BIASES IN INDIVIDUAL DECISION
MAKING
Forthcoming in the “Handbook of
Behavioral Operations Management”
Andrew M. Davis
Samuel Curtis Johnson Graduate School of Management,
Cornell SC Johnson College of Business
Cornell University, Ithaca, NY 14853
[email protected]
LOGO
Chapter 5
Biases in Individual Decision Making
5.1. Introduction
When making operational decisions, managers may be influenced by a number of behavioral biases.
For instance, a planning manager, when constructing a forecast distribution for a product, could be
susceptible to overconfidence and underestimate the variance of demand, or a procurement director,
when deciding how best to bid for a particular component, may expect to feel regret if they bid
too high and obtain the component at a higher price than necessary. Even an executive, in the
middle of a lengthy project that requires future investment, could fall prey to a sunk cost bias and
make a poor decision. Fortunately, as operations management researchers, there is an extensive
literature in both psychology and experimental economics that can inform us and help determine
what specific biases may be responsible for any observed operational decisions. In this chapter, I
will attempt to convey a summary of what I believe are the most relevant results from these two
streams of literature, specifically focusing on one-shot, individual decisions.
The literature on individual decision making in psychology and experimental economics is vast.
Therefore, rather than provide an exhaustive list of all results from both fields, this chapter is
meant to highlight some of the more prevalent behavioral biases that have been well-established,
and illustrate how they have been (or can be) used to help explain results in behavioral operations management contexts.1 . In terms of application, the primary focus will be on human-subject
experiments, but the results can also extend to field experiments, behavioral modeling, and more
1
For those interested in further results of individual decision making in psychology and experimental economics,
there are a number of useful references, including Daniel Kahneman, Paul Slovic, and Amos Tversky’s Judgment
under Uncertainty: Heuristics and Biases [1982], and Colin Camerer’s individual decision making chapter in the
Handbook of Experimental Economics [1995].
1
general empirical studies as well.
In order to describe the overall framework for this chapter, let me briefly refer to what I believe is
the most common approach for modeling individual decisions in operations management: expected
utility theory. For a (very) short history, expected utility theory originated in the early 18th century,
with the St. Petersburg paradox. The St. Petersburg paradox involves a game where a fair coin is
tossed repeatedly, with earnings starting at $2 and doubling every time a head appears ($2, $4, $8,
etc). Once a tail appears, the game ends and the player wins their total earnings. The expected
value of this game is ∞, however, most people are not even willing to pay $25 to play it. Daniel
Bernoulli addressed this paradox by proposing that if one values the game based on its expected
utility to the decision maker, rather than the expected payoff, the paradox can be resolved (such as
a logarithmic function which depends on total wealth, which also relates to the idea of diminishing
marginal utility).
Following Bernoulli, von Neumann and Morgenstern [1944] further proved that if a decision
maker satisfies four axioms (completeness, transitivity, continuity, and independence), a numerical utility index can represent their preferences, where the expected utility, E(u(·)), of n lottery
outcomes, Oi , each occurring with probability pi , i ∈ {1, ..., n}, is equal to the utility of the gamble:
E(u(p1 O1 + ... + pn On )) = p1 u(O1 ) + ... + pn u(On ).
However, shortly after the introduction of this theorem, there were a number of disputes and
controversies. For instance, empirical studies began to demonstrate that the probabilities of outcomes are often evaluated by decision makers in non-linear ways [e.g. Yaari, 1965]. Furthermore,
in 1953, Allais introduced his well-known paradox. Specifically, consider experiment 1, where one
must choose between option 1A and 1B:
1A: $1 million with probability (w.p.) 100%
1B: $1 million w.p. 89%, $5 million w.p. 10%, $0 w.p. 1%
Now consider experiment 2, where one must choose between option 2A and 2B:
2A: $1 million w.p. 11%, $0 w.p. 89%
2B: $5 million w.p. 10%, $0 w.p. 90%
2
Allais demonstrated that a majority of decision makers prefer 1A in experiment 1, and prefer
2B in experiment 2. However, preferences such as these run counter to expected utility theory.
Instead, expected utility theory prescribes that a decision maker should choose 1A and 2A, or 1B
and 2B, due to the independence axiom (which states that when an identical outcome is added
to two sets of choices, a decision maker’s preferences over the choices should not change, as the
identical outcomes effectively cancel each other out). This is more apparent if one rewrites the
payoffs from Allais’ work in an alternative way. For experiment 1:
1A: $1 million w.p. 89%, $1 million w.p. 11%
1B: $1 million w.p. 89%, $5 million w.p. 10%, $0 w.p. 1%.
And experiment 2:
2A: $0 w.p. 89%, $1 million w.p. 11%
2B: $0 w.p. 89%, $5 million w.p. 10%, $0 w.p. 1%.
As one can see, if one removes the first outcome from each experiment, highlighted in bold,
then experiment 1 and experiment 2 are identical. Thus, anyone who does not prefer both 1A and
2A, or 1B and 2B, contradicts the independence axiom.
Expected utility theory, and results similar to the Allais paradox, triggered a plethora of research
in psychology and experimental economics that aimed to better understand how humans make
individual decisions. Interestingly, much of this work revolved around (1) the probabilities of each
outcome, (2) the utility of each outcome, and (3) that individuals make decisions which maximize
their expected utility. Broadly speaking, these three features constitute a rough framework that
capture many of the pertinent results in psychology and experimental economics, specifically those
relating to (1) judgments regarding risk, (2) evaluations of outcomes, and (3) bounded rationality,
which will represent the three main sections of this chapter.
Given this general framework, Figure 5.1 depicts a summary of included topics in the chapter,
where each topic constitutes its own subsection. As a result, this may look a bit like a laundry
list of behavioral results. This is intentional, so that someone interested in a particular topic can
spend a majority of their time on the appropriate (ideally, somewhat self-contained) subsection.
Furthermore, within each subsection for a particular topic, I attempt to follow a basic structure
of: (a) providing a snapshot that describes the topic, often through an example, (b) highlighting
the most relevant “greatest hits” papers which first established the result, and/or review articles
on the topic, and (c) briefly describing how current and future behavioral operations management
3
Figure 5.1: Chapter 5 Structure and Included Topics.
Biases in Individual
Decision Making
Judgments Regarding
Risk
Evaluations of Outcomes
Bounded Rationality
The Hot Hand and
Gambler’s Fallacies
Risk Aversion and Scaling
Satisficing
The Conjunction Fallacy
and Representativeness
Prospect Theory
Framing
Decision Errors
Base Rate Neglect and
Bayesian Updating
Anticipated Regret
Reference
Dependence
System I and System II
Decisions
The Availability Heuristic
Mental Accounting
Probability Weighting
Intertemporal Choice
Overconfidence
The Endowment Effect
Ambiguity Aversion
The Sunk Cost Fallacy
Counterpoint on Heuristics
and Biases
studies might apply the topic.
Lastly, one may recognize, in Figure 5.1, that this chapter omits a number of results in psychology and experimental economics. For instance, some topics which are not included are those in
repeated settings (such as learning and the recency bias), and those in social or strategic environments. If I neglected to include a particular topic, it does not necessarily mean that it is irrelevant
to behavioral operations management. Instead, it is most likely due to one of two reasons: the topic
is detailed in another chapter, or (more likely) I did not have the foresight to properly include it.
Nevertheless, I hope that this chapter not only provides a review of many results in psychology and
experimental economics that pertain to behavioral operations, but also stimulates fellow researchers
to think beyond the results presented here, and develop their own unique applications of known
behavioral results in future operations management studies.
5.2. Judgments Regarding Risk
Managers in operational settings often face decisions that involve uncertainty. Past research has
demonstrated that, when evaluating or predicting the likelihood or probability of an outcome, individuals are prone to a number of biases. For instance, perhaps a recent string of successful outcomes
chosen by a manager will lead them to believe that there is an even higher likelihood of a favorable
outcome for their next decision, when in fact the events are independent. In another example, when
4
exact probabilities are known for future outcomes, a manager may take these probabilities and interpret them in a biased way before making a final decision. This section will provide a snapshot
of established results on judgments regarding risk, including the hot hand and gambler’s fallacy,
the conjunction fallacy, base rate neglect and Bayesian updating, probability weighting functions,
overconfidence, and ambiguity aversion. It will also touch on some of the heuristics which are used
by people when forming beliefs about probabilities and risk, such as representativeness and availability. Lastly, I would like to point out that I present a counterpoint to some of the results in this
area, in the final section of the overall chapter (Section 5.4.4).
5.2.1. The Hot Hand and Gambler’s Fallacies
When making judgements about risk, people often form incorrect beliefs about future predictions.
For instance, imagine that Natalia is rolling dice at a craps table in a casino, and has a favorable
“run” of good tosses. One typical belief in this scenario is that Natalia has a “hot hand,” and
therefore, will continue having success rolling the dice. In fact, it is not uncommon for other gamblers
at the table to give Natalia a portion of their winnings, as though she was accountable for increasing
the probability of favorable dice rolls. This “hot-hand fallacy,” more formally, is the belief in positive
autocorrelation for a sequence of attempts that are in fact independent of one another.
The hot-hand fallacy received considerable attention when Gilovich et al. [1985] analyzed whether
the bias was in fact a reality, or a figment of one’s imagination, for basketball fans and players. More
specifically, during basketball games, a player is often labeled as having a hot hand when he/she
has made successive shots. As a result of this recent success, it is believed that the likelihood of this
player making a future shot increases. In fact, when this occurs, other players and coaches will even
make an effort to ensure that a player with a hot hand is given the ball in subsequent possessions.
To investigate the hot hand phenomenon, Gilovich et al. [1985] conducted a study that included
three parts: (a) a questionnaire of basketball fans from Cornell University and Stanford University,
(b) a dataset that included shooting records from professional basketball teams, and (c) a controlled
basketball shooting experiment. Their results suggest that, despite both fans and players believing in the hot hand, there was no positive correlation between the outcomes of successive shots.
Furthermore, in their controlled shooting experiment, which involved Cornell University basketball
players, they observed that the outcomes of previous shots influenced the players’ own predictions
about making shots, but not their actual performance in making shots.
5
In contrast to the hot-hand fallacy, individuals may actually form opposite beliefs based on
prior outcomes. For example, suppose that Brad is tossing a fair coin, and observes three tails
in a row. When predicting whether the next toss will be heads or tails, he assumes that the
probability of landing heads is more than 50%, because the average should be 50% in the long run
and therefore, a heads result is due. This belief, that there is negative autocorrelation for a sequence
of independent attempts, is called the “gambler’s fallacy.” Compared to the hot-hand fallacy, note
that the gambler’s fallacy revolves strictly around the probability of outcomes, whereas the hot
hand often assumes that the decision maker actually influences the likelihood of outcomes.
The gambler’s fallacy was first noted in controlled laboratory experiments on “probability
matching.”2 But it has also been observed empirically in the field as well. For example, Clotfelter and Cook
[1993] analyzed data from a daily lottery in Maryland, and found that as soon as a lottery number
was announced as a winning number, people were less likely to bet on it again. However, after a
few months passed, the winning number gradually became just as popular as before. Additionally,
Metzger [1985] showed that in horse racing, individuals bet on the favored horses less when the
favored horses won the previous two races (even when they were different horses).
The hot-hand fallacy and gambler’s fallacy are two biases that have been shown to exist in
a variety of settings involving risk, including both laboratory studies and the field (please see
Croson and Sundali [2005] and references therein for further examples). Given the extensive amount
of documentation, it is unlikely that a behavioral operations management study which simply
shows that the hot-hand fallacy or gambler’s fallacy extends to an operations context, will be
particularly ground breaking. However, similar to other fields, explaining a phenomenon observed
in the laboratory (or field), through these biases can be extremely valuable. For instance, in finance,
it is common for investors to sell stocks that have increased in value, and conversely, to hold
onto those which have lost value. Many have argued that the gambler’s fallacy is the cause for
this behavior and have taken steps to control for it (and hopefully lead to increased payoffs). In
operations management, many decisions and problems involve estimating probabilities and risk. If
one is able to recognize when a hot hand or gambler’s fallacy may be at play, such as in revenue
management, forecasting, or inventory decisions, and the degree to which they impact outcomes
and theoretical models, then taking action to mitigate these biases can be extremely valuable to
2
Probability matching is the idea that prediction rates are tied to base rate likelihoods. For instance, if Kristi is
asked to predict which of two lights, A or B, will turn on, where A has a 60% chance of turning on and B has a
40% chance of turning on, she will tend to pick light A roughly 60% of the time, even though the optimal Bayesian
strategy is to pick light A every time.
6
firms.3
5.2.2. The Conjunction Fallacy and Representativeness
Consider the following scenario from Tversky and Kahneman [1983], typically referred to as the
“Linda problem”:
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student,
she was deeply concerned with issues of discrimination and social justice, and also participated in
anti-nuclear demonstrations.
Linda
Linda
Linda
Linda
Linda
Linda
Linda
Linda
is a teacher in elementary school.
works in a bookstore and takes Yoga classes.
is active in the feminist movement. (F)
is a psychiatric social worker.
is a member of the League of Women Voters.
is a bank teller. (T)
is an insurance salesperson.
is a bank teller and is active in the feminist movement. (T&F)
Tversky and Kahneman wrote this description in a way such that Linda is representative of
an active feminist (F ), but not representative of a bank teller (T ). They then asked a group of
subjects to rank the eight possible statements with the description of Linda. Of the three options
highlighted above, (F ), (T ), (T &F ), they found that 85% of the subjects provided the following
order: (F ) > (T &F ) > (T ).
Most individuals are aware that the probability of two events occurring, such as a conjunction
of events, P (A&B), cannot be greater than the probability of each event occurring by itself, P (A)
or P (B). Extending the Linda example, consider that the probability of Linda being a bank teller
is quite low, P (T ) = 0.10, and that the probability of Linda being a feminist is quite high, P (F ) =
0.90. Assuming independence, then the probability that Linda is both a bank teller and feminist
is P (T &F ) = 0.10 × 0.90 = 0.09, which is lower than the probability that Linda is a bank teller,
P (T ) = 0.10. Yet, when facing the Linda problem, a majority of individuals believe that the
probability of Linda being a bank teller and a feminist exceeds that of only being a bank teller.
Judgments about probabilities like these observed in the Linda problem, are referred to as the
“conjunction fallacy.”
3
At the time of writing this chapter, there are some new studies suggesting that the hot-hand and gambler’s
fallacies may not be fallacies at all. Instead, they may be due to a bias in measuring outcomes of streaks in finite
sequences of data. The interested reader is referred to Miller and Sanjurjo [2016] for more details.
7
Many efforts have been made to determine the pervasiveness of the conjunction fallacy in various
settings and contexts. For instance, Tversky and Kahneman conducted a number of extensions and
manipulation checks in their original work on the conjunction fallacy [1983]. In one case, they
presented the same description of Linda, but only provided two options:
Linda is a bank teller. (T)
Linda is a bank teller and is active in the feminist movement. (T&F)
They inverted these two options for half of the subjects, which had no effect, and then asked
which of the two statements was more probable. Surprisingly, once again, 85% of respondents stated
that (T &F ) was more probable than (T ). Tversky and Kahneman found further support for the
conjunction fallacy in a series of other experiments, which considered different subject groups and
contexts (e.g. tennis, crime, risk). Indeed, they even conducted an experiment with physicians, and
had them make medical judgements similar to that of the Linda problem, and found evidence of
the conjunction fallacy. In another experiment, Tversky and Kahneman asked subjects:
Consider a regular six-sided die with four green faces and two red faces. The die will be rolled 20
times and the sequence of greens (G) and reds (R) will be recorded. You are asked to select one
sequence, from a set of three, and you will win $25 if the sequence you chose appears on successive
rolls of the die. Please check the sequence of greens and reds on which you prefer to bet:
RGRRR
GRGRRR
GRRRR
Note that the first option is a subset of the second option, by removing the first G. As such,
the first option must be more probable than the second one. Despite this, 88% of subjects ranked
the second sequence highest (and the third sequence lowest).4
The most commonly accepted explanation of the conjunction fallacy is attributed to individuals
using a heuristic called “representativeness,” which is defined as “the degree to which an event (i)
is similar in essential characteristics to its parent population, and (ii) reflects the salient features of
the process by which it is generated” [Kahneman and Tversky, 1972]. Indeed, in the Linda problem,
people feel as though Linda being a feminist and a bank teller is more representative of the description for her, even though, mathematically, it is less likely that she is a bank teller. Furthermore,
in the example of the red and green die, the second option appears to be an improvement over the
4
Some recent work has investigated means to eliminate, or mitigate, the conjunction fallacy. For example,
Charness et al. [2010] conduct a series of experiments that mimic the Linda problem and find that incentives, and
the ability to communicate with other subjects, decreases the number of subjects who exhibit the conjunction fallacy.
8
first option because it has a higher proportion of the more likely color, G, and is therefore more
representative of the true probabilities.
Turning to operations management, the conjunction fallacy and representativeness have not
been extensively applied to behavioral operations management problems. Although, one recent
study that has successfully applied these psychological findings to operations management is the
work of Tong and Feiler [2016]. They use a combination of representativeness (and bounded rationality), to develop a behavioral forecasting model. They then show that it can account for decisions
often seen in newsvendor and service operations contexts. Examples such as this suggest that future work, which takes a similar approach, can undoubtedly yield further insights and benefits for
operations management.
5.2.3. The Availability Heuristic
Another heuristic that is often used when making judgments about risk is that of “availability,” or
the ease with which specific and relevant instances come to mind for a decision maker. For example,
suppose someone asks you to determine the likelihood that an individual in your town will have a
driving accident. One mental process for estimating this probability is for you to consider friends,
family, and acquaintances, evaluate whether they had an accident or not, and then use that to make
your decision. Alternatively, suppose two individuals are asked what the likelihood is of a crime:
one person has recently witnessed a crime, and the other has never experienced or witnessed any
wrongdoing. Whom do you think will give a higher likelihood? Most likely the former, since they
recall witnessing the crime and use that as a basis for their judgment.
In their work on availability, Tversky and Kahneman [1973, 1974] conducted a series of controlled
experiments to assess the impact of availability when making decisions. For instance, in one study,
they asked subjects whether they believed that, if a random word was drawn from an English text,
it is more likely that the word starts with a K, or that K is the third letter. Their hypothesis was
that, if availability was a heuristic driving subjects’ judgments, then subjects will use a mental
process where they think of words where the letter K is first, and words where the letter K is third.
Tversky and Kahneman, recognizing that it is more difficult to think of examples of the latter,
posited that if availability is mediating the subjects’ judgments, then a majority will state that it
is more likely that the word begins with the letter K. When the truth is that it is roughly twice as
likely that the letter K is the third letter of the word. They conducted multiple experiments such
9
Figure 5.2: Median Judgments (on a logarithmic scale) for the “Stops” Problem (the “Committees”
problem is another example not highlighted in this chapter). (Taken from Tversky and Kahneman,
“Availability: A Heuristic for Judging Frequency and Probability,” Cognitive Psychology, 1973, 5
207-232. Reprinted by permission.)
as this, with various manipulations, and found that subjects made a roughly 2:1 prediction, that
it is more common for the letter K to be first than third.
Tversky and Kahneman [1973] extended this result and demonstrated that availability affects
judgments in a wide range of settings, including visual tasks. For instance, one of their studies asks
the following:
In the drawing below, there are ten stations (s) along a route between START and FINISH. Consider
a bus that travels, stopping at exactly r stations along this route. What is the number of different
patterns of r stops that the bus can make?
START
s
s
s
s
s
s
s
s
s
s
FINISH
The correct answer to this problem is given by the binomial coefficient
10
r .
While it is unrea-
sonable to expect that a subject can do this calculation without time and decision support, it is
important to note that the number of patterns for two stops is the same as the number of patterns
for eight stops, in the same way that the number of patterns for three stops is the same as the
number of patterns for seven stops, because, for any pattern of stops, there is a complementary
pattern of non-stops. However, for the cases of two or three stops, one may be able to think of
immediate patterns by having many stations to choose from, compared to paths with high numbers
of stops. The results from this “Stops” task are given in Figure 5.2. As one can see, the predicted
number of patterns decreases as r increases, which deviates significantly from the correct solution.
10
A valid question regarding availability pertains to what types of recalled instances carry excessive weight when making a judgment. In other words, do decision makers apply more weight
to negative or positive instances? Recently, in an investment banking context, Franklin Templeton asked individuals how they believed the S&P 500 Index performed in 2009, 2010, and 2011
[Franklin Templeton Investments, 2012, accessed January 6, 2016]. A majority of respondents felt
as though the market was either flat or down in 2009, and roughly half said the same about 2010
and 2011. But in reality, the S&P 500 saw double digit gains in 2009 and 2010, and a modest gain
in 2011. This is consistent with other results in that more painful, negative events, that can be
recalled, often have a larger influence than positive events, when making judgments.
It is important to note that while representativeness (Section 5.2.2) and availability heuristics
involve similar mental processes (pulling a memory and then using it to make a judgment), they are
fundamentally different. In short, representativeness involves a mental procedure where the decision
maker considers characteristics of the average or the “stereotypical” example, and then makes a
decision, whereas availability involves a decision maker drawing from specific instances, and then
making a decision based on those specific examples.
Coming back to availability, in operations management contexts, judgments often include more
than just visual cues and wordplay. However, availability has also been shown to influence both
extrapolation and quantitative decisions. For example, if you were asked to estimate the product
8×7×6×5×4×3×2×1, in five seconds, and then estimate the product 1×2×3×4×5×6×7×8, also in
five seconds, you may find that you generate a larger estimate for the former than the latter. If you
are like me, this stems from the fact that you made your calculations based on what was available
during the short timeframe, the first few calculations, and then attempted to extrapolate. This
example is also from Tversky and Kahneman [1973], where the median estimate for the descending
sequence was 2,250, and the median estimate for the ascending sequence was 512.5 I highlight this
example because it captures the essence of many operational decisions by managers: decisions that
must be made quickly, are quantitative in nature, and require some level of extrapolation for what
will happen in the future. Behavioral operations management should be sure to leverage this body
of work on availability when evaluating decisions.
5
Note that there is some anchoring and insufficient adjustment as well taking place in this problem
[Tversky and Kahneman, 1974].
11
5.2.4. Base Rate Neglect and Bayesian Updating
When making judgments about risk, one frequent error of decision makers relates to the use of base
rates. In particular, when attempting to calculate a posterior probability through Bayes’ theorem,
base rates are sometimes neglected.6 Consider the following question, which was presented to 60
associates of Harvard Medical School by Casscells et al. [1978]:
If a test to detect a disease whose prevalence is 1/1,000 has a false positive rate of 5 per cent, what
is the chance that a person found to have a positive result actually has the disease, assuming that
you know nothing about the person’s symptoms or signs?
The average answer from the Harvard Medical School participants was 56%, with nearly half of
the subjects answering 95%. However, the correct answer is less than 2%. Let’s walk through the
details. Our objective is to find the probability that a patient is sick (i.e. has the disease), given
that the test indicated that the patient is sick, P (sick|A), where A represents when the test is
positive. Bayes’ theorem is:
P (sick|A) =
P (A|sick)P (sick)
P (A)
(5.1)
And from the problem we know that:
P (sick) = 0.001
P (healthy) = 0.999
P (A|sick) = 1
P (A|healthy) = 0.05
1/1000 is sick,
999/1000 is healthy,
The test is always positive if someone is sick,
The test is positive, 5%, if someone is healthy.
But we still need P (A), which we can calculate as follows:
P (A) = P (A|sick)P (sick) + P (A|healthy)P (healthy) = 0.05095
Plugging in to Bayes theorem in Equation (5.1), we arrive at P (sick|A) = 0.01963, just under 2%.
The error that people make in evaluating this problem, is by focusing too heavily on the specific
information pertaining to the false positive rate, 5%, and ignoring the general base-rate probabili6
Note that probability matching is also related to a base rate bias, where an individual makes a series of choices that
coincide with the base rate probabilities. However, some studies suggest that probability matching largely disappears
in the presence of financial incentives [e.g. Shanks et al., 2002].
12
ties. This is often referred to as the “base rate fallacy” or “base rate neglect,” and is what leads to
so many respondents claiming that the probability that a patient with a positive test actually has
the disease is 95%. Instead, the correct answer requires one to consider the base-rate information,
that is, only 1 out of 1000 patients actually has the disease where the test is always correct (1 true
positive test result), and for the remaining 999 healthy patients, the test is incorrect 5% of the time
(roughly 50 false positive test results). Hence, roughly 2%.
Operations managers frequently face choices that involve various base rate probabilities, and
often require calculations that involve conditioning on events for accurate decisions. Recognizing
base rate neglect, and its effect on Bayesian updating, is therefore of particular importance to
operations management. In addition to managers, consumers may also be susceptible to these same
biases, which can be valuable information for firms. For instance, in a paper with Vishal Gaur and
Dayoung Kim, we study a service operations setting where consumers must choose between visiting
two firms with unknown service quality, and must learn over time as to which has a higher quality
(i.e. a higher probability of a satisfactory outcome). Sure enough, we find evidence that human
subjects, acting as consumers, do not make decisions that coincide with perfect Bayesian updating.
As a result, we develop a model that can better forecast consumer decisions in this setting, thus
allowing firms to make better operational planning decisions [Davis et al., 2016].
5.2.5. Probability Weighting
When making a decision, past research suggests that decision weights of outcomes are used by
individuals, rather than the probabilities themselves. This is best seen with an example. Would
you prefer a 0.1% chance at $5,000 or $5 with certainty? [Kahneman and Tversky, 1979] found
that 72% of respondents favored the risky alternative, 0.1% chance at $5,000, suggesting that an
individual applies a weight to the 0.1% that makes it higher than its actual probability. Another
example from [Kahneman and Tversky, 1979], which humors me, is the following:
Suppose you are compelled to play Russian roulette, but are given the opportunity to purchase the
removal of one bullet from the loaded gun. Would you pay as much to reduce the number of bullets
from four to three as you would to reduce the number of bullets from one to zero?
As you might expect, people would pay far more to reduce the number of bullets from one to
zero. In this example, reducing the probability from 4/6 to 3/6 feels smaller than the reduction
from 1/6 to 0, suggesting that decision makers do not treat probabilities in a linear fashion.
13
Figure 5.3: Probability Weighting Function Example with β = 0.65 using the Form w(p) = pβ /(pβ +
(1 − p)β )1/β .
1.0
prob
0.9 0
0.000
0.01
0.010
0.8
0.02
0.020
0.70.03
0.030
0.04
0.040
0.6
0.05
0.050
0.50.06
0.060
0.070
0.40.07
0.08
0.080
0.30.09
0.090
0.100
0.2 0.1
0.11
0.110
0.1
0.12
0.120
0.00.13
0.130
0
0.1 0.140
0.2
0.14
0.15
0.150
0.16
0.160
Probability Weighting Function, w(p)
beta = 0.65 beta = 0.7 beta = 0.8 beta = 1
0.000
0.000
0.000
0.000
0.047
0.038
0.025
0.010
0.071
0.060
0.042
0.020
0.091
0.079
0.058
0.030
0.107
0.095
0.072
0.040
0.122
0.109
0.086
0.050
0.135
0.122
0.098
0.060
0.147
0.135
0.110
0.070
0.158
0.146
0.122
0.080
0.169
0.157
0.133
0.090
0.179
0.168
0.144
0.100
0.188
0.178
0.155
0.110
0.197
0.188
0.165
0.120
0.206
0.197
0.176
0.130
0.3 0.215
0.4 0.5 0.206
0.6 0.7 0.185
0.8 0.9 0.140
1
Probability,
p
0.223
0.215
0.195
0.150
0.231
0.224
0.205
0.160
0.170
0.180
To account for these types of results, research suggests that decision0.190
makers utilize “probability
0.200
weighting” functions, which allow probabilities to be weighted in non-linear
ways.7 . With regards
0.210
0.220
to the nature of this non-linearity, most studies indicate that a probability
weighting function
0.230
0.240
should coincide with the empirical regularity of decision makers overweighting
low probability
0.250
events (such as in the 0.1% chance of $5,000 above), and underweighting
0.260 high probability events.
0.270
As a consequence, a number of probability weighting functions have 0.280
been developed that satisfy
0.290
this requirement. More specifically, that the function should represent0.300
an inverse S-shape, which
0.310
is concave below and convex above some probability, say p ≈ 0.40 Wu
and Gonzalez [1996]. An
0.320
0.330
β )1/β , with β = 0.65, from
example of this is depicted in Figure 5.3, using w(p) = pβ /(pβ + (1 − p)
0.340
0.350
[Tversky and Kahneman, 1992].8
0.360
0.370 include [Camerer and Ho,
Some excellent studies which have further analyzed probability weighting
0.380
1994], [Wu and Gonzalez, 1996] and [Prelec, 1998]. Many of these works demonstrate that the degree of bias in a probability weighting function can be manipulated through the setting and size
of certain parameters. For instance, [Camerer and Ho, 1994] fit the probability weighting function
outlined above to data from eight different studies. They find that the value of β is significantly
different from 1 in seven of the eight studies. However, the value of β varies considerably, from
0.28 to 1.87, with a weighted average of 0.56. In fact, when β = 1.87 > 1 there is no longer an
7
Probability weighting is a key component of prospect theory, which is detailed in Section 5.3.2.
Technically, there are a variety of shapes the function can take, but most traditionally the inverse-S shape is
consistent with probability weighting biases.
8
14
inverse S-shape, rather, a regular S-shaped probability weighting function where low probabilities
are underweighted and high probabilities are overweighted (although, it is worth noting that in
Camerer and Ho’s [1994] work β > 1 in only one data set). In short, one should take caution when
assuming a specific degree of probability weighting bias, as it can vary across different contexts and
settings, and even deviate from the traditional inverse S-shape at times.
Relating to operations management settings, probability weighting may influence a variety of
decisions. For instance, in a procurement context, in a recent paper with Elena Katok and Anthony
Kwasnica, we found that by applying a probability weighting function, one can partially explain
how auctioneers set reserve prices in an independent private values context [Davis et al., 2011]. In
addition, one of the beneficial aspects of probability weighting is that most functional forms have
the flexibility to capture a variety of data. Whether used by itself, such as in my work with Elena
Katok and Anthony Kwasnica, or simply as a part of a broader model, such as prospect theory,
probability weighting can be extremely useful for modeling operational decision making.
5.2.6. Overconfidence
Numerous studies have shown that a decision maker’s confidence in his or her judgments, for
moderate or difficult tasks, is greater than the actual accuracy of those judgments. For instance,
when faced with a 10 question general knowledge quiz, an individual may state that they believe
they answered all 10 problems correctly, yet in reality, they answered only eight or less correctly.
This “overconfidence” bias, which has been cited in a number of tasks, has been offered as an
explanation for more significant events as well, including legal disputes, such as labor strikes, and
even wars [Thompson and Loewenstein, 1992, Johnson, 2004].
Most exercises to evaluate degrees of overconfidence take one of two types. Individuals are asked
to either (a) answer a question, and then state how confident they are in their answer, or (b) answer
a question that requires them to estimate a confidence interval, say 90%, around their answer. For
an example of the former, in a well-known paper on overconfidence, Fischhoff et al. [1977] pose
the following research question: “How often are people wrong when they are certain that they
know the answer to a question?” To address this, they present subjects with a number of general
knowledge questions such as “absinthe is [a] a liqueur or [b] a precious stone” and then ask subjects
to indicate the degree of certainty that their answer was correct (between 50% and 100%, often
called “half-range” answers). For these types of overconfidence studies, when attempting to examine
the degree of overconfidence, researchers focus on the calibration of answers, which compares the
15
Figure 5.4: Calibration Curves from Four Half-range, General Knowledge Tasks. (Taken from Lichtenstein, Fischhoff, and Phillips, “Calibration of Probabilities: The State of the Art to 1980,”
Judgment Under Uncertainty: Heuristics and Biases, 1982, 306-334, Cambridge University Press.
Reprinted by permission.)
subjects’ beliefs about their answers to the actual proportion correct. Figure 5.4 plots a number
of calibration curves in four different half-range studies on overestimating one’s own performance.
Note that the curves almost all lie below the 45 degree line, which implies that there is considerable
overconfidence with respect to one’s own abilities.
For the second type of overconfidence task, where individuals must state a confidence interval
around their answer to basic questions, such as “How long is the Nile River?” a number of studies
have demonstrated that the confidence intervals, usually 90%, contain the correct answers less than
60% or 70% of the time [e.g. Soll and Klayman, 2004].
Overconfidence is a relatively well established bias. Recently, however, there has been a surge on
the topic. In their paper “The Trouble with Overconfidence,” Moore and Healy [2008] argue that
there are generally three types of overconfidence: overestimation of one’s own ability, overestimation
with respect to others’ abilities, and overprecision. They go on to claim that some seminal papers
on overconfidence cannot necessarily tease out these types of overconfidence from one another. Take
the example from Fischhoff et al. [1977], where they ask individuals to answer a question and state
their confidence in their answer (50% to 100%). In this experiment, Moore and Healy posit that
overestimation and overprecision are one in the same, and cannot be separated. They go on to
propose alternatives that can address this, as well as provide a simple theoretical model. I refer the
interested reader to their work for further details.
16
Note that when I first introduced overconfidence, I mentioned that it is present in moderate
and difficult tasks. This is because there are a number of studies demonstrating that, for some
simple tasks, overconfidence is not present, to the point that even a reversal may take place. For
example, take the planning fallacy, which states that when forecasting the end date of a project,
decision makers typically state too short of a time horizon, and end up taking more time than
they originally planned (coinciding with overconfidence). Some studies show that for short-term
projects (or the task is easy), people actually overestimate completion times, and thus exhibit
underconfidence [Burt and Kemp, 1994].
The fact that overconfidence tends to increase in the difficulty of the task is especially useful
for operations management settings, where tasks are not simple general knowledge quizzes, and
may require multiple judgments, oftentimes in stochastic environments. Despite this, little work
has been done on overconfidence in operations management settings. Instead, most people associate
overconfidence with studies in general management, such as measuring the amount of overconfidence
executives exhibit when forecasting their firms’ future earnings [Ben-David et al., 2013]. However,
overconfidence is beginning to gain traction in the behavioral operations management literature.
For example, Ren and Croson [2013] recently applied overprecision to the newsvendor problem,
and found that overprecision correlates positively with biased order decisions. In sum, there is still
much work that can be done on overconfidence in operations management.
5.2.7. Ambiguity Aversion
Consider the following experiment, proposed by Ellsberg [1961]:
There is an urn with 30 red balls and 60 other balls that are either black or yellow. Choose among
the following two options:
A: $100 if you draw a red ball
B: $100 if you draw a black ball.
You must also choose between these two options:
A’: $100 if you draw a red or yellow ball
B’: $100 if you draw a black or yellow ball.
If you are like me, you may choose A in the first exercise, and B’ in the second. Taking a
step back, let’s introduce some notation and look at this result more closely. Let the estimated
probabilities of each color ball (red, black, and yellow), be given by r, b, y, and assume utility
17
function, u(·), is increasing in payoffs. Suppose that one strictly prefers A to B, implying that:
r × u($100) + (1 − r) × u($0) > b × u($100) + (1 − b) × u($0)
r(u($100) − u($0)) > b(u($100) − u($0))
r > b.
Yet, if one also strictly prefers B’ to A’, then, we have a contradiction:
b × u($100) + y × u($100) + r × u($0) > r × u($100) + y × u($100) + b × u($0)
b(u($100) − u($0)) > r(u($100) − u($0))
b > r.
One key explanation for this result relates to “ambiguity aversion” (or Knightian uncertainty).
This idea is that decision makers prefer to avoid options where exact probabilities are unknown or
ambiguous, almost as if they assign their own probabilities which are unfavorable. Indeed, in the
example above, if someone prefers A and B’, it’s almost as if they are applying a lesser weight to
the unknown probabilities (the probability of a black ball in the first exercise is unknown, as is the
probability of a red or yellow ball in the second), or, analogously, a heavier weight to the known
probabilities (the probability of a red ball in the first exercise is 1/3 and the probability of a black
or yellow ball in the second is 2/3). I often like to describe ambiguity aversion through the classic
expression “the devil you know is better than the devil you don’t.”
There is no single accepted explanation for what drives ambiguity aversion. However, there have
been a number of empirical tests that shed light about when ambiguity aversion may exist or be
more pronounced. For instance, even when decision makers are provided with written arguments
as to why their choices are that of a contradiction or paradox, or when the decision makers admit
that they do not believe the urn could be biased, ambiguity aversion persists [Slovic and Tversky,
1974, Curley et al., 1986]. It has also been well established that people pay a considerable premium
to avoid ambiguity Curley and Yates [1989]. For more nuanced results pertaining to ambiguity
aversion, and aspects like the range of ambiguous probabilities, please see Curley and Yates [1985].
Interestingly, despite the popularity in experimental economics, such as studying ambiguity
in financial markets [Mukerji and Tallon, 2001], there are few papers that investigate ambiguity
aversion in behavioral operations management (or consider it as an explanation). I find this par18
ticularly surprising because in practice, managers are sometimes faced with problems that include
unknown probabilities. For instance, in new product development, a product may have the potential
to be a “home run” or a complete disappointment. Without knowing the probabilities of these two
outcomes one may choose to avoid introducing the product altogether, and instead opt for a less
profitable alternative. That being said, one study relevant to operations management on ambiguity
aversion is that of Chen et al. [2007]. Specifically, while there is a considerable amount of useful
research on procurement where bid valuations (or distributions) are known, it is unlikely that in
reality, every bidder truly knows the bidding distribution of each of their competitors. Therefore,
Chen et al. conduct a novel experiment in procurement, and study first and second price sealed bid
auctions where the distribution of bid valuations may be potentially unknown. Indeed, they find
that bids are much lower in first price auctions when there is ambiguity. It is studies like these that
behavioral operations can extend to other settings where ambiguity aversion might be present, and
learn important managerial implications and insights.
5.3. Evaluations of Outcomes
In addition to being influenced by behavioral biases when judging risk in operational decisions,
another facet in which managers may be affected is in their evaluation of outcomes. For instance, a
manager may evaluate the first $1 million in revenue from a project quite differently from the tenth
million, suggesting diminishing marginal utility. In fact, speaking of the utility of outcomes, some
behavioral theories have emerged which neglect to consider a utility function altogether, such as
prospect theory, which states that a decision maker uses a value function to evaluate options. This
section will include behavioral results which, broadly speaking, pertain to how decision makers
evaluate outcomes, including risk aversion, prospect theory and framing, anticipated regret and
reference dependence, mental accounting, intertemporal choice, the endowment effect, and the sunk
cost fallacy.
5.3.1. Risk Aversion and Scaling
In decision making under uncertainty, when an individual fails to act in a way that coincides with
the predictions of a risk-neutral expected-utility maximizer, one of the first possible explanations
that behavioral operations researchers turn to is risk aversion. Risk aversion represents a decision
19
maker’s preference for accepting a lower, more certain expected payoff, compared to a higher,
but relatively more uncertain, expected payoff. That is, they prefer more certain outcomes over
uncertain ones.9 While I omit the modeling details revolving around the different types of risk
aversion, such as constant relative risk aversion versus constant absolute risk aversion, risk aversion
states that a decision maker’s utility function is increasing and concave.
The literature on risk aversion in individual decision making is quite rich, with evidence of it
in a variety of settings (e.g. finance, operations, healthcare, etc). Of this literature, one result that
I would like highlight relates to small-scale and large-scale tasks. In order to describe this, let me
take a step back and comment on why behavioral researchers often investigate risk aversion as a
potential explanation for any observed decisions. In particular, while risk aversion is commonplace
in many decision making contexts, it is also relatively straightforward to elicit subjects’ levels of risk
aversion in the laboratory. For instance, after a primary experimental session takes place, subjects
can then complete a separate, final stage task, where they choose among a series of lotteries, and
one is randomly selected for payment. While more details on risk elicitation can be found in Chapter
1, I depict an example of such an exercise in Table 5.1.
Table 5.1:
Sample Lottery Choice Risk
Aversion Elicitation Task (50-50 Chance Between
$5.50 and $4.50 for Option A, and 50-50 Chance
Between $X and $1.00 for Option B).
Lottery
1
2
3
4
5
6
7
8
9
10
Option A
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
$5.50
$4.50
Option B
$9.00
$1.00
$9.50
$1.00
$10.00
$1.00
$10.50
$1.00
$11.00
$1.00
$12.00
$1.00
$13.00
$1.00
$14.50
$1.00
$17.00
$1.00
$20.00
$1.00
Ideally, referring to Table 5.1, a decision maker will start with preferring Option A for Lottery 1,
9
While risk aversion is a relatively straightforward concept, its distinction from ambiguity aversion (Section 5.2.7)
is rather subtle. Specifically, risk aversion assumes that a probability is known for each potential outcome, and a risk
averse decision maker may prefer to pay a premium (accept a lower expected value alternative) to avoid potential
risk, whereas ambiguity aversion implies that certain probabilities for an alternative are unknown, and an ambiguity
averse decision maker pays a premium (or incurs a cost) to avoid the alternative with unknown probabilities, as if
the probabilities are unfavorable to them. Studies have shown that risk preferences are independent of ambiguity
preferences (e.g. Cohen et al. [1985]).
20
and at some point, when moving down to subsequent lotteries, switch to Option B. These decisions,
in conjunction with a specific functional form of risk aversion, can then be used to estimate the
level of risk aversion of the decision maker. However, one must take care when extrapolating these
estimates, from a small-scale task, to large-scale situations. In particular, Rabin [2000] wrote an
excellent note that provides a theorem illustrating that even the most minor level of risk aversion
in small-scale stakes implies unrealistic decisions in large-scale tasks. He presents a number of
examples of the form “If an expected-utility maximizer always turns down modest-stakes gamble X,
she will always turn down large-stakes gamble Y.” To provide a more concrete example, he shows
that for any level of wealth, if a decision maker turns down a 50-50 chance of losing $100 or gaining
$110, then he/she will turn down a 50-50 gamble of losing $1,000 and gaining an infinite amount
of money. A summary of some of Rabin’s initial results are shown in Table 5.2. As one can see, the
results implied for moderate levels of risk aversion, in small-scale tasks, do not translate well for
larger stakes.
Table 5.2:
Recreation of Table 1 from
Rabin (2000). If Averse to 50-50 Lose
$100 and Gain g, Will Turn Down 50-50
Lose L and Gain G, G’s Entered in
Table.
g
L
$400
$600
$800
$1,000
$2,000
$4,000
$6,000
$8,000
$10,000
$20,000
$101
400
600
800
1,010
2,320
5,750
11,810
34,940
∞
∞
$105
420
730
1,050
1,570
∞
∞
∞
∞
∞
∞
$110
550
990
2,090
∞
∞
∞
∞
∞
∞
∞
$125
1,250
∞
∞
∞
∞
∞
∞
∞
∞
∞
As one might expect, Rabin’s work generated a number of reactions. For instance, in response
to his note, Holt and Laury [2002] conducted a study that administered a series of lottery choice
exercises, with different payment scales. Compared to the values used in Table 5.1, where average
earnings are less than $10, the exercises in the work of Holt and Laury led to average earnings
between $26 and $226, depending on the treatment, with a maximum of $391.65! Sure enough, for
those treatments where the potential earnings were higher (90 times that of the baseline treatments),
they observed higher levels of risk aversion. They proceeded by fitting their data to different risk
21
aversion models, but ultimately, in order to fit all of the data well, they had to incorporate bounded
rationality and random errors (which assumes that decision makers may err when trying to choose
the option that maximizes expected utility, reviewed in Section 5.4.2). Once doing this, however,
the fit was quite favorable.
So where does this leave us as behavioral operations researchers who are interested in risk aversion? First, it is well known that decision makers are prone to bounded rationality and random
errors in a variety of operations management settings (see Section 5.4). And as Holt and Laury
[2002] illustrated, once one combines random decision errors with risk aversion, levels of risk aversion in small-scale tasks translate reasonably well to large-scale tasks. Second, absent bounded
rationality, instead of using lottery exercises to predict exact levels of risk aversion, they can be
used to identify correlations between general risk preferences and decisions. For instance, did a
subject who frequently selected the safer choice in the lottery exercise (i.e. Option A in Table 5.1)
make operational decisions in a particular way, such as setting a lower reserve price for a product,
or proposing a weaker initial offer in a structured bargaining environment? In short, this approach
helps recognize whether more or less risk averse managers will behave in a certain way in various
operational decisions. Lastly, Rabin [2000] does point out that there are some theoretical models
that can account for risk aversion over modest stakes, such as loss aversion, which is used frequently
in operations management, and is detailed in the following section on prospect theory.
5.3.2. Prospect Theory
In the Introduction of this chapter I claimed that expected utility theory is used extensively in
studying individual decision making in behavioral operations management settings, especially when
it comes to developing normative benchmarks to test in the lab. However, I then proceeded to
highlight some of the controversies and criticisms of expected utility theory. While there is no
doubt that expected utility theory is still useful in behavioral operations, some of the criticism,
evidenced by exercises such as the Allais and Ellsberg paradoxes, opened the door for alternative
ways to model individual decision making. One alternative model which has garnered considerable
attention, and rose from much of the empirical evidence that questioned expected utility theory, is
“prospect theory,” introduced by Kahneman and Tversky in 1979.
There are multiple components of prospect theory, but the main intuition is that decision
makers set a reference point, and then evaluate the value of the outcomes based on gains or losses,
rather than considering absolute wealth. That being said, the main tenets that comprise the theory
22
are: (1) decisions makers are risk averse when dealing with potential gains, and risk seeking when
dealing with potential loses, (2) losses are more painful than gains feel good, also referred to as
“loss aversion,” and (3) decision makers tend to overweight low probability events, and slightly
underweight high probability events, also called “probability weighting.” Given space constraints,
I will briefly summarize each of these three factors below, and refer the interested reader to their
original paper, Kahneman and Tversky [1979], along with their paper on “cumulative” prospect
theory, Tversky and Kahneman [1992], for additional details.
For the first main aspect of prospect theory, consider the following example from Kahneman and Tversky
[1979], which is based on Allais’ work [1953]. Would you rather play a gamble where there is a 80%
chance of earning $4,000, or receive $3,000 with certainty? Now consider the following choice:
Would you rather play a gamble where there is a 80% chance of losing $4,000, or pay $3,000 with
certainty? In the former exercise, a vast majority of respondents, 80%, chose the $3,000 with certainty option, despite it having a lower expected value, indicating general risk aversion by decision
makers when facing choices over gains. But for the latter problem, only 8% of respondents chose the
$3,000 loss with certainty, suggesting risk seeking behavior when facing losses. These results, which
are further supported through additional experiments by Kahneman and Tversky [1979] and other
studies, are evidence of what they dub the reflection effect, in that preferences reverse depending
on whether outcomes are in the domain of gains or losses.
The second tenet of prospect theory, which has been demonstrated in various works, is that
losses are more painful to a decision maker, than gains feel beneficial. For instance, suppose that
your boss is going to give you a pay raise of $100 a week starting next year. Chances are that
you will be pleased with this increase. However, now consider the opposite, in that your salary
will be cut by $100 a week starting next year. In this latter scenario, you are most likely more
than disappointed. This idea, that losses hurt more than gains feel good, is often referred to as loss
aversion. A combination of loss aversion, and the results about risk averse preferences in gains and
risk seeking preferences in losses, leads to the general shape of the value function, which is assumed
for prospect theory, and shown in Figure 5.5.
The third aspect of prospect theory is that of probability weighting. While covered in detail in
Section 5.2.5, in short, probability weighting states that an individual does not use given probabilities when making choices, rather, they apply their own weighting function to these probabilities,
and then subsequently make their decision. For example, Would you prefer a 0.1% chance at $5,000
or $5 with certainty? Kahneman and Tversky [1979] found that 72% of respondents favored the
risky alternative, 0.1% chance at $5,000, suggesting that an individual applies a weight to the 0.1%
23
Figure 5.5: Value Function of Prospect Theory.
Losses
Gains
that makes it higher than its actual probability. More specifically, probability weighting typically
assumes that decision makers tend to overweight the likelihood of a low probability event, and
underweight the likelihood of a high probability event, generating an inverse S-shaped function (see
Figure 5.3 for an example).
Prospect theory has become one of the main models for explaining individual decisions in
operations management settings, even considering its individual facets in isolation. For example,
Ockenfels and Selten [2014] include loss aversion in their “impulse-balance equilibrium” model to
explain asymmetry in the pull-to-center behavior in the newsvendor problem (see Chapter 11 for
details). Also in the newsvendor setting, Long and Nasiry [2015] show that prospect theory can
explain decisions when allowing for reference points that are not necessarily a payoff of zero. In a
procurement context, in a recent paper with Elena Katok and Tony Kwasnica, as mentioned previously, we found that the probability weighting function alone can partially explain how auctioneers
set reserve prices in an independent private values setting [Davis et al., 2011]. Furthermore, loss
aversion and reference dependence, which relate to prospect theory in that an individual makes a
decision about the value gained or lost from a reference point, can account for a variety of decision
in supply chain contracting settings [e.g. Ho and Zhang 2008, Davis et al. 2014, Davis 2015]. In
short, prospect theory has been able to capture a wide range of decisions thus far in operations
management settings. One can only assume that as the field begins to explore new topics, it will
continue to play a significant role in describing, and to some extent, predicting, behavior.
24
5.3.2.1. Framing
Stemming from prospect theory’s claim that preferences can reverse when considering gains versus
losses, often called the reflection effect, a similar result can exist even when a choice is simply
framed according to these domains. Consider the following example from Tversky and Kahneman
[1981], where people had to choose from two options:
Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected
to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that
the exact scientific estimate of the consequences of the programs is as follows:
Program A: 200 people will be saved.
Program B: There is a 1/3 probability that 600 people will be saved, and 2/3 probability
that no people will be saved.
A majority, 72% chose Program A. In a second group of respondents, Tversky and Kahneman
presented the same scenario, but with the following options:
Program C: 400 people will die.
Program D: There is a 1/3 probability that nobody will die and 2/3 probability that 600
people will die.
In this follow-up exercise, 78% of respondents chose Program D. Note that in this example,
programs A and C are identical, as are programs B and D. Yet there is a preference reversal. This
example is particulary interesting because it simply phrases the options in such a way as to mimic
gains and losses, even though they are identical. In short, the first experiment is written in a way to
have a positive frame, focusing on those saved, and prospect theory prescribes that decision makers
act risk averse in the domain of gains, hence Program A is chosen more often. Whereas the second
experiment is framed in a negative way, discussing potential deaths, and, because people act like
risk seekers in the domain of losses, a majority tend to choose the riskier choice, Program D. Hence,
simply switching the frame of a decision can lead to preference reversals.
Framing, although a relatively simple concept, can have profound implications. For instance,
consider the possibility that an executive, when choosing from a list of high-level initiatives or
actions, may prefer one over another, simply because of frame in which the actions are presented.
However, while an idea such as this is exciting, it is important to note that preference reversals from
framing appear to be sensitive to the setting and context. For instance, Schultz et al. [2007] evaluate
framing in an inventory setting and find little evidence of its effect. In short, further research on
framing in operations management contexts is required before we can make broader claims.
25
5.3.3. Anticipated Regret
Often times, decision makers are influenced by outcomes that “might have been,” or experience
regret. More formally, Marcel Zeelenberg [1999] describes regret as “a negative, cognitively based
emotion that we experience when realizing or imagining that our present situation would have been
better, had we decided differently.” In everyday decision making, regret may be experienced from
buying a gallon of milk at one store, only to find out that it is cheaper at another. Aside from this,
in a business setting, one can imagine that a variety of operational decisions made under risk and
uncertainty, may evoke this type of feeling. “Anticipated regret” theory, or regret aversion, takes
this idea a step further and assumes that a decision maker anticipates the potential regret, and
takes this into account when choosing a particular course of action.
Anticipated regret was formalized simultaneously by Bell [1982] and Loomes and Sugden [1982].
I refer the reader to both of these papers for more detail, but to summarize, the idea behind
anticipated regret is to follow expected utility theory, but assume that there is an additional term
that is subtracted from a decision maker’s original expected utility function. This additional term
is non-negative, represents the amount of regret a decision maker may experience, and increases
relative to a salient reference point. This reference point often represents an ideal outcome where
there is no regret experienced.
In the psychology literature, there is considerable evidence of regret in decision making under
uncertainty, usually in everyday decisions, or simple gambles or lotteries. Some of the main results
from this work demonstrate that regret aversion exists in both gain and loss domains, under high
and low risk decisions [Zeelenberg et al., 1996], and that it increases when there is an abundance
of options available [Schwartz, 2004]. Regret has also been an explanation for the “disposition
effect” in finance, which states that investors tend to sell stocks whose prices have increased, while
keeping assets that have dropped in value [Fogel and Berry, 2006]. Regarding this explanation for
the disposition effect, note that regret is most salient when the reference point is known ex post.
For instance, if an investor sells a stock at a loss, one can feel more regret by comparing the selling
price to the original purchase price, whereas selling a stock for a gain, it is unlikely that the investor
will continue to see if the stock increases in value in perpetuity, thus minimizing regret.
In addition to incorporating a regret term into an expected utility function, some researchers
argue that decision makers follow a “minimax regret” principle. That is, a decision maker calculates
the maximum potential regret for each option, and then chooses an action that minimizes the
potential regret. Importantly, notice that when one follows this heuristic, they need not know the
26
probabilities of each outcome occurring. However, when probabilities are known, then a decision
maker should certainly incorporate this knowledge into their choice. For instance, if one follows a
minimax regret rule, they may avoid an option that has a large regret penalty, but has a very low
likelihood of occurring.
A natural application of anticipated regret in operations management is auctions. In this setting,
for example, Engelbrecht-Wiggans [1989] assumes that a bidder cares not only about her own profit,
but also potential regret that stems from her bidding behavior. When she wins the auction, she
might experience winner’s regret by overbidding and leaving money on the table, and when she
loses the auction, she might experience loser’s regret if she knows she underbid and still could
have won the object at a price below her value (assuming the winning bid is announced to all
participants). In this case, the amount of regret is relative to the winning bid for the object. In a
subsequent experimental study, Engelbrecht-Wiggans and Katok [2008] test the anticipated regret
theory in auction experiments, and find considerable evidence that it affects bidding behavior.
Additional procurement studies that have used regret aversion as a driver of decisions include
Greenleaf [2004], Filiz-Ozbay and Ozbay [2007], and Davis et al. [2011].
5.3.3.1. Reference Dependence
Closely related to anticipated regret are “reference dependence” models. Consider Ho et al. [2010],
who find that a reference dependence model can explain newsvendor decisions. They show that
a newsvendor’s expected utility function, under reference dependence, is comprised of the regular
expected profit function, plus two disutility terms: one term associated with the psychological cost
of having leftover units or overages, and a second term associated with the psychological cost of
stockouts or underages. Ho et al. [2010] argue that decision makers use observed demand as the
reference point, as it is one of the most salient pieces of information provided to newsvendors after
setting a stocking quantity. In this example, one can immediately see the parallels to anticipated
regret: when there are overages, this is analogous to winner’s regret, and when there are stockouts,
this is analogous to loser’s regret. I take a similar approach to this when evaluating supply chain
contracts in a pull context, and find that it coincides with behavior quite well [Davis, 2015]. For
those interested in more details on reference dependence, please see Kőszegi and Rabin [2006], who
consider a formulation where the reference point is endogenous, and references therein.
27
5.3.4. Mental Accounting
Another concept related to evaluating outcomes and decisions is that of “mental accounting.” For
instance, an individual may manage a separate budget for groceries and a separate budget for
eating at restaurants, even though both come from the same source of income. Or others may
consider their paycheck as used for common expenses, and any tax refund for personal purchases or
vacations. In a slightly different vein, an individual may neglect to make an investment decision if
they only consider the short term gains/losses, rather than the long term outcomes. These examples
all fall under the umbrella of mental accounting.
In a summary article, Thaler [1999] claims that there are three general components to mental
accounting. The first component relates to the examples of categorizing activities and outcomes into
certain accounts. For instance, expenditures might be grouped into different categories, or different
types of spending could be restricted through self-imposed budgets. One example of research in
this area focuses on consumer purchases when using cash versus credit cards. Both use a decision
maker’s income as a source, yet, many studies show that people spend more when using credit
cards. An even more extreme example of this is from Morewedge et al. [2007], who showed that
when people buying lunch were simply primed to think about money in their bank accounts, versus
the amount of cash in their wallets, they spent 36% more money on their meals.
The second component of mental accounting that Thaler highlights deals with the frequency
as to when mental accounts are evaluated, which was identified by Read et al. [1999] as “choice
bracketing.” They claim that if people are frequently evaluating accounts and outcomes, then the
bracketing is narrow, and if people evaluate an account over a larger timeframe, the bracketing is
broad. For example, in a famous paper, Paul Samuelson asked a colleague if he would accept a
50-50 chance between winning $200 or losing $100 [1963]. The colleague said that he would only
accept if there were 100 repeated gambles of this type. In other words, the colleague was loss
averse, but at the same time, revealed something interesting about choice bracketing. To elaborate,
suppose that the loss aversion estimate for Samuelson’s colleague is greater than 2, perhaps 2.5,
such that a single play of the gamble yields negative expected utility and is thus unattractive (i.e.
E(u) = 0.5 × $200 − 0.5 × 2.5 × $100 < 0). If each play of the gamble is treated as a separate
event, then two plays are twice as bad as one play, but if the two gambles are combined into a
single account, then the two gambles provide positive expected utility (i.e. E(u) = 0.25 × $400 +
0.5 × $100 − 0.25 × 2.5 × $200 > 0). Therefore, if the colleague can avoid treating (and watching)
each gamble separately, and consider a broad choice bracket that allows him to wait until multiple
28
gambles are played, then he will receive a positive expected utility for any number of trials greater
than one (certainly 100).
The third primary component of mental accounting considers how outcomes are perceived and
how a decision maker chooses among alternatives. An abbreviated example from Thaler [1999] is
the following:
A friend of mine is shopping for a bedspread. She is pleased to find the model she liked on sale. The
spreads come in three sizes: double, queen, and king, with prices $200, $250, and $300. However,
during a sale, all were priced at $150. My friend bought the king-size quilt, and was quite pleased,
even though the quilt was too large for her double bed.
In this example, the decision maker’s choice is influenced by the value of the sales prices. That
is, the outcome of choosing the (too large) a bedspread appears more favorable since the discount
for it is greater than the other alternative sizes. As one can see, in this way, mental accounting
is similar in spirit to prospect theory (Section 5.3.2) in that a reference point affects the decision
making process. I refer the interested reader to Thaler’s [1999] article for additional information.
Mental accounting is relatively common in the behavioral operations management literature.
In a newsvendor setting, Chen et al. [2013] find that the manner in which a newsvendor finances
their inventory can affect ordering quantities. They posit that a newsvendor may mentally segregate payments into two time buckets, before and after, the demand realization. For instance, they
consider three settings that manipulate the timing of payments: one where the newsvendor pays for
the inventory upfront, a second where the payment is delayed until after demand is realized, and a
third where the newsvendor actually receives advanced revenue and must refund any revenue from
leftover units after demand is realized. They show that ordering behavior differs across all three
scenarios.
In addition to newsvendor studies, experimental supply chain contracting studies have also
developed behavioral models that incorporate mental accounting. For instance, in Becker-Peth et al.
[2013], they develop a behavioral model for buyback contracts which assumes that the two sources
of income, income from sales to customers and income from returns to suppliers, may be accounted
for in different ways by decision makers. In Davis [2015], I find that in a service-level agreement
contract, a retailer may overweigh the cost of awarding a supplier a bonus, relative to its true
cost, also consistent with mental accounting. In summary, given the overwhelming evidence that
consumers and managers think about expenses, incomes, and revenues in different ways, mental
accounting is sure to play a role in a variety of operations management contexts.
29
5.3.5. Intertemporal Choice
Operations managers are constantly faced with decisions that involve future outcomes. Fortunately,
there have been a few approaches to understanding choices over time, or “intertemporal choice.”
Originally, Samuelson [1937] was first to touch on discounted utility, which is the idea that the
utility of some future outcome, when being evaluated presently, must be discounted according to
some factor. Importantly, this discount factor was assumed to decrease by a constant rate per unit
delay, or be time-consistent. In other words, the discount factor depends strictly on how far apart
the two points in time are from one another.
After discounted utility was first introduced, and, despite Samuelson’s concerns about its descriptive ability, it was widely accepted as the main intertemporal choice model. One possible reason
for this may be because of its simplicity and the fact that it was similar to that of a continuous
compound interest equation. For instance, one commonly adopted form of a constant discount factor is that of exponential discounting. Under exponential discounting, if dE (T ) is the total factor
that multiplies the value of the payment, T is the total time until receiving the payment, and r is
the degree of discounting, then the factor takes the form dE (T ) = e−rT .
Ironically, in his original work, Samuelson [1937] states that “It is completely arbitrary to
assume that the individual behaves so as to maximize an integral of the form envisaged in the
discounted utility model.” This suggests that Samuelson recognized the limitations of the model
from a descriptive standpoint. Sure enough, a number of empirical studies soon demonstrated that
a decision maker’s valuation of an outcome diminishes quickly for short time periods, and then
slowly for longer time periods, which is time-inconsistent. For example, Thaler [1981] posed the
following scenario (abbreviated) to subjects:
You have won some money in the lottery which is being held by your bank. You can take the money
now, $15, or wait until later. How much money would you require to make waiting [3 months, 1
year, 3 years] just as attractive as getting the $15 now?
The median answers were $30 to wait three months, $60 to wait one year, and $100 to wait
three years, implying annual discount rates of 277%, 139%, and 63%. In particular, $15 = $30 ×
e(−2.77×3/12) = $60 × e(−1.39×1) = $100 × e(−0.63×3) . Clearly, these discount factors do not change
at a constant rate per unit delay, which has also been documented in a number of studies involving
cash payoffs, such as Benzion et al. [1989].
Further issues with exponential discounting stem from preference reversals observed by decision
makers. For example, a typical thought experiment poses the question “Would you rather have $100
30
today, or $110 tomorrow? ” A majority of respondents typically prefer $100 today. However, when
asked “Would you rather have $100 a year from now, or $110 a year and one day from now? ” A
majority of those who preferred the $100 option in the previous question, choose to wait the year
and one day for $110, leading to a preference reversal.
One common approach to capture these types of empirical results is referred to as “hyperbolic
discounting,” and has been shown to fit intertemporal choices better than exponential discounting
in a number of studies [e.g. Kirby, 1997]. Using the same notation for the exponential discounting
approach, the total discount factor under hyperbolic discounting often takes the form dH (T ) =
1/(1 + rT ). Interestingly, in addition to a variety of financial decisions made over time by humans,
hyperbolic discounting has even been used to explain animal behavior, who strongly prefer a smaller
immediate prey than a larger one in the future [Green and Myerson, 1996].
Some other results that have been observed under intertemporal choice are that gains are
discounted more than losses, and that small outcomes are discounted more than large outcomes
[Thaler, 1981]. For instance, in the latter case, Thaler [1981] finds that respondents were indifferent
between $15 now and $60 in a year, $250 now and $350 in a year, and $3000 now and $4000 in a
year, implying that smaller discount rates are applied to larger amounts, holding the time frame
constant.
In the operations management literature, one recent study which incorporates intertemporal
choice, among other behavioral tendencies, is Baucells et al. [2017], who investigate markdown
management for firms when consumers make wait-or-buy decisions. Indeed, due to the fact that
almost all managerial decisions involve outcomes that will not be realized until some time has
passed, there are many opportunities for applying intertemporal results in future behavioral operations management work. For those interested in further details on time discounting models, please
see Frederick et al. [2002], who provide an excellent review of past literature, and Chapter 3, which
provides more modeling details for intertemporal choice, including “quasi-hyperbolic” discounting.
5.3.6. The Endowment Effect
When I was a student, I took a class on “Risk and Decisions.” In one session, the professor, Gary
Bolton, began with a simple exercise: half of the students were randomly selected and given a “very
nice” university themed pencil, and were dubbed the “owners,” while the remaining half of the
students were dubbed as “non-owners” and paired up with the owners randomly. Gary then had
each owner write down the minimum price that they would be willing to accept to sell their pencil,
31
and simultaneously, had each non-owner write down the maximum price they would be willing to
pay for a pencil. Following this, a random price was drawn (which ranged from zero to above any
anticipated maximum price). For a given pair of students, if the random price was higher than
the owner’s minimum selling price, and lower than the non-owner’s maximum paying price, then a
transaction would take place at the random price.
After repeating this exercise with various classes for many years, Gary has observed that owners’
average minimum selling prices frequently exceed non-owners’ average maximum paying prices,
typically by a two-to-one ratio. This result is even more startling when one considers that the item
is somewhat innocuous, a pencil, and that it is only provided to owners minutes before eliciting
their prices. This result, referred to as the “endowment effect,” was dubbed by Richard Thaler in
1980, when he observed that once a product became part of an individual’s endowment, they then
had a tendency to increase their own valuation of the product [Thaler, 1980]. For instance, many
people can relate to this effect when they attempt to trade in their car for a new vehicle. Almost
always, it seems as though the owner values the car more than the true market trade-in value of
the vehicle.
The endowment effect has been observed in a variety of studies. For instance, Kahneman et al.
[1990], conducted a series of experiments with over 700 participants and demonstrated the robustness of the result, which involved different items such as coffee mugs, chocolate bars, pens,
and binoculars. However, it is interesting to note that Kahneman, Knetsch, and Thaler failed to
observe an endowment effect when the item was simply monetary tokens, suggesting that for an
endowment effect to exist, the product should be at least somewhat unique to owners.
While many experiments demonstrate the prevalence of the endowment effect in controlled
settings, there are many examples that extend this effect to practice. For instance, many products
can be used during a trial period, with a money back guarantee. At first, a buyer considers that the
only costs she may incur are the transaction costs of buying/returning the product, and if these
costs are less than the gains from using the product during the trial period, then the buyer purchases
the product. Following the trial period, if the endowment effect is present, then the buyer’s value for
the product increases, and they are more likely to keep the product. Similarly, many retailers now
allow full refund, no questions asked, return policies, and car dealerships, when selling a vehicle,
encourage you to take extended test drives (even overnight at times), before making your final
decision. In all of these cases, firms are using the endowment effect to their advantage.
There have been a number of theoretical explanations for the endowment effect. A frequent
one is that once the item is added to an individual’s endowment, it effectively acts as an updated
32
reference point for the individual, and selling the product will be perceived as a loss to the individual,
whereas any money received, a gain. Combining this with the idea from prospect theory, that losses
hurt more than gains feel good, can account for the endowment effect.10
Coming back to Gary’s pencil exercise, another key aspect is the mechanism he employed to
elicit truthful prices from players. That is, he has players write down their respective prices, and
then has a random price drawn, which determines the price at which a transaction takes place, if
any. Suppose that, rather than using a random price, Gary told players that trade will take place
at the mid-point between the owner’s minimum willingness-to-accept price and the non-owner’s
maximum willingness-to-pay price. In this case, it is in the owner’s best interest to increase the
true price they are willing to accept, and non-owners, to decrease the price they are willing to pay,
such that neither party reveals their truthful price. This would lead to erroneous and misleading
results. By using a random price in this exercise, which is referred to as the “BDM” procedure,
introduced by Becker et al. [1964], a utility maximizer is provided the incentive to truthfully reveal
their reservation price, and is thus incentive compatible.
There are a variety of operations management settings where the endowment effect may influence
outcomes and run counter to the normative theoretical benchmarks. Some of these may include
revenue management models and closed-loop supply chains with returns. Although a simple concept,
the endowment effect can have significant implications in operations, especially when considering
the consumer side.
5.3.7. The Sunk Cost Fallacy
Imagine that you are at a restaurant eating dinner. After enjoying much of your meal, you find
yourself full, but food remains on your plate. However, you continue eating and gorge yourself,
despite the fact that no leftover food is going to be recycled or given to other individuals. If you are
like me, and ever found yourself experiencing a situation like this, you have fallen prey to the “sunk
cost fallacy.” More formally, the sunk cost fallacy is the tendency of a decision maker to continue
on an endeavor, after some type of investment, such as money or time, has been made and is not
recoverable.
The sunk cost fallacy is an extremely robust phenomenon, and can be found in a variety of
domains with significant stakes. Consider Arkes and Blumer [1985], which cite a classic example
10
Please see Section 5.3.2 for details on prospect theory and loss aversion.
33
of the sunk cost fallacy by congressional decision makers. In 1981, funding for the TennesseeTombigbee Waterway Project, which was in the middle of construction and over budget, was set
for congressional review. Opponents felt that it was a waste of taxpayer dollars, whereas senators
supporting the project made claims such as:
“Completing Tennessee-Tombigbee is not a waste of taxpayer dollars. Terminating the project at
this late stage of development, would, however, represent a serious waste of funds already invested,”
and
“To terminate a project in which $1.1 billion has been invested represents an unconscionable mishandling of taxpayers’ dollars.”
Economic theory states that the sunk cost fallacy is irrational, as decisions should be made
based on their present value. For instance, in the previous example, if the marginal costs of completing the Tennessee-Tombigbee project exceed the benefit of the finished project, then continuing
construction is a poor decision. Despite this logic, decision makers often consider the size of the sunk
cost in their future decisions. Indeed, to investigate whether the size of the investment influences
the rate of the sunk cost fallacy, Arkes and Blumer [1985] conducted a field experiment where they
sold tickets for a theater series at different prices to different consumers. One group of consumers
paid $15 for a single series ticket, a second group received a $2 discount per ticket, and a third
received a $7 discount per ticket (the different ticket prices were randomly ordered). They found
that the group which paid full price attended more shows than those who received discounts.
Studies such as Arkes and Blumer [1985] provide considerable evidence supporting the notion
that as the size of a sunk cost grows, decision makers tend to exhibit even stronger sunk cost
fallacy behavior. In this context, the sunk cost fallacy is often referred to as the “escalation of
commitment.” To provide support of this, Staw [1976] conducted an experiment with business school
students where they had to choose where to invest a certain amount of research and development
funding. He found that in situations where individuals’ prior investment decisions led to negative
consequences, those same individuals would commit even more resources to the same course of
action in subsequent decisions. In other words, they were “throwing good money after bad.”
Given the pervasiveness of the sunk cost fallacy, economists and psychologists have made many
attempts to formally model it. As with the endowment effect, a model that captures some of the
features of the sunk cost fallacy is prospect theory (Section 5.3.2). This is due to the fact that, if
there was a prior investment that was costly, it essentially moves the decision maker’s reference
point to the loss domain, where they become risk seeking.
34
While the sunk cost fallacy has been studied extensively by psychologists and economists over
the last 40 years, there has been little experimental work done in operations management settings.
This could be due to a number of reasons. However, one plausible reason is the fact that the sunk
cost fallacy is more natural in a repeated setting, and the current body of behavioral operations
management literature is only beginning to run experiments in repeated environments. That being
said, as the field begins to tap into repeated settings, the sunk cost fallacy may play a role in various
operations management decisions, such as capacity investment problems or project management.
5.4. Bounded Rationality
One critical assumption of many models on individual decision making is that one is perfectly
rational and maximizes some sort of function (expected utility, value, etc). In practice, there are a
multitude of reasons as to why managers or consumers may not choose the best course of action.
For instance, they may find that a number of solutions provide a “good enough” outcome, without
extensive searching. Similarly, they may not have the cognitive ability to identify the best course
of action, and subsequently make errors in their choices. Indeed, much literature has demonstrated
that individuals often neglect to choose the best outcome because of reasons such as these, which
are often referred to collectively as “bounded rationality” [Simon, 1955]. Bounded rationality is not
necessarily a bias, but can have dramatic consequences on choices in operations settings, especially if
one considers strategic games with interactions among players, where one side must anticipate how
the other will act.11 In this section, I will review some results on bounded rationality in individual
decision making settings, including satisficing, decision errors, and system I and II thinking. I will
also provide some alternative perspectives on bounded rationality and heuristics in decision making.
5.4.1. Satisficing
Often times, a decision maker does not necessarily concern themselves with finding the optimal
choice. Instead, they search the alternatives until they find one that they deem acceptable. This
concept, first posed by Simon [1956], is referred to as “satisficing.” In his original article, Simon argues that assuming perfect rationality for a decision maker, and that the decision maker will choose
11
Please see Chapters 6 and 7 for more details on these settings.
35
an outcome that maximizes their utility, is unreasonable in reality. To illustrate his point, Simon
provides an example of a simple organism which is capable of limited actions, in an environment
with certain features. Yet despite these limitations, the organism can satisfy a number of distinct
needs without any complicated mechanism or utility maximization. In the conclusion of Simon’s
[1956] article, he states the following:
We have seen that an organism in an environment with these characteristics requires only very
simple perceptual and choice mechanisms to satisfy its several needs and to assume a high probability of its survival over extended periods of time. In particular, no “utility function” needs to
be postulated for the organism, nor does it require any elaborate procedure for calculating marginal
rates of substitution among different wants.
The analysis set forth here casts serious doubt on the usefulness of current economic and statistical theories of rational behavior as bases for explaining the characteristics of human and other
organismic rationality.
In addition to Simon’s claims, one key argument in favor of satisficing as a heuristic is when
the differences between a satisfactory solution and optimal solution are small, and/or when the
costs of optimizing are high. For instance, when looking to purchase a new car, a consumer might
decide to buy one of the first vehicles they find that satisfies a number of features (e.g. all-wheel
drive, space, reliability, safety, and price) rather than continue and search for every used car in the
market before making a decision.
Satisficing is also useful in settings where an optimal solution may not be identifiable. Rather,
if an optimal solution is unlikely to be obtained, a decision maker or manager may be satisfied
once a certain amount of effort has gone into the decision. For example, a firm may incur serious
costs and effort to develop a set of demand forecasts. At some point, they may recognize that as
they spend more time and effort, the improvement in the accuracy of their forecasts will probably
diminish and not lead to significant gains, and therefore, it is best to stop after a certain amount
of time and choose from their existing forecasts, rather than develop more.
Interestingly, there is research suggesting that decision makers who take a satisficing approach
to choices tend to have higher rates of happiness and satisfaction than those who optimize. That
is, they have lower levels of regret, and neglect to second guess their original decision, compared to
those who perfectly maximize and are constantly wondering if they made the right choice (much
like a perfectionist would). Furthermore, Roets et al. [2012], in an empirical study, find that in
societies where choice is abundant, such as the United States, optimizers report less well-being
than satisficers, primarily due to different levels of experienced regret. Similar results have been
found when consumers face a high number of options in their choices: satisficing can lead to higher
36
satisfaction rates compared to optimizers.
In operations, one might imagine that an executive or manager, whose time is scarce and costly,
would frequently employ a satisficing heuristic. Yet there are few behavioral operations studies that
consider this as an explanation for decisions. This could be due to the difficulty in determining if
decision makers are indeed satisficing, versus some alternative explanation, such as making random
errors (discussed next). Nevertheless, given the cost of managers’ time, it is very likely that many
employ a satisficing heuristic when facing decisions that have many options, which can have serious
consequences on profitability. In addition, on the other side of a transaction, if a firm recognizes
that consumers are employing a satisficing heuristic for purchases, it can help them make more
informed operational decisions, such as how to design a new product and where to invest resources.
5.4.2. Decision Errors
One of the most common approaches to modeling bounded rationality assumes that a decision
maker attempts to optimize, but that they are either limited in their computational abilities or
prone to some unobserved, noisy bias. This is quite common in practice, after all, when a manager
is facing a highly complicated decision, and has little time to evaluate every option in detail, it is
unlikely that they will be able to make the optimal decision. Instead, managers may make mistakes,
and there will be some error in their decisions, which I will refer to collectively as “decision errors.”
When attempting to account for decision errors, researchers usually follow the quantal choice
theory [Luce, 1959].12 In particular, the quantal choice framework assumes that if a decision maker
is presented with multiple options, each one has a likelihood of being chosen, but more attractive
options (i.e. ones that lead to higher levels of utility) are chosen with higher likelihoods. For instance,
it is typical to consider a classic logit choice framework in which the probability of choosing option
i is proportional to eui , where u is the utility for a decision maker [Luce, 1959, McFadden, 1981].
As a result of this, a decision maker’s choice is instead interpreted as a random variable.
The idea of decision errors in operational decision making has gained considerable attention,
especially since Su’s work [2008], where he applied it to the newsvendor problem. I refer the interested reader to his work for more details, but feel that a short summary of his general model
provides a good example as to how decision errors can be applied to operational contexts. With
12
Because this chapter focuses on individual decisions, I will not detail the quantal response equilibrium, which
can be found in Chapters 3 and 7.
37
that, if one assumes errors for a decision maker who has to set a stocking quantity in the face of
uncertain demand, then this implies that (a) the order quantity is now a random variable, versus
deterministic and equal to the normative optimal quantity, and (b) order quantities that yield
higher expected profits will be chosen more often than those which yield lower expected profits.
To capture these effects more formally, Su assumes the multinomial logit choice model, and that a
decision maker chooses alternative i ∈ J with probability:
ψi = P
eui /β
ui /β
i∈J e
for the discrete case, and for the continuous scenario:
ψ(y) = R
with distribution Ψ(y) =
Ry
−∞ ψ(v)dv.
eu(y)/β
u(y)/β
y∈Y e
This approach ensures that a choice is a random variable, and
that better alternatives are chosen more often than others. Lastly, the parameter β, often referred
to as the precision parameter, is interpreted as the level of errors one can expect from the decision
maker. That is, as β → ∞, the decision maker chooses each alternative with equal probability,
regardless of their resulting expected payoffs, and as β → 0, the decision maker chooses the expected
profit maximizing option with probability 1. Su [2008] uses this framework in the newsvendor
setting, and shows, among other things, that if demand follows a uniform distribution, which is
common in behavioral operations experiments, then the stocking quantities follow a truncated
normal distribution.
Decision errors have been successfully used to account for a variety of operational decisions.
In a procurement context with entry costs for bidders, I worked with Elena Katok and Anthony
Kwasnica to show that if bidders cannot perfectly choose the optimal bid, or make a perfect decision
when choosing to enter an auction or sequential mechanism, then the standard theoretical prediction
that auctions generate more revenue than sequential mechanisms may be reversed [Davis et al.,
2014a]. Furthermore, in a supply chain contracting setting, Ho and Zhang [2008] demonstrate that
decision errors, combined with reference dependence, can account for decisions made by retailers
when proposing a fixed fee payment as part of a contract.
Lastly, it is important to note that one drawback of decision errors is that they may not always
represent the true underlying cause for decisions. For instance, researchers (myself included) often
assume errors in order to capture some observed set of decisions, which is useful in explaining
38
outcomes. However, instead of true decision errors driving behavior, there may be some alternative
underlying bias that causes the decision maker to appear as though they are making decision
errors. In these instances, if one cannot determine the specific behavioral bias, then one cannot find
ways to mitigate the bias and improve behavior. That being said, despite this limitation, there is
undoubtedly significant value to using decision errors to model operational decisions and outcomes.
5.4.3. System I and System II Decisions
It is well known that in certain situations humans can make decisions without any considerable
cognitive effort. For example, complete the following sentence “peanut butter and [blank] sandwich,”
or answer the question “1+1=?” In fact, in a different context, some people are able to recognize
if a stranger is upset, without even speaking to them. On the other hand, some decisions require
more deliberate and timely thought. For instance, “what is 18 × 19?” or “how many tennis balls
will fit in a 55 gallon trash can?”
Psychologists have dubbed these two types of thinking as “System I” and “System II.” Specifically, System I represents quick, frequent, automatic, and subconscious types of responses and
decisions. As another example, even driving down an empty road with clear visibility may be
managed by System I thinking. Whereas System II accounts for slow, infrequent, high effort, and
conscious types of decisions.
At first glance, it would appear as though System I and System II thinking is not particularly
relevant for operations management. After all, virtually all of the decisions are almost certainly
System II thinking. However, it is not unreasonable to assume that in practice, where experienced
managers are making many decisions, often times repeated ones, System I may begin to play a role.
In these situations, it may be worthwhile to determine whether some sort of managerial intervention
should be put in place. That is, if one believes that a slower, more deliberate thought process will
lead to better decisions. In other words, System I thinking, while quick (and correct in many cases),
might not necessarily lead to good decisions. To provide an example, Frederick [2005] developed a
clever test of three questions, called the “cognitive reflection test” (CRT) which helps determine
how effective a decision maker is at suppressing an automatic System I answer, and instead respond
with a more deliberate System II answer. The three questions are as follows:
(1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the
ball cost?
39
(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to
make 100 widgets?
(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days
for the patch to cover half the entire lake, how long would it take for the patch to cover half of the
lake?
Immediate responses to these questions, from System I, are (1) $0.10, (2) 100 minutes, and (3)
24 days, whereas the correct solutions are (1) $0.05, (2) 5 minutes, and (3) 47 days. Despite these
being three relatively straightforward questions, the average number of correct responses was 1.24
in a study of over 3,000 total participants (from a combination of nine different schools, including
Harvard University and Princeton University, those attending public events, such as a fireworks
display, and web-based studies). This lack of performance on the CRT test is attributed to peoples’
tendency to rely on their gut reactions, from System I, instead of forcing themselves to take the
time to think carefully about their answers and utilize System II thinking. For those interested in
more examples and information on System I and II thinking, please see Daniel Kahneman’s book,
Thinking Fast and Slow [2011].
The CRT has been found to correlate well with intertemporal discounting and risk preferences, and has also been shown to be a favorable predictor of performance in tasks that require
various cognitive abilities or mental heuristics [Frederick, 2005, Toplak et al., 2011]. From an operations perspective, there has recently been studies showing links between managers’ performance
on the CRT and their decisions in both newsvendor [Moritz et al., 2013] and forecasting settings
[Moritz et al., 2014]. Given this recent work, it is likely that further work can be done on System
I and System II decisions in additional operations contexts, for instance consumer decision making
in service settings.
5.4.4. Counterpoint on Heuristics and Biases
Despite the vast amount of support that humans are indeed boundedly rational, and that we often
resort to common heuristics due to limited computational abilities, there is another stream of literature that claims heuristics are not necessarily suboptimal, and that many simple heuristics can
lead to accurate decisions with little effort. For example, Gerd Gigerenzer and Daniel Goldstein,
two psychologists who are leaders in this field (and often critics of the work of Kahneman and Tversky), were the first to propose the “recognition heuristic” and “take-the-best heuristic,” which are
from their “fast and frugal” algorithms [Gigerenzer and Goldstein, 1996, Goldstein and Gigerenzer,
40
1999]. In particular, a combination of these states that some lack of recognition can actually help
an individual come to a better decision than one with more knowledge. For example, in one study,
students from the University of Munich in Germany, and the University of Chicago in the United
States, were quizzed about populations of cities in the United States. One question asked them
whether San Diego or San Antonio had more inhabitants. Interestingly, 62% of students from
the United States got the correct answer (San Diego), however, 100% of students from Germany
provided the correct answer [Goldstein and Gigerenzer, 1999]. In short, Gigerenzer and Goldstein
attribute this to American students not being ignorant enough to be able to apply the recognition
heuristic. I refer the interested reader to their work for further details on their fast and frugal
algorithms [Gigerenzer and Goldstein, 1996].
In another work “How to Make Cognitive Illusions Disappear: Beyond Heuristics and Biases,”
by Gigerenzer [1991], he claims that many common biases in probabilistic reasoning, overconfidence,
the conjunction fallacy, and the base rate fallacy, are not biases at all. Starting with overconfidence
(covered in Section 5.2.6), Gigerenzer claims that probability theory has not been violated if one’s
own degree of belief in a single event (overconfidence) is different from the relative frequency of
correct answers one generates in the long run. For example, Gigerenzer et al. [1991] conducted
an experiment where they asked subjects several hundred questions of the “Which city has more
inhabitants? (a) City A or (b) City B?” type, and, after each question, asked for a confidence
judgment. Indeed, they found considerable evidence of overconfidence. However, in addition to the
confidence judgments, after each set of 50 questions, they also asked the subjects “How many of
these 50 questions do you think you got right?” The responses to this additional question yielded
estimates that were extremely close to the actual number of correct answers. In short, the authors
claim that the overconfidence bias disappeared.
Turning to the conjunction fallacy and the “Linda” problem (covered in Section 5.2.2), Gigerenzer again claims that there is no violation of probability theory [Gigerenzer, 1991]. More specifically,
he supports his claim by stating that subjects, in the classic Linda problem, are asked which description of Linda is more probable, but are not asked for frequencies. For example, Fiedler [1988]
performed a similar experiment to that of the original Linda problem, but after providing the
description of Linda, asked subjects the following question:
There are 100 persons who fit the description above (Linda’s). How many of them are:
A: bank tellers
B: bank tellers and active in the feminist movement
41
With this particular wording, Fiedler found that there was a dramatic reduction in the conjunction fallacy compared to past studies (roughly 22% compared to the original result of 85%).
Lastly, regarding base rate neglect or the base rate fallacy (detailed in Section 5.2.4), there is
evidence that framing certain problems in terms of frequencies can mitigate the bias. In particular,
Cosmides and Tooby [1996] asked subjects the following:
1 out of every 1000 Americans has disease X. A test has been developed to detect when a person has
disease X. Every time the test is given to a person who has the disease, the test comes out positive
(i.e. the “true positive” rate is 100%). But sometimes the test also comes out positive when it is
given to a person who is completely healthy. Specifically, out of every 1000 people who are perfectly
healthy, 50 of them test positive for the disease (i.e. the “false positive” rate is 5%).
Imagine that we have assembled a random sample of 1000 Americans. They were selected by a
lottery. Those who conducted the lottery had no information about the health status of any of these
people.
How many people who test positive for the disease will actually have the disease? [blank] out of
[blank] ?
In this version, both the information presented and question are shown in terms of frequencies.
Shockingly, 56% of respondents correctly answered “one out of 50 (or 51),” vastly reducing the
amount of base-rate neglect (in the control condition, where they used the same wording as in the
original Casscells et al. [1978] study, only 12% answered correctly). Furthermore, in an additional
condition that was identical to the wording of the problem above, Cosmides and Tooby added a
few supplementary questions before asking the final one (i.e. how many people have the disease),
and found that the percentage of respondents providing the correct answer increased further, to
76%.
I am not presenting this stream of work to discount all of those previous results outlined earlier
in the chapter. Rather, I feel it would be remiss to present so many results without a counterpoint.
Indeed, Gigerenzer and others have received considerable criticism from their colleagues through
their attempts to show that heuristics are not necessarily suboptimal, and that some biases can be
mitigated through wording and presentation. Instead, this stream of work demonstrates that we
must be careful when determining whether a potential bias is driving the outcome in an operational
setting, as many biases and heuristics may be diminished, or exacerbated, depending on how we
conduct our experiments and what types of operational problems we investigate.
42
5.5. Final Comments and Future Directions
Managers are often susceptible to behavioral biases or tendencies, which can affect their decisions.
When facing operational problems that involve uncertainty, which is quite common, these biases
may be due to miscalculating probabilities, evaluating outcomes in alternative ways, or neglecting
to make a decision that is the “optimal” choice. Indeed, there are a multitude of results in the
psychology and experimental economics literature that relate to these three categories. In this
chapter, I attempted to provide a summary of, what I believe are, the most relevant of these results
pertaining to individual, one-shot decisions in operations management.
Many of the topics outlined in this chapter originated with the aim of questioning expectedutility theory. In fact, in a related setting, Colin Camerer [2003], when motivating behavioral game
theory, writes:
Game theory, the formalized study of strategy, began in the 1940s by asking how emotionless geniuses
should play games, but ignored until recently how average people with emotions and limited foresight
actually play games.
This statement is analogous to the role of expected-utility theory in modeling individual decisions in operations management settings. More specifically, even though expected utility theory
received considerable criticism over the last 70 years, it is still a widely accepted approach to modeling choices in various contexts, including operations management. This is primarily due to the fact
that the standard risk-neutral expected-utility maximizing model can be enriched to account for
behavioral tendencies, much like behavioral game theory. For example, many of the topics reviewed
in this chapter actually assume some sort of standard expected-utility model for a decision maker,
which is then extended to capture behavioral biases, such as adding disutility terms to represent
anticipated regret.
Looking forward, I believe that in order to improve our ability to accurately predict human
behavior in operational settings, theorists and experimentalists must adopt a collaborative, and
iterative, approach. In particular, theorists develop a model, then experimentalists test it empirically
with human subjects, theorists revise the model, experimentalists test it again, and so forth, until
the two converge. Indeed, I feel one side without the other will find difficulty in identifying ways to
better understand human behavior in operational contexts.
Another opportunity for future work is to better understand de-biasing techniques. In particular, identifying a behavioral bias, and showing that it accounts for decisions is certainly useful, but
actually demonstrating how to mitigate the bias and improve decisions would be especially benefi43
cial. Another opportunity for future research pertains to the consumer side of decisions. While there
is no doubt that managers are influenced by behavioral biases, the same can be said for consumers,
and if a firm can better understand consumer behavior, then they can make operational decisions
which better prepare them for this behavior, leading to increased profitability.
In this chapter I presented a review of behavioral results in psychology and experimental economics for individual decision making and how they relate to operations management. For some of
the topics, one may have noticed that there are relatively few operations management papers that
apply said topic. For instance, to my knowledge, few behavioral operations management studies
consider results such as the availability heuristic, or explore decisions that involve intertemporal
choice. Personally, I view this as a positive, as it suggests that there are a number of exciting future
studies that we, as behavioral operations researchers, can investigate, thus shedding further light
on how managers make decisions in operational settings.
Acknowledgments
This chapter has benefited greatly from the feedback of Tony Cui, Karen Donohue, Elena Katok, Stephen Leider, Amnon Rapoport, Natalia Santamarı́a, and Vincent Yu. I would also like to
thank discussion participants at the University of Texas at Dallas for their helpful comments and
suggestions. All errors and omissions are my own.
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