basal component, which
is adjusted to the cumulated data.16 Finally, suppose that the
impression can change even if no new information is provided,
perhaps due to memory decay (Broadbent, 1958; Erev & Roth,
1998; Yechiam & Busemeyer, 2005). Simulations show that this
would weaken the bias but not eliminate it.
The bias would also be stronger and more permanent if one
assumed that the probability of sampling changed over time. In
particular, as more information is accumulated and confidence
grows, individuals may be less likely to interact with an individual
of whom they have a negative estimate. For example, A may
follow a strategy of never sampling B again if A’s impression after
10 observations is sufficiently negative. If so, these negative
estimates will never change, and the bias will be permanent even
if the estimate was the average of all observations so far, which
otherwise would converge to 0. The bias would also be stronger if
one assumed, following prospect theory (Kahneman & Tversky,
1979), that the probability of sampling is not symmetric around c
but more sensitive to estimates below c.
Finally, all the examples in this section have assumed that the
true mean of the observation is 0. The bias in the estimate,
however, depends on the mean of the observation (relative to c). If
the mean is very high so that sampling is very likely, or very low
so that sampling is very unlikely, the bias is much smaller. This
also implies that the average bias in A’s estimate of many different
individuals, with different means, is smaller.17 This does not
change the fact that A’s bias of many individual members of a
population can be significant. Still, it does suggest that the average
impression of a large and widely varying group of individuals is
not likely to be biased very much if each impression is formed
independently and then averaged. However, if the impression of
one individual influences the probability of interacting with other
individuals of this group, the bias for the group as a whole will be
larger.
The Influence of the Sampling Process
Although the general negativity bias is interesting, the most
important theoretical implication of the model of experience sampling is that evaluations will be sensitive to interaction patterns and
961
other influences on the sampling process. Because the negativity
bias is due to the fact that individuals believed to be inferior are not
given a second chance, evaluations are more likely to be positive
whenever sampling is likely, even when impressions are negative.
Such a pattern was also observed in the experiment on the development of attitudes described above (Fazio et al., 2004). In particular, manipulations that increased the probability of approaching
beans with negative energy values reduced the probability of
erroneously classifying beans as negative. As a result, the probability increased that a bean would be classified as having a positive
energy level.
In the above model, sampling when the estimate is negative can
occur for several different reasons, illustrated graphically in Figure
6. First, as discussed above, individuals may be forced to continue
the interaction, even if their impression is negative. For example,
individuals may have to continue to interact with colleagues or
with friends of their friends, even if their impression is negative.
More generally, interactions are sometimes determined by exogenous factors. This case is illustrated in Figure 6A, where Line (B)
starts at a baseline probability of sampling equal to 0.4, whereas
Line (A) starts from 0. As illustrated in Figure 4, such forced
sampling implies that the bias will be smaller and that evaluations
will be higher. This is also demonstrated formally in Appendix C.
Second, individuals may feel that sampling is justified even if
their impression is low. For example, individuals may be motivated by accuracy and put little weight on the expected outcome of
15
To model such a contrast effect, I assumed that the weight of the latest
observation was bn ⫽ [␭(1/n)␪]1/(1⫹兩D兩k), where 兩D兩 is the absolute difference
between the observation and the prior estimate, divided by the standard
deviation of the observation. Thus, the weight of the most recent observation is an increasing function of the absolute difference between the
estimate and the observation. I estimated this model using Stewart’s (1965)
data with eight, six, and four adjectives, Anderson’s (1968) data, and
Anderson and Farkas’s (1973) data. I then simulated the bias using these
estimates and compared the bias, as measured both by the average estimate
and the probability of a negative estimate, with the bias if no contrast effect
is assumed (i.e., using estimates from the best fitting model when k ⫽ 0).
The results show that the bias is larger in four cases and smaller in one
case.
16
The estimate was modeled as
x̂t⫹1 ⫽ (1 ⫺ bn)
冘
1
n⫹1
xi ⫹ bnxt⫹1.
Here,
1
n⫹1
冘
xi
is the average of all observations so far including the prior (assumed to be
0), capturing the basal component, and bn ⫽ ␭(1/n)␪ captures the weight of
the surface component. A model based on these assumptions does provide
a better fit to Anderson and Farkas’s (1973) data (the estimates are ␭ ⫽
0.56 and ␪ ⫽ 0.43) than does a model assuming only a declining weight.
Nevertheless, simulations using estimates from this model show that the
bias is as strong as or stronger than it is when only a declining weight is
assumed.
17
For example, if b ⫽ 0.34, the probability of a negative impression is
0.67 if the mean is 0, whereas it is 0.58 if the mean is normally distributed
with a mean of 0 and a variance of 1 (S ⫽ 3, c ⫽ 0).
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DENRELL
even if the impression is somewhat negative. As demonstrated in
Appendix C, such less selective sampling implies that the bias will
be smaller and that evaluations will be higher. For example,
although the probability of a negative impression after the 10th
period is 0.75 for Line (A), it is only 0.63 for Line (B).18
Finally, the probability of sampling may not be very sensitive to
the impression—that is, S may be low. This case is illustrated in
Figure 6C, where Line (B) is less sensitive to the impression than
Line (A). As illustrated by the survey reported above, such less
sensitive sampling may happen for interactions that do not require
much engagement or investment (such as in “engage in a brief
conversation”). It may also happen if the current impression is not
very important for expectations about how rewarding future interactions will be. As illustrated in the above simulations, a small
value of S implies that the bias will be smaller and the average
estimate higher.
The Influence of First Impressions
Figure 6.
How the probability of sampling can vary with the impression.
interactions. Individuals may also have a low comparison level
(Thibaut & Kelley, 1959) for deciding whether to continue sampling. For example, few satisfactory interaction partners may exist,
perhaps because the individual has a low status or reputation. As
a result, the individual may have to be less selective in sampling.
Consistent with this, Van Duüren and Di Giacomo (1997) showed
that individuals who had experienced failure had a greater propensity to affiliate with others and were also less discriminating in
choosing a partner. Such less selective sampling is illustrated by
Line (B) in Figure 6B. The probability of sampling is always
higher (for any given impression) for Line (B) than for Line (A).
Moreover, the probability of sampling for Line (B) is quite high
The above models assumed that there is a recency effect in
impression formation, consistent with many experiments on belief
updating. Nevertheless, these experiments typically exclude, by
design, confirmatory hypothesis testing and self-fulfilling prophecies (Hilton & von Hippel, 1996; Snyder & Stukas, 1999), which
can both lead to a primacy effect. If there was a strong primacy
effect, perhaps due to confirmatory hypothesis testing and selffulfilling prophecies, simulations show that the bias from experience sampling would be smaller. In fact, if only the first impression mattered, the expected estimate would be the expected value
of the first observation, and there would be no bias. Thus, confirmatory hypothesis testing and self-fulfilling prophecies will tend
to weaken the bias from experience sampling.
There is little reason to expect, however, that confirmatory
hypothesis testing and self-fulfilling prophecies would nullify the
effect of experience sampling. Although much research has demonstrated that primacy effects can emerge through confirmatory
hypothesis testing and self-fulfilling prophecies, the magnitude of
the effect produced by these phenomena varies depending on the
context (Snyder & Stukas, 1999). Thus, for example, although the
existence of confirmatory hypothesis testing is well-established,
“how general it is remains at issue” (Fiske & Taylor, 1991, p. 543).
Similarly, although self-fulfilling prophecies have been established
in many contexts, meta-analyses of experimental studies and field
studies have shown that the average effect size is quite small
(Jussim & Eccles, 1995; Madon, Jussim, & Eccles, 1997). In
addition, several studies have shown that subjects are sensitive to
data violating expectations (Fiske & Taylor, 1991). In particular,
individuating information has been shown to reduce the effects of
stereotypes and categorizations (Gawronski, Ehrenberg, Banse,
Zukova, & Klauer, 2003; Hilton & Fein, 1989; Weber & Crocker,
1983), sometimes even after only one piece of information (Locksley, Borgida, Brekke, & Hepburn, 1980). Thus, although first
impressions and expectations can matter, there is no reason to
suggest that impressions are not sensitive to subsequent observations. Instead, the bias produced by experience sampling should be
seen as a different and complementary mechanism, by which
false-negative expectations may fail to be disconfirmed.
18
This was based on 500,000 simulations when b ⫽ 0.5.
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
The Possibility of Correcting for the Bias
If an individual is aware of the bias, is there any way of
correcting for it? Suppose, for example, an individual has sampled
n times out of t times possible, and the observations are x1, x2, . . . ,
xn. As explained above, a simple average of these observations
would be biased. To obtain an unbiased estimate, one would have
to control for the sample bias produced by experience sampling.
Although not impossible, it would be very difficult to perform this
correction intuitively.19 Nevertheless, the biggest obstacle to obtaining unbiased estimates is probably not the computational difficulty of correcting for the bias, but the fact that most people are
likely to be unaware of the sampling bias and its consequences.
Most individuals would probably not intuitively recognize that an
estimate, such as the average of all observations taken, is biased if
sampling depends on the current impression. Given the difficulties
many individuals have in dealing with other subtle points in
probability, such as regression to the mean (Kahneman & Tversky,
1973), and with selection bias in data and experiments (see Fiedler,
2000, for a discussion), it seems unlikely that individuals would be
aware of this bias. People may be aware, however, that it is
valuable to continue sampling even if the initial impression is
negative, to obtain additional information. Because continued sampling will reduce the bias, it provides a different way to correct for
it. However, if accuracy is not the only goal, continued sampling
is not always a reasonable strategy. If the current impression is
sufficiently negative, the value of additional information may not
compensate for a negative expected value of future interactions,
and further sampling may be avoided. Because sampling should
only be avoided if the current impression is negative, this also
implies that false negatives will be more common than false
positives.20
Judgment Biases Originating in Experience Sampling
Interaction Patterns and Evaluation Bias
The model of experience sampling shows how systematic differences in evaluations can emerge as the result of systematic
differences in interaction patterns. If A is more likely to interact
with individuals of Type B than with individuals of Type C, for
any given level of impression, evaluations of individuals in Group
C are more likely to be negative than evaluations of individuals of
Group B. This section illustrates how this mechanism can provide
a novel explanation for several biases in impression formation.
Population structure and attitudes toward outgroups. Numerous studies have shown that outgroup members are typically
evaluated more negatively than ingroup members (Brewer &
Kramer, 1985; Hewstone et al., 2002; Mullen et al., 1992). Although a variety of different processes and historical events can
contribute to such a bias (Hewstone et al., 2002), existing psychological explanations have emphasized the motive to maintain a
positive social identity (Tajfel, 1982; Tajfel & Turner, 1979). In
this explanation, an ingroup bias emerges because individuals
bolster evaluations of their own group. Persistent negative attitudes
toward outgroups have also been attributed to stereotypes or schemata that influence the interpretation and recall of observations or
induce self-fulfilling prophecies (Chen & Bargh, 1997; Hilton &
von Hippel, 1996). Alternatively, an ingroup bias can emerge if
individuals rely on information about the self and generalize
963
positive evaluations of the self to members of their own group
(Cadinu & Rothbart, 1996; Krueger, 1996). Finally, experiments
have shown that subjects can develop illusory correlations between
negative attributes and minority group membership (Fiedler, 1996;
Fiedler & Walther, 2004; Hamilton & Gifford, 1976).
The model of experience sampling suggests an additional mechanism for why outgroup members are evaluated more negatively
than ingroup members. To develop this, suppose first that impressions of individuals belonging to a specific group are determined
in part by experiences in previous encounters with individuals of
this group (Fiedler, 1996). Positive previous encounters lead to
more positive impressions and negative encounters lead to more
negative impressions. Although strongly held stereotypes about
groups imply that impressions may be relatively insensitive to new
experiences (Fiske & Taylor, 1991) or that positive impressions
may not generalize to other members of the group (Brewer &
Miller, 1984; Gaertner & Dovidio, 2000; Rothbart & John, 1985),
numerous studies have shown that positive encounters can, under
the right conditions, lead to changes in group impressions (e.g.,
Gaertner & Dovidio, 2000, chap. 5; Pettigrew, 1998; Pettigrew &
Tropp, 2000; Stephan & Stephan, 1984; Triandis, 1994). Plant and
Devine (2003, Study 1) also showed that individuals with more
positive previous contacts with outgroup members had more positive expectations about future interactions with outgroup
members.
Second, the probability of future interactions with outgroup
members depends on current impressions of members from this
group. In particular, individuals may avoid members of a specific
group if their experiences with other members of this group have
been negative (T. M. Newcomb, 1947; Pettigrew, 1997, 1998;
Plant, 2004; Towles-Schwen & Fazio, 2003). Such avoidance was
demonstrated in the experiment of Plant and Devine (2003, Study
1), who showed that negative outcome expectancies lead to anxiety
in interracial interactions, which in turn was a good predictor of the
desire to avoid future interactions. Another study, in which actual
behaviors rather than intentions were studied, showed that negative
outcome expectancies reduced the probability that subjects would
return for an additional session (Plant & Devine, 2003, Study 2;
see also Plant, 2004). In addition, Henderson-King and Nisbett
(1996) showed that exposure to negative behavior of a Black
person increased the probability that subjects would avoid Black
people in the future. Finally, S. Levin et al. (2003) found that
negative attitudes toward an outgroup after the first year of college
19
Obtaining an unbiased estimate would require calculating the value of
E[X] that maximizes the likelihood of the data, given the sampling and
updating processes. This would be possible if the character of the distribution of X was known (e.g., normal), but computationally challenging. For
example, if it was known that X was normally distributed with a variance
of 1 and that the weight of the most recent observation was constant and
equal to 0.5, and the sampling rule was known, simulations could be used
to calculate the value of E[X] that is most likely if the estimate after 10
periods was, say, ⫺0.4. However, if the sampling and updating rules were
not known—that is, if one only had information about the impressions at
which others had arrived—it could be impossible to identify E[X] (cf.
Heckman, 2001; Manski, 1995).
20
Indeed, Denrell (2005) showed that this result holds even if individuals follow a strategy that maximizes expected value in a one-armed bandit
problem.
964
DENRELL
reduced the number of outgroup friends in subsequent years, even
when initial attitude and the initial number of outgroup friends
were controlled for.
Given these assumptions, the model of experience sampling
implies that average evaluations of outgroup members will contain
a negativity bias. This occurs even if negative impressions would
not influence information processing or behavior during interactions and lead to a self-fulfilling prophecy. Thus, experience
sampling suggests a different mechanism that leads to negative
impressions of outgroup members.
The result will likely be different for evaluations of members of
the ingroup, however. As demonstrated in several field studies
(Islam & Hewstone, 1993a; S. Levin et al., 2003) individuals are
likely to interact with members of the ingroup, even if the ingroup
is relatively small. A tendency to associate with members of the
ingroup was also illustrated in an experiment by Shah, Brazy, &
Higgins (2004). In one of their studies (Experiment 2), group
membership was manipulated, and the seating preferences of subjects were observed. Subjects sat at a significantly smaller average
distance from a chair when they thought it was occupied by an
ingroup member than when they thought it was occupied by an
outgroup member.21 If the ingroup is defined so that it includes
members of the family, close colleagues, or fellow students, it may
also be difficult to avoid interacting with ingroup members. Finally, observations of oneself may be integrated into ingroup
evaluations (Cadinu & Rothbart, 1996).
When individuals are likely to interact with members of the
ingroup but can more easily avoid members of the outgroup if they
have had negative experiences with them, the model of experience
sampling implies that average evaluations of the ingroup will be
higher than average evaluations of the outgroup. Thus, experience
sampling suggests a different mechanism leading to an ingroup
bias. The argument is not that experience sampling could provide
an alternative explanation for the findings of experiments with
minimal groups (Tajfel et al., 1971), in which subjects are arranged
randomly into groups and do not have any opportunity for interaction.22 Rather, the claim is that experience sampling provides a
different mechanism by which ingroup bias can develop in real
groups, in which there are opportunities for interactions. Metaanalyses have also shown that the effect size is larger in real
groups than it is in artificially created groups (Mullen et al., 1992).
Moreover, experience sampling is likely to reinforce any existing
biases that may have been generated by the motive to maintain a
positive social identity, self-fulfilling prophecies, or illusory correlations. If outgroup members are avoided, negative views about
them are less likely to be exposed to disconfirming evidence.
Beyond this, the model of experience sampling also suggests
that attitudes toward outgroups depend on group size. In particular,
negative attitudes are especially likely to develop toward members
of minority groups. Whereas individuals may avoid individuals
belonging to outgroups with which they have negative experiences, they may nevertheless sometimes encounter such individuals. They may have to interact with them at work, in school, or in
their neighborhood. Such encounters provide sources of additional
information and may lead to acquaintances and friendship with
outgroup members, as demonstrated by van Dick et al. (2004).
Acquaintances and friendship with outgroup members, in turn,
have been shown to be especially important in reducing negative
views about outgroups (Ellison & Powers, 1994; Pettigrew, 1997;
van Dick et al., 2004).
The probability of such encounters, however, depends on group
size. As noted by Blau, in his work on intergroup contact (Blau,
1977, 1994), due to the numerical dominance of the majority,
members of the majority group are less likely than members of
minority groups to meet members of other groups (unless there is
substantial segregation). More generally, outgroup size should be
positively associated with outgroup contact and familiarity, as
demonstrated in several studies of intergroup contact (Islam &
Hewstone, 1993a; Liebkind, Nyström, Honkanummi, & Lange,
2004), familiarity with the outgroup (Kalin, 1996; Kalin & Berry,
1982), and intergroup marriage (Blau & Schwartz, 1984).
Because one is less likely to encounter members of small
outgroups, negative impressions will be more persistent for small
outgroups. Thus, attitudes toward the outgroup will be positively
associated with the size of the outgroup. In particular, because
members of the minority are more likely to meet members of the
majority than members of the majority are to meet members of the
minority, the attitudes of members of the minority toward members of the majority should be more favorable than vice versa.
Several studies have found this pattern. Brewer and Campbell
(1976, pp. 65– 66), on the basis of a survey of 30 ethnic groups in
Kenya, Tanzania, and Uganda, showed that the favorability of the
attitude toward the outgroup was positively and significantly correlated with outgroup population size (the average correlation was
0.37). Although it is possible that the effect of size is a result of
differences in group status, Kalin and Berry (1982), on the basis of
a census in Canada and a survey of attitudes toward seven ethnic
groups, showed that the favorability of the attitude toward the
outgroup was positively and significantly correlated with the proportion of the outgroup in the respondents’ census unit. Outgroup
proportion was also associated with familiarity with the outgroup.
Kalin (1996) replicated these findings using a later survey and
census. Liebkind et al. (2004), on the basis of a national probability
sample in Sweden and Finland, also showed that outgroup size was
associated with outgroup contact, which was associated with more
favorable attitudes toward the outgroup.23
In a series of studies, Verkuyten (1992 [Table 1], 1996 [Table
1], 2005 [Table 1]) and Kinket and Verkuyten (1999) have also
shown that members of minority groups in Holland have more
favorable attitudes toward the Dutch majority than the Dutch
majority has toward minority members. Similarly, Tropp and
Wright (2003) found that Mexican American children had more
favorable attitudes toward European American children than vice
versa. Stephan and Stephan (1984, Table 11.1) also found that
21
The tendency to avoid the outgroup was also stronger for individuals
with a higher motivation for interpersonal security. I am grateful to James
Shah, Paige Brazy, and Tory Higgins for providing these data, which were
not reported in Shah et al. (2004).
22
This is unless it is assumed that ingroup judgments are anchored on
the self (Cadinu & Rothbart, 1996). In such a case, because the sample size
of performances by the self is larger than the sample size of the performances by others, an ingroup bias can still emerge.
23
This was found even when controlling for age, education, reported
ingroup identification, and perceived status difference between the ingroup
and the outgroup.
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
students of Hispanic origins had more favorable attitudes toward
Anglo American students in a New Mexico high school than vice
versa.24 Several other surveys of students and children have found
similar results (Aboud & Skerry, 1984; Bagley & Verma, 1975;
Brand, Ruiz, & Padilla, 1974; D’Souza, 1978; Rice, Ruiz, &
Padilla, 1974). Although such results could be due in part to
differences in status between minorities and majorities, Li and
Hong (2001) also showed that the mainland Chinese minority in
Hong Kong had a more accurate perception of the cultural values
of the majority than vice versa. Some studies, however, have found
a conflicting pattern. Islam and Hewstone (1993a) showed that the
Hindu minority in Bangladesh had less favorable attitudes toward
the Muslim majority than vice versa.25 Corenblum and Stephan
(2001, Table 1) showed that native Canadians had a less favorable
attitude toward the white majority than vice versa.26
The proposition that a small group would show more favorable
attitudes to outgroups may seem to go against arguments and
findings that ingroup bias is inversely associated with the relative
size of the ingroup (for a meta-analysis, see Mullen et al., 1992).
However, attitudes toward outgroups are not the same as ingroup
bias, usually defined as the difference between the evaluation of
the ingroup and the outgroup.27 Nevertheless, the different arguments can be reconciled by noticing that relative ingroup size is
likely to have two different effects on attitudes toward the outgroup. First, as the relative size of the ingroup increases, the
probability of contact with the outgroup decreases, which leads to
less favorable attitudes toward the outgroup. Second, as the relative size of the ingroup increases, members of the ingroup may feel
less threatened by the outgroup (Giles & Evans, 1986; R. A.
Levine & Campbell, 1972; D. M. Taylor & Moghaddam, 1994),
and ingroup membership may become less salient (Leonardelli &
Brewer, 2001), both of which may lead to more favorable attitudes
toward the outgroup. The above discussion focused on the first
effect. To examine the second effect in field studies, one needs to
control for the probability of contact. If the second effect is also
present, the effect of ingroup size on outgroup attitudes should be
positive when the probability of contact is controlled for. Liebkind
et al. (2004) found precisely this pattern of results. Ingroup size
was negatively associated with favorable attitudes toward outgroups, and this was due to the negative effect of ingroup size on
outgroup contact. However, if the probability of contact was
controlled for, ingroup size had a positive effect on attitudes
toward outgroups.
In summary, whereas differences in contact have long been
argued to be an important predictor of outgroup attitudes (Allport,
1954; Pettigrew, 1998), the model of experience sampling suggests
a simple mechanism that can explain both the origins of a negativity bias in attitudes toward outgroups as well as the consequences of additional contact. It should be noted, however, that the
argument assumes that contact provides information that can lead
to more positive attitudes. Even if there is broad support for this
effect (Pettigrew, 1998; Pettigrew & Tropp, 2000), there are exceptions. In particular, if a majority is strongly prejudiced against
a minority, contact may have the opposite result. Islam and Hewstone (1993a) argue that this explains why Hindus (the minority in
Bangladesh) who had more contact with the Muslim majority than
vice versa also had more negative attitudes to the majority. Similarly, Kalin (1996) suggests that this may explain the conflicting
965
findings of the effects of a high concentration of African Americans (e.g., Pettigrew, 1959; M. C. Taylor, 1998; Williams, 1964).
Homophily and biases in performance evaluation. Experience
sampling also suggests a different mechanism leading to systematic biases in performance evaluations and selection decisions.
Most research on performance evaluation has focused on cognitive
and social factors that influence impression formation (DeNisi,
1997; Feldman, 1981; Flynn, Chatman, & Spataro, 2001; Hogan,
1987; Ilgen, Barnes-Farrell, & McKellin, 1993; Judge & Ferris,
1993) and systematic biases have been attributed to prior expectations based on schemas and stereotypes of ethnicity or gender
(Arvey, 1979; Heilman, 2001; Kanter, 1977; Klein & Snyder,
2003). Numerous studies have also demonstrated the influence of
stereotypes and group membership on evaluations, attributions,
and selection decisions (e.g., Arvey, 1979; Biernat & Kobrynowicz, 1997; Davison & Burke, 2000; Elliott & Smith, 2004; Heilman
& Guzzo, 1978; Kraiger & Ford, 1985; Nieva & Gutek, 1980;
Olian, Schwab, & Haberfeld, 1988; Sackett & DuBois, 1991;
Swim, Borgida, Maruyama, & Myers, 1989). Stereotypes and prior
expectations have also been shown to lead to behavioral confirmation and self-fulfilling prophecies (e.g., Chen & Bargh, 1997;
Klein & Snyder, 2003; Word et al., 1974).
As a complement to explanations emphasizing the influence of
stereotypes, experience sampling suggests that the tendency to
associate with socially similar others can lead to systematic differences in evaluations as a function of group membership. In
particular, systematic differences in evaluations of individuals of
different groups would emerge under the following four
conditions.
First, impressions and evaluations are based on, or influenced
by, observations obtained through personal encounters. By working together with others, seeking their advice, or discussing professional matters with them, individuals form impressions about
the abilities of colleagues. In many organizations, as well as in
professions, such impressions provide the basis for, or provide an
important input to, evaluation and selection decisions. In other
settings, evaluations may be based on information about performance on tasks with measurable outcomes, such as sales, and
personal observations in interactions matter less.
Second, the probability of future interactions is influenced by
current impressions of abilities. In some organizations this may not
be possible because assignment and interactions are regulated by
senior management. However, in several professions and in many
organizations, individuals, and especially managers, have some
discretion over the individuals with whom they will work. In
addition, individuals can often decide whom they will approach for
advice on professional matters (Blau, 1962; Borgatti & Cross,
2003; Lazega, 2001; Wilensky, 1967). In such cases, current
impressions of ability may influence the probability of future
24
According to the 1990 census, 38% of all individuals in New Mexico
had Hispanic origins.
25
The Muslim majority made more negative attributions about the
minority than vice versa, however (Islam & Hewstone, 1993b).
26
The majority had more negative stereotypes about native Canadians,
however.
27
The meta-analytic findings are also mainly based on experiments with
little opportunity for interaction.
966
DENRELL
contact and, thus, the probability of future sampling. If a manager
believes that a colleague is especially competent, the manager may
be more likely to ask this colleague for advice and to include him
or her in future working groups. Consistent with this, several
studies have shown that perceived competence, based on observations of successful task performance in previous interactions,
strongly influences the choice of future working partners (Colella,
DeNisi, & Varma, 1998; Gilchrist, 1952; Hinds, Carley, Krackhardt, & Wholey, 2000; J. M. Levine, Snyder, & Mendez-Caratini,
1982; Miller & Suls, 1977; Zander & Havelin, 1960). Studies of
advice networks in organizations have also shown that individuals
are more likely to be asked for advice if they are perceived to be
competent (Blau, 1962; Borgatti & Cross, 2003; Lazega, 2001, pp.
95–96).
Current impressions of abilities may also influence the probability of future observations of abilities if task assignments depend
on current impressions of abilities. A subordinate who is believed
to be inferior may only be given less challenging tasks and, thus,
have little chance to display his or her talents. On the basis of a
study of career paths in a large firm, Rosenbaum (1979) suggested
that this is an important reason for the limited opportunities facing
individuals with poor initial performance:
Early winners are seen as “high-potential people” who can do no
wrong and who are given additional opportunities and challenges,
while those who do not win in the early competition are given little or
no chance to prove themselves again. (p. 236)
Similarly, Manzoni and Barsoux (2002), on the basis of interviews
with managers and subordinates, argued that managers typically
give seemingly poor performers routine assignments and projects.
Third, evaluators sometimes interact with the individuals they
may be evaluating for reasons unrelated to their professional
estimate of them. In particular, the reason for interaction may be
noninstrumental and social (Blau, 1962; Greenberger & Sorensen,
1971). In many organizations and professions, there are numerous
occasions for such socially motivated interactions. A large amount
of research has also shown that such social interactions are more
likely to occur among individuals with similar characteristics, such
as gender, ethnicity, education, and age (Byrne, 1971; Fischer,
1982; Marsden, 1987; McPherson & Smith-Lovin, 1987; McPherson et al., 2001). Research on informal interactions in organizations also has shown that this principle holds for social and other
informal networks within organizations (Blau, 1962; Brass, 1985;
Greenberger & Sorensen, 1971; Ibarra, 1992, 1993; Lazega, 2001;
Lincoln & Miller, 1979; Sykes, Larntz, & Fox, 1976). Studies have
also shown that social similarity between raters and ratees leads to
interpersonal attraction (Ferris, Judge, Rowland, & Fitzgibbons,
1994; Judge & Ferris, 1993; Tsui & O’Reilly, 1989; Varma &
Stroh, 2001).
Fourth, socially motivated interactions provide information
about behaviors and characteristics that may influence impressions
and evaluations. Social interactions may lead to discussions about
professional events and issues that provide information about the
knowledge and insight of others. For example, studies have shown
that friendship predicts whom individuals ask for advice and
information (Cross, Rice, & Parker, 2001). If individuals are likely
to be friends with socially similar others (Byrne, 1971), they are
likely to have many conversations about professional events and
issues with socially similar others. Consistent with this, Ibarra
(1992) found that male employees in an advertising agency were
most likely to choose another male employee when asked about
whom “you see socially outside of work” and “you know you can
count on,” and were also most likely to choose another male
employee when they were asked with whom “you discuss what is
going on in the organization” and who “are important sources of
professional advice” (Ibarra, 1992, p. 431). Similarly, Lazega
(2001, pp. 121–123) showed that lawyers in a law firm were both
more likely to seek advice from and socialize outside work with
lawyers of the same gender.
Social interactions also make it possible to observe personal
attributes of others, such as leadership ability and creativity. In
addition, through social interactions one may hear about accomplishments of which one was unaware. Information about such
accomplishments can also come from other people in the same
social network. Finally, social connections can directly influence
the choice of working partners. As demonstrated in experiments
and field studies (French, 1956; Hinds et al., 2000), individuals are
more likely to continue to work with another whose past performance is low if he or she is a friend. If this is true, individuals are
more likely to get additional observations of individuals who are
socially similar and, thus, more likely to be a friend.
If these conditions are satisfied, the model of experience sampling implies that negative impressions will be less stable, and thus
evaluations will be higher for individuals who are socially similar
to evaluators, consistent with findings from numerous field studies
(Elliott & Smith, 2004; Ferris et al., 1994; Judge & Ferris, 1993;
Kraiger & Ford, 1985; Sackett & DuBois, 1991; Tsui & O’Reilly,
1989; Turban & Jones, 1988; Varma & Stroh, 2001).28 The model
is also consistent with findings that interpersonal attraction is
associated with high performance ratings (Cardy & Dobbins, 1986;
Ferris et al., 1994; Judge & Ferris, 1993; Tsui & O’Reilly, 1989;
Varma & Stroh, 2001; for a review, see Lefkowitz, 2000), a result
usually attributed to a direct influence of attraction on either
perceived or actual performance (Robbins & DeNisi, 1994).29
In the model of experience sampling, a bias emerges even if it
is assumed that stereotypes and cognitive and perceptual biases do
not influence observations or evaluations. Again, this does not
imply that stereotypes and cognitive biases are not important.
Rather, experience sampling is likely to reinforce biases due to
flaws in information processing and preexisting stereotypes. Nevertheless, the model of experience sampling implies that theories
relying on cognitive or perceptual biases are not necessary to
explain biased evaluations. Thus, observations of biases in evaluations in field studies should not necessarily be attributed to
cognitive biases. The model of experience sampling also suggests
that biases may be underestimated in experiments on performance
evaluation in which information is exogenously provided or sam28
Moreover, the effect sizes observed in field studies, which have
seldom been large (e.g., Kraiger & Ford, 1985), are well within the range
of what the model can generate under reasonable assumptions about
parameter values.
29
Varma, DeNisi, and Peters (1996) found that diary keeping strengthened the influence of affect, which seems inconsistent with arguments
based on cognitive biases but is consistent with a model with experience
sampling, if memories of past impressions are strengthened by diary
keeping (see the above discussion about the effect of memory).
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
pling is unrelated to impressions. Even if biases are small in such
contexts, as they sometimes are, they may be larger in field
settings in which information has to be actively sampled. Metaanalyses have also shown that effect sizes in studies of biases in
performance evaluation are larger in field studies (Kraiger & Ford,
1985).
If biases in evaluations can emerge even in the absence of any
cognitive bias, this also implies that efforts to eliminate cognitive
biases may not eliminate biases in evaluations. To eliminate biases
in evaluations one may also have to formalize interactions among
raters and ratees. The bias should be lower in firms with more
formal interactions among raters and ratees, consistent with findings that the proportion of women in managerial jobs is higher in
firms with more formalized personnel practices (Reskin &
McBrier, 2000). Moreover, because interactions are often more
regulated in jobs at lower levels in the organization, and job
performance at lower levels is typically easier to measure, the bias
should be weaker at lower levels in the organization, consistent
with findings of decreasing disparity in promotions and wages of
minorities and majorities at lower levels in organizations (Cotter,
Hermsen, Ovadia, & Vanneman, 2001 [but see Baxter & Wright,
2000]; Elliott & Smith, 2004; Maume, 2004).
Finally, experience sampling is likely to be especially important
in professional communities, such as academia, in which interactions are seldom structured but are determined mainly by assessments of professional and social benefits. If professionals tend to
associate with socially similar others, and thus get more information about their accomplishments and capabilities, evaluations will
be higher for socially similar others, consistent with findings of
systematic differences in promotion rates between men and
women in academia (Long, Allison, & McGinnis, 1993; McBrier,
2003; Rosenfeld, 1981) and professions (Hagan & Key, 1995;
Spurr & Sueyoshi, 1994).
Proximity. Several studies have documented that proximity is
an important determinant of liking (Brewer & Campbell, 1976;
Festinger, Schachter, & Back, 1950; Segal, 1974). Even if students
are randomly assigned to rooms, individuals are more likely to
become friends with and have a favorable impression of individuals who are nearby (Segal, 1974). Although this effect can be
explained by several different mechanisms—including simple
availability, the possibility that people tend to reward each other
more often than they punish one another (T. M. Newcomb, 1956),
as well as mere exposure (Moreland & Beach, 1992; Zajonc,
1968)—it is also an implication of experience sampling. Numerous
studies have shown that spatial proximity is likely to lead to
informal communication through frequent exposure to others
(Allen, 1978; Bochner, Duncan, Kennedy, & Orr, 1976; Hagstrom,
1965/1975; Kraut, Egido, & Galegher, 1990; Zahn, 1991). Proximity also predicts whom individuals ask for advice in organizations (Borgatti & Cross, 2003; Lazega, 2001, p. 121). Because
individuals are likely to be frequently exposed to spatially proximate others, and because such people are easily accessible, individuals are more likely to interact with spatially proximate others
of whom they may have a negative impression than with spatially
distant others of whom they have a negative impression. The above
arguments then imply that individuals who are nearby will, on
average, be evaluated higher. This applies to both competency and
liking evaluations, whereas other explanations, such as T. M.
Newcomb’s (1956) thesis, are more plausible for liking than for
967
competency evaluations. Ferris et al. (1994) also found that performance ratings were negatively correlated with spatial distance
between the supervisor and the subordinate.
The influence of physical attractiveness. Experience sampling
can also lead to systematic differences in evaluations of individuals who have attributes that make them more or less attractive to
interact with. Consider, for example, the effect of physical attractiveness. Several studies have documented that physically attractive individuals are often perceived in a more positive light than
others (Dion, Berscheid, & Walster, 1972; Eagly, Ashmore,
Makhijani, & Longo, 1991; Feingold, 1992; Landy & Sigall, 1974;
Langlois et al., 2000; Webster & Driskell, 1983), even for traits
that are not objectively associated with physical attractiveness
(Feingold, 1992). Existing explanations of this phenomenon have
focused on evolutionary theories and on how positive feelings for
attractive people may contribute to behavioral confirmation or a
self-fulfilling prophecy (e.g., Feingold, 1992; Langlois et al.,
2000).
Experience sampling suggests an additional mechanism of how
attractiveness could influence impressions of other traits. Suppose
that people are more willing to interact with physically attractive
people. Such an assumption is consistent with studies that have
found that physically attractive individuals are paid more attention
and are less likely to be avoided (for a review, see Langlois et al.,
2000). In addition, studies have shown that physical attractiveness
predicts popularity, both with the opposite and the same sex
(Feingold, 1992). Reis et al. (1982) also showed that physical
attractiveness of males was associated with a larger quantity of
social interactions with the opposite sex. Suppose also that physical attractiveness can compensate, to some extent, for other negative traits. People may be willing to interact with a physically
attractive individual even if they believe that he or she is not very
competent, for example. If this is true, false negative impressions
regarding other traits, such as competence, will be less likely to
persist for physically attractive individuals. Thus, experience sampling suggests a simple mechanism for how an illusory correlation
can develop between physical attractiveness and other traits, such
as competence.
Other Areas of Application
Although this article has focused mainly on systematic differences in evaluations, experience sampling also has implications
for beliefs about the prevalence of attitudes and individual
characteristics.
Trust. The bias produced by experience sampling suggests that
individuals will, on average, underestimate the trustworthiness of
others. To develop this, note that perceptions of trustworthiness are
often based on events in which individuals have trusted other
individuals and such trust has not been betrayed (e.g., Boyle &
Bonacich, 1970; Deutsch, 1958; Lindskold, 1978). In other words,
beliefs are based on historical observations. Beliefs about trustworthiness, however, are also likely to influence the probability
that an individual will put him or herself in a situation so that he
or she will have to trust another individual (Hardin, 1992). If an
individual, based on previous observations, is considered to be less
than trustworthy, such an individual may be avoided (Gambetta,
1988). Moreover, even if this individual cannot be avoided, safeguards can be used, such as formal contracts or other types of
DENRELL
968
incentives that protect against any adverse consequences of opportunistic behavior (Williamson, 1975). However, because such
safeguards typically imply that individuals will be punished for
opportunistic behavior, the absence of opportunistic behavior does
not provide much information about whether an individual is
trustworthy (Eagly, Wood, & Chaiken, 1978; Strickland, 1958). As
demonstrated in an experiment by Malhotra and Murnighan
(2002), a binding contract may lead partners to attribute cooperative behavior to the restrictions imposed by the contract rather than
to the individuals themselves. This also implies that an initial false
belief about an opponent can result in actions (i.e., the use of
safeguards) that make it very difficult to disconfirm the belief. This
analysis also suggests that in social settings in which safeguards
are considered inappropriate or are not used, such as in families or
in some organizations, the level of trust may be higher. In such
settings, individuals cannot avoid others and have to rely on them,
and false beliefs about untrustworthiness will be less stable. More
generally, this reasoning suggests that (a) several moral traits may
be underestimated if individuals avoid others who seem to lack
such traits, and (b) the perceived level of morality will be higher
in settings in which avoidance or the use of safeguards is not
possible.
Social influence. Experience sampling also suggests a novel
way in which beliefs may be influenced by the immediate social
environment (e.g., Festinger et al., 1950). Even if individuals have
no intrinsic preference for agreeing with the individuals they
interact with most, they may nevertheless have more positive
opinions about activities in which several of their friends and
colleagues are engaged than about activities in which few of their
friends and colleagues are engaged. The reason is that frequent
interaction with friends and colleagues will provide individuals
with many observations of these activities, irrespective of their
opinion of these activities. Thus, false negative impressions are
more likely to be disconfirmed for such activities. For an illustration, consider researchers’ opinions about various theories or fields
of research. Because one cannot read everything, impressions
about fields of research in which one is not personally involved
must be based on a limited set of observations. If the initial
impression is negative, one is less likely to examine this field in
more detail. As a result, a negative opinion will be stable. However, if there are several researchers at your school who are active
in a particular field of research, you may have to interact, in
seminars and otherwise, with individuals doing research in this
field. Thus, more observations will be available, and the opinion
may be corrected if unjustifiably negative, which might not have
happened otherwise.
Conclusion
Even if impressions are based on all available evidence, and the
evidence is accurately interpreted, impressions may nevertheless
be biased. This result is an implication of a common characteristic
of impression formation: the tendency for individuals with a positive impression to continue sampling and for individuals with a
negative impression to stop sampling. Though not necessary, such
sequential sampling is often the only practical way to allocate
attention between alternative interaction partners. When sampling
is sufficiently sensitive to the impression, this simple mechanism
can provide an alternative explanation of several biases in impres-
sion formation. It also suggests a number of new hypotheses about
moderators of such biases.
The fact that sampling can explain systematic biases in impression formation does not imply that cognitive–perceptual biases are
not significant. Many systematic biases in impression formation,
such as ingroup bias, are probably overdetermined and are the
result of both sampling and cognitive–perceptual biases. Nevertheless, as emphasized by Fiedler (1996, 2000), sampling models
provide an alternative null model for evaluating the significance of
cognitive–perceptual biases. Standard null models typically assume that if no systematic mental operations of distortions are at
work, no systematic bias in impressions is expected. Sampling
models challenge this assumption and suggest that the appropriate
baseline, against which psychological effects should be evaluated,
is not 0.
More generally, the model of experience sampling suggests that
pragmatic constraints in impression formation are important. Much
research on impression formation implicitly assumes that the goal
of impression formation is, or should be, accuracy. However,
accuracy is seldom the only goal regulating impression formation
processes, because outcomes also matter (Einhorn & Hogarth,
1978; Friedrich, 1993). Except in laboratory experiments, people
cannot always afford to continue to sample events or individuals if
they believe the outcome will be negative. As discussed above, and
as illustrated by the experiment by Fazio et al. (2004) on attitude
formation, such a concern for outcomes implies that negative
impressions may be persistent even if beliefs and evaluations
would be sensitive to new evidence. It also implies that biases in
impression formation are likely to be stronger in situations in
which information has to be actively sampled and individuals care
about the outcome of interactions as well as accuracy. Incorporating such active sampling into experiments on impression formation would make it possible to examine the relative magnitude of
experience sampling and flawed information processing in the
persistence of negative impressions.
Finally, experience sampling also implies that interventions that
try to eliminate individual biases, such as confirmation bias, may
not be sufficient. For example, although accountability can reduce
the effect of first impressions and expectations (Tetlock, 1983), it
may not eliminate the bias produced by experience sampling.
Evaluators may still be able to justify their decisions by referring
to information to which they have access, without realizing that the
sample to which they have access may be biased. To minimize the
effect of experience sampling, the evaluation process should be
made more formal, with structured interactions (cf. Desforges et
al., 1991). Although this may be possible in formal organizations,
it is difficult in most other settings, such as social and professional
communities.
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EXPERIENCE SAMPLING IN IMPRESSION FORMATION
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Appendix A
Derivation of the Asymptotic Density
Let Z be the random variable that the estimate, X̂t, would converge to as
t 3 ⬁, if instead of sequential sampling it was assumed that the individual
was sampled in each period. Denote the density of Z by g(z). In addition,
let Y be the random variable that X̂t converges to as t 3 ⬁. To derive the
density of Y, note that the process can be viewed as a semi-Markov process.
In a semi-Markov process, transitions between states follow a Markov
process. The duration between transitions, however, is not fixed, as in
ordinary Markov processes, but follows a probability distribution that may
depend on the current state (e.g., Karlin & Taylor, 1975). In the above
process, the (continuous) state space is the set of estimates. Because the
transitions between these states depend only on the existing state and the
value of the new observation, transitions are Markovian. Transitions are
only made, however, if the alternative is sampled. In this case, durations
between transitions follow a geometric probability distribution with mean
w(z) ⫽ 1/p(z).
Using the theory of semi-Markov chains, it is possible to derive the
limiting distribution of the density of the estimates, h(y). To do so, note that
for a semi-Markov chain with finite state space, the limiting proportion of
time that the process will be in state i is
␲ i␭ i
冘
i
␲ i␭ i
,
(A1)
where ␲i is the limiting probability that the underlying Markov process will
be in state i, and ␭i is the expected duration in state i (e.g., Karlin & Taylor,
1975). In this case, the underlying Markov process has a limiting distribution with density g(z), and the expected duration in state z is w(z). The
probability that the underlying Markov process will be in the region [z, z ⫹
⌬z] is thus G(z ⫹ ⌬z) ⫺ G(z). The expected duration in this region is
approximately w(z). The limiting proportion of time that the process will be
in state [z, z ⫹ ⌬z] is thus
关G共z ⫹ ⌬z兲 ⫺ G共z兲兴w共z兲
冘
关G共z ⫹ ⌬z兲 ⫺ G共z兲兴w共z兲
h共y兲 ⫽
冕
⬁
.
(A3)
ec⫹Sy
,
1 ⫹ ec⫹Sy
(A4)
S ⬎ 0, the mean duration of an estimate Y ⫽ y is a geometrically distributed
random variable with an expected value of
1 ⫹ ec⫹Sy
1
⫽
⫽ e⫺c⫺Sy ⫹ 1.
p共y兲
ec⫹Sy
(A5)
Moreover, if X is a normally distributed variable with a mean of 0 and
variance ␴2, it follows that Z is normally distributed with a mean of 0 and
variance
冉
␴2
1
2 ⫺1
b
冊
⫺c⫺Sy
共e
e⫺y / 2v
2
⫹ 1兲
⫺⬁
2
,
1
冑2 ␲ v
⫺y2 / 2v2
e
(A7)
dy
or
1
冕
e⫺y / 2v ⫺Sy⫺c ⫹
2
冑2 ␲ v
⬁
1
e⫺y / 2v ⫺Sy⫺cdy ⫹
2
冑2 ␲ v
⫺⬁
2
2
1
冑2 ␲ v
冕
⬁
e⫺y / 2v
2
.
1
冑2 ␲ v
⫺⬁
2
(A8)
e⫺y / 2v dy
2
2
Note that
⫺
(y ⫹ Sv2 ) 2 S2 v2
y2
.
⫹
2 ⫺ Sy ⫽ ⫺
2v
2v2
2
(A9)
The limiting density can thus be written as
2 2
eS v / 2⫺c
S2 v2 / 2⫺c
e
冕
⬁
1
冑2 ␲ v
1
⫺⬁
冑2 ␲ v
2 2
e⫺关共y⫹Sv ) ]/ 2v ⫹
⫺关共y⫹Sv2 ) 2 ]/ 2v2
e
2
dy ⫹
1
e⫺y / 2v
2
冑2 ␲ v
冕
⬁
.
1
⫺⬁
2
冑2 ␲ v
⫺y2 / 2v2
e
.
(A6)
(A10)
dy
Because the integrals equal 1 (the expressions in the integrals are normal
densities), the limiting density is
eS v / 2⫺c
1
冑2 ␲ v
2 2
e⫺关共y⫹Sv ) ]/ 2v ⫹
2
1
冑2 ␲ v
e⫺y / 2v
2
2
(A11)
2 2
w共y兲g共y兲dy
b␴2
⫽
共2 ⫺ b兲
⬁
1
冑2 ␲ v
eS v / 2⫺c ⫹ 1
If the probability of sampling the alternative is
v2 ⫽
冕
(A2)
⫺⬁
w共y兲 ⫽
共e⫺c⫺Sy ⫹ 1兲
2 2
.
Dividing with ⌬z and taking limits as ⌬z goes to 0, it is the case that the
limiting density of the proportion of time that the process spends in state y
is
w共y兲g共y兲
The density, h(y), is thus
or
2 2
eS v / 2⫺c
2 2
1 ⫹ eS v / 2⫺c
1
冑2 ␲ v
2 2
e⫺关共y⫹Sv ) ]/ 2v ⫹
2
1
2 2
1 ⫹ eS v / 2⫺c
1
冑2 ␲ v
e⫺y / 2v .
2
2
(A12)
Thus, the density is a weighted combination of the density of a normal
random variable with a mean of ⫺Sv2 and the density of a normal random
variable with a mean of 0. It follows that the density of Y will be shifted
to the left in comparison with the density of a normal random variable with
a mean of 0. It is also the case that the expected estimate is lower the higher
the value of S (S both reduces the mean of the first term and increases its
weight). Moreover, the expected estimate is higher the higher the value of
c (which increases the weight of the second term). Finally, because v2 is an
increasing function of b and the expected value of Equation A12 is a
decreasing function of v2 (v2 reduces the mean and increases the weight of
the first term), the expected estimate is inversely associated with the value
of b.
To illustrate the resulting distribution, Figure A1 plots the density
when S ⫽ 3, c ⫽ 0, b ⫽ 0.5, and ␴2 ⫽ 1 together with the density that
would have resulted from random sampling. As illustrated, the distribution produced by experience sampling has been shifted to the left. In
this case, the expected estimate, E(Y), can be shown to be ⫺0.82, and
the probability of a negative estimate is 0.87. As noted above, the bias
would be smaller if S were lower and sampling were less sensitive to the
estimate.
(Appendixes continue)
DENRELL
976
Figure A1. The asymptotic density of the estimate Y for random and experience sampling. In this example, the
probability of sampling is e3x̂t/共1 ⫹ e3x̂t兲, and b ⫽ 0.5.
Appendix B
A General Model
Belief Formation
Assume that the estimate in period t ⫹ 1, x̂t⫹1 , is a weighted combination of the past estimate, x̂t, and the new observation in period t ⫹ 1, xt⫹1,
if any. Formally,
x̂t⫹1 ⫽
冦
For all processes satisfying these assumptions, and for any random
variable X with finite expectation and variance, the expected estimate,
E(X̂t), will always be below E(X):
Proposition
共1 ⫺ bt⫹1 兲x̂t ⫹ bt⫹1 xt⫹1
if an observation is made in period t ⫹ 1
.
x̂t
if no observation is made in period t ⫹ 1
For all t ⬎ 1, E(X̂t) ⬍ E(X).
(B1)
Proof
Assume also that bt 僆 (0, 1). Note that the value of bt can differ between
periods. As a result, the above specification includes several different
belief-formation processes. For example, it includes a process in which the
first impression is especially important (i.e., where b1 is large). Moreover,
it includes a belief-formation process in which the estimate at the beginning of period t ⫹ 1 is the average of all observations made in period t or
before. In this case,
bt⫹1 ⫽
1
,
关n共t兲 ⫹ 1兴
The expected value of X̂t⫹1, conditional upon the fact that X̂t ⫽ x̂t is
E共X̂t⫹1 兩X̂t ⫽ x̂t兲 ⫽ pt⫹1 共x̂t兲关共1 ⫺ bt⫹1 兲x̂t ⫹ bt⫹1 E共X兲兴 ⫹ 关1 ⫺ pt⫹1 共x̂t兲兴x̂t
(B3)
or
E共X̂t⫹1 兩X̂t ⫽ x̂t兲 ⫽ x̂t ⫹ bt⫹1 pt⫹1 共x̂t兲E共X兲 ⫺ bt⫹1 pt⫹1 共x̂t兲x̂t.
(B4)
EX̂ t关E共X̂t⫹1 兩X̂t ⫽ x̂t兲兴 ⫽ E共X̂t⫹1 兲
(B5)
(B2)
where n(t) is the number of observations made in period t and before. If X
is normally distributed and the prior is also normally distributed, the above
process also includes Bayesian updating. In this case, the mean of the
posterior distribution is simply a weighted average of the mean of the prior
and the new observation.
Sampling Process
Let pt⫹1(x̂t) be the probability of sampling in period t ⫹ 1 given the
estimate X̂t ⫽ x̂t at the beginning of period t ⫹ 1. Note that the function
pt⫹1(x̂t) may differ between periods. Assume that pt⫹1(x̂t) is a strictly
increasing function—that is, if x̂t,1 ⬎ x̂t,2, then pt⫹1(x̂t,1) ⬎ pt⫹1(x̂t,2).
Assume also that for all values of x̂t, pt⫹1(x̂t) 僆 (0, 1) that is, assume that
pt⫹1(x̂t) cannot be 0. Finally, assume that all individuals sample in the first
period.
Because
(e.g., Williams, 1991), this implies that
E共X̂t⫹1 兲 ⫽ EX̂ t共X̂t兲 ⫹ bt⫹1 EX̂ t关pt⫹1 共X̂t兲兴E共X兲 ⫺ bt⫹1 EX̂ t关pt⫹1 共X̂t兲X̂t兴.
(B6)
Because
EX̂ t关pt⫹1 共X̂t兲X̂兴 ⫽ covX̂ t关pt⫹1 共X̂t兲, X̂t兴 ⫹ EX̂ t关pt⫹1 共X̂t兲兴EX̂ t共X̂t兲,
(B7)
this equals
EX̂ t共X̂t兲兵1 ⫺ bt⫹1 EX̂ t关pt⫹1 共X̂t兲兴其
⫹ bt⫹1 EX̂ t关pt⫹1 共X̂t兲兴E共X兲 ⫺ bt⫹1 covX̂ t关pt⫹1 共X̂t兲, X̂t兴.
(B8)
EXPERIENCE SAMPLING IN IMPRESSION FORMATION
Note that covX̂t[pt⫹1(X̂t), X̂t] ⬎ 0 if pt⫹1(䡠) is a strictly increasing function
(Ross, 2000, p. 626).
Because EX̂1(X̂1) ⫽ E(X), one gets
E共X̂2兲 ⫽ E共X兲 ⫺ b2 covX̂ 1关p2 共X̂1 兲, X̂1 兴 ⬍ E共X兲.
(B9)
More generally, suppose that EX̂t(X̂t) ⬍ E(X). It then follows that E(X̂t⫹1)
is strictly less than
E共X兲兵1 ⫺ bt⫹1 EX̂ t关pt⫹1 共X̂t兲兴其 ⫹ bt⫹1 EX̂ t关pt⫹1 共X̂t兲兴E共X兲
⫺bt⫹1 covX̂ t关pt⫹1 共X̂t兲, X̂t兴,
(B10)
or
977
E共X̂t⫹1 兲 ⬍ E共X兲 ⫺ bt⫹1 covX̂ t关pt⫹1 共X̂t兲, X̂t兴 ⬍ E共X兲.
(B11)
The proposition now follows from the principle of induction. Q.E.D.
This proof assumes that the first impression is equal to the first observation. However, exactly the same proof holds if there is a prior and the
prior is equal to the expected value of the observation. If the prior differs
from the expected value of the observation, however, it is possible that
experience sampling will, temporarily, lead to overestimation. This could
happen if the expected value of the observation is strongly negative while
the prior is, say 0. In this case, individuals might avoid sampling after the
first observation. If the estimate is a weighted average of the prior and the
first observation, however, the estimate, although strongly negative, might
still be higher than the expected value of the observation.
Appendix C
The Influence of the Sampling Process
If w(y) ⫽ [dw1 ⫹ (1 ⫺ w1)p(Y)]/[dw2 ⫹ (1 ⫺w2)p(Y)], this implies that
Case A
To model the influence of other factors on sampling, suppose that the
probability of sampling is wd ⫹ (1 ⫺ w) pt⫹1(x̂t), where w 僆 (0, 1), and
d 僆 (0, 1) is an arbitrary constant. Here, w is a parameter regulating the
probability that sampling will be independent of the estimate and will be
determined exclusively by the arbitrary constant, d. It may be expected that
as w increases, the bias will decrease, and the estimate will increase. To
show this, consider the model in which bt is identical for all t (as in the A
Simple Example of the Effect of Experience Sampling section) and X is
normally distributed with a mean of ␮ and variance ␴2. For this model, it
is the case that the expected asymptotic estimate, E(Y), is an increasing
function of w.
E2 共Y兲 ⫽
冕
冕
1
⬁
cov1 关w共Y兲, Y兴 ⫹ E1 关w共Y兲兴E1 共Y兲
cov1 关w共Y兲, Y兴
⫽ E1 共Y兲 ⫹
E1 关w共Y兲兴
E1 关w共Y兲兴
E2 共Y兲 ⫽
Proof
冕
⬁
⫺⬁
1
g共y兲dy
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
h2 共y兲 ⫽
冕
1
g共y兲
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲
⬁
⫺⬁
冕
⬁
⫺⬁
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
h 共y兲dy
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲 1
册
.
(C6)
冋
册
⫽
p⬘共y兲d共w2 ⫺ w1 兲
⬎ 0,
关w2 ⫹ 共1 ⫺ w2 兲p共y兲兴 2
(C7)
this implies that [dw1 ⫹ (1 ⫺ w1)p(y)]/[dw2 ⫹ (1 ⫺ w2)p(y)] is a strictly
increasing function of y. It follows (Ross, 2000, p. 626) that
冋
册
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
, Y ⬎ 0.
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲
(C8)
Thus, E2 (Y兩D ⫽ d) ⬎ E1 (Y兩D ⫽ d) for all values of d, which implies that
E2(Y) ⬎ E1(Y).
Notice also that because
.
(C2)
1
dw ⫹ 共1 ⫺ w兲p共y兲
(C9)
is a strictly decreasing function of y for all w 僆 (0, 1), it still follows that
E(Y) ⬍ E(X).
Notice that h2(y) can be written as
h2 共y兲 ⫽
册
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
,Y
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
E1
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲
⭸ dw1 ⫹ 共1 ⫺ w1 兲p共y兲
⭸y dw2 ⫹ 共1 ⫺ w2 兲p共y兲
1
g共y兲dy
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
h 共y兲
dw2 ⫹ 共1 ⫺ w2 兲p共Y兲 1
冋
冋
Because
cov1
and
(C5)
or
E2 共Y兲 ⫽ E1 共Y兲 ⫹
(C1)
(C4)
where the index denotes that the expectation is with respect to the random
variable with density h1(y) or h2(y). This can be expressed as
E(Y) is an increasing function of w.
h1 共y兲 ⫽
E1 关w共Y兲Y兴
,
E1 关w共Y兲兴
⫺⬁
cov1
1
g共y兲
dw1 ⫹ 共1 ⫺ w1 兲p共Y兲
yw共y兲h1 共y兲dy ⫽
⫺⬁
w共y兲h1 共y兲dy
Observation 1
Let w2 ⬎ w1. As demonstrated in Appendix A, the corresponding
densities are
⬁
Case B
.
(C3)
To illustrate the effect of the selectivity of sampling, suppose that the
probability of sampling is pt⫹1(x̂t)m, where m 僆 (0, 1). Here pt⫹1(x̂t) can be
any strictly increasing function. A smaller value of m implies that the
(Appendixes continue)
DENRELL
978
probability of sampling, for any given estimate, is higher, as illustrated in
Figure 6B. This also implies that the bias will be smaller and the estimate
higher.
Let r ⫽ m1 ⫺ m2 ⬍ 0. It then follows that
1
p共y兲 m1
⫽ p共y兲 r ⫽
,
p共y兲 m2
p共y兲 ⫺r
Observation 2
(C11)
E(Y) is a decreasing function of m.
which is a strictly decreasing function of y. This implies (Ross, 2000, p.
626) that
Proof
Let m2 ⬎ m1. Following the same reasoning as above, it is the case that
冋 册
冋 册
p共Y兲 m1
cov1
,Y
p共Y兲 m2
E2 共Y兲 ⫽ E1 共Y兲 ⫹
p共Y兲 m1
E1
p共Y兲 m2
cov1
.
冋
册
p共Y兲 m1
,Y ⬍0
p共Y兲 m2
(C12)
(C10)
and, thus, that E2(Y) ⬍ E1(Y).
Appendix D
Estimates of Belief Updating
The available data consist of the development of the average impression
over time for different presentation orders and combinations of high-valued
and low-valued adjectives. Because most studies display only the average
impressions in graphs, the values had to be approximated from these
graphs, although exact figures are available in Anderson (1968; for the last
impression, see Table 2), Furnham (1986), Hogarth and Einhorn (1992),
and Levin and Schmidt (1969, 1970, on like responses). Although this
procedure introduces errors, small changes in values do not change the
estimates much. Because no data on individuals are available, and because
I am interested in parameter values that provide a good fit rather than tests
of significance, I chose to estimate parameters by minimizing the mean
absolute deviation between the predictions of the model and the data. The
numerical minimizations were performed with Excel’s solver function,
using several different starting points, and were checked by numerical
simulations programmed in C⫹⫹.
In addition to estimating the parameters of the models (i.e., b, ␭, ␪, etc.),
the values of the stimuli—that is, the adjectives presented— often have to
also be estimated. Few experiments (with the exception of Levin and
Schmidt, 1969, 1970) have reported the average impression of the adjectives presented. Thus, if an experiment made use of high- and low-valued
adjectives, in different orders, the values of both of these had to be
estimated. The estimates of the values of the adjectives were constrained to
fall within the scale used (i.e., 1– 8 for the data presented in Stewart, 1965).
In addition, I also required that the estimates of the values of the adjectives
be above the highest observed average impression and below the lowest
observed average impression, an implication of both a model with a
constant and a model with a declining weight. Thus, if the average
impression after six highly valued adjectives was 17.5, I required that the
value of the highly valued adjective be at least 17.5. In only one case
(Anderson, 1968) did this constraint influence the estimates (by producing
a lower estimate of the weight of the most recent observation).
Finally, some assumptions must be made about the initial impression
(i.e., the starting value for belief updating). One possibility is to assume
that the initial impression is equal to the middle point of the scale used.
Alternatively, to incorporate any upward or downward bias in evaluations,
the initial impression can be set equal to the average impression after
receiving the first piece of information, where the average is taken over a
counterbalanced set of combinations of high and low adjectives. This
procedure is consistent with a model in which the weight of the most recent
observation is constant or declining. I made use of the second assumption.
However, both assumptions produce very similar estimates. For the data in
Levin and Schmidt (1969, 1970), which only present the proportion of like
responses and not the average impression, I took the middle point of the
scale they used (i.e., 3).
Received November 11, 2003
Revision received March 6, 2005
Accepted March 24, 2005 䡲