Social Networks
North-Holland
213
14 (1992) 213-229
An expected value model of social power:
predictions for selected exchange networks
Noah E. Friedkin
Departments of Education and Sociology, UniLwsity of California, Santu Barbara, USA
The paper carries forward a line of work on an expected
illustrates the application
of this model to selected networks
value model of social
of social exchange.
power
and
Introduction
This paper builds on Friedkin (1986, 1991bl in which an expected
value model of social power is developed
and applied to social
exchange. I present a schematic description
of the expected value
approach to social exchange; see Friedkin (1991b) for details on the
connection
of this approach with previous work on social exchange
networks and a discussion of the broader model of social power from
which the approach is developed.
Then, for the nine exchange networks illustrated in Fig. 1, I present the model’s predictions concerning the resources network members are expected to acquire from their
exchange transactions.
Expected value model of social power
The expected value model of social power may be applied to different
types of social relations including interpersonal
influence, information
flow, social support, and social exchange. The present application
is
concerned
with outcomes
of interpersonal
networks comprised
of
Correspondence to: N.E. Friedkin,
Barbara, CA 93106, USA.
037%8733/92/$05.00
Graduate
0 1992 - Elsevier
School of Education,
Science
Publishers
University
of California,
B.V. All rights reserved
Santa
N.E. Friedkin / Expected value model
214
two-party transactions
in which each transaction
provides one party
with a fraction of some amount of resources and the other party with
the remaining fraction. Such exchange networks have been the focus
of considerable
experimental
work during the past several decades
(Cook 1987; Willer and Patton 1987).
The expected value approach to exchange outcomes involves five
steps; these steps will be described in tandem with a simple illustration. A computer program implements
the approach and is available
from the author upon request (Friedkin 1991~). ’
Delineation
of the power structure
The approach
starts with the delineation
of a power structure:
a
network comprised
of (a> points indicating collective or individual
actors and (b) undirected
lines indicating the potential transactions
for each actor. The presence of a line between two actors indicates
that they may exchange and the absence of a line between two actors
indicates that they cannot exchange.
Two simplifying assumptions
are made about a power structure’s
actors and potential transactions:
(A,) The actors in a power structure are rational actors who seek
to maximize their net receipt of resources over any set of transaction opportunities
provided to them.
Later in the paper, the assumption of rational action is replaced by
operational
statements describing the type of action that is assumed to
occur.
(A,) A power structure is stable with respect
potential exchange transactions.
to its configuration
of
Accordingly,
a power structure
is stable even with changes in the
identities
of the actors who occupy the different
positions in the
structure.
Nine power structures
{S,, S,, . . . , S,) are illustrated
in Fig. 1. I
consisting of four positions
concentrate
initially on S,, a structure
(1, 2, 3, 4) and three lines (l-2, 2-3, 2-4).
I This program is designed
or 387 math coprocessor.
WXTlOly.
to run on an IBM PC-XT-AT-PS/2
or compatible with an 8087, 287,
DOS 3.3 or above is required.
You should have at least 640K of
215
N.E. Friedkin / Expected r,alue model
Delineation of the sample space
The next step is to delineate the sample space of the power structure.
The sample space will consist of the k different networks of exchange
transactions
{R,, R,, . . . RK} that might occur in the context of the
power structure; i.e. those subgraphs of the power structure that are
feasible under a given set of empirical or theoretical
conditions.
I refer to the sample space of a power structure as unrestricted if it
contains all the theoretically
possible R-networks.
If the number of
lines among actors in the power structure is u then a maximum of 2”
alternative,
labelled, R-networks
are possible. Table 1 illustrates the
eight members of the unrestricted
sample space of S,. In R 1 none of
the possible transactions
occur; in R, the only transaction
is between
actors 2 and 4; and so forth.
Unrestricted
sample spaces may contain a large number of networks. For example, in a power structure with 25 lines there are over
23 million R-networks
in the unrestricted
sample space. However,
restrictions on the sample space may dramatically
reduce the number
of its members. The restriction may be empirical; i.e. certain possibilities are never observed and so they are eliminated.
The restriction
may be theoretical;
i.e. certain possibilities cannot occur on theoretical grounds. The restriction
may be experimentally
imposed;
i.e.
certain possibilities are not allowed to occur under the conditions of
an experiment.
Experiments
on social exchange typically limit an actor to no more
than a predetermined
number of transactions with different actors on
each trial of the experiment;
limiting actors’ exchanges in this fashion
has important effects on the sample spaces of power structures. I refer
to these common
restrictions
on social exchange
as e-exchange
regimes, where e = 1, 2, . . . . The l-exchange regime limits actors to at
most one transaction
per trial of an experiment;
the 2-exchange
regime limits actors to at most two transactions
with different actors;
the 3-exchange regime limits actors to at most three transactions with
different actors; and so on (Markovsky et al. 1988: 227). *
Consider the restricted
sample spaces illustrated
in Table 1. The
sample spaces of the (1, 2,3)-exchange
regimes for S, consist respec’ Application
of the expected value model is not limited to e-exchange regimes;
on such regimes to facilitate comparison
of the model with other approaches.
I presently
focus
216
N.E. Friedkin / Expected clalue model
s,
S2
S,
S,
S,
S6
S,
58
Fig. 1. Networks.
‘L. /:
/;““““i:
N.E. Friedkin
Table 1
Illustrative
sample
Rk
llnrestricted
spaces
for power
sample
structure
Restricted
Network
image
1
2
2
2
0
3
0
4
0
.
.
217
talue model
S,
space
Power
lines
RI
/ Expected
e-Exchange
sample spaces
regimes
e-l
e=2
e=3
.
no
no
IlO
.
yes
tl0
no
yes
IlO
fl0
IlO
yes
no
l
yes
no
no
l
no
yes
n0
n0
yes
no
no
no
yes
.
R2
.
.
I
l
RX
l
.-.
.
R4
.
.-.
I
.
R,
.-.
l
R,
.-t
I
l
R,
.-.-.
.
R,
.-.--•
I
.
tively of the networks (R,, R,, R,}, (R4, R,, R,), and {R,J. The
three sample spaces are non-overlapping and, apart from the vacuous
R, network, exhaust the membership of the unrestricted sample space
of s,.
Each of the networks in the restricted sample spaces illustrated in
Table 1 are maximal with respect to e, i.e. the number of feasible
transactions:
(A,) Any network in the sample space of a power structure is
maximal with respect to e in that no further transaction can occur.
Rational actors (see assumption A,,) do not absent themselves from
exchange opportunities. Thus, R ,, in which none of the exchanges
that might occur, do occur, is irrational and does not appear in any of
the sample spaces. On the same grounds, no network in the sample
space of an i-exchange regime appears in the sample space of a
j-exchange regime for i <j; for example, R, does not appear in the
sample spaces of the 12, 3)-exchange regimes because it is irrational
218
N.E. Friedkin
for actor 2 to negotiate
are feasible.
Relative frequency
/ Expected calue model
only one exchange
when additional
exchanges
of exchange networks
The third step of the approach determines
the probability of each of
the R-networks in the sample space of a power structure. Ideally, the
required probabilities
are derived from a formal model of the social
exchange process. Alternatively,
in experiments where data on a large
number of trials are gathered, these probabilities
may be estimated by
the observed relative frequencies
of R-networks.
In the absence of
probability
estimates based on data or theory, baseline assumptions
may be employed. The most rudimentary
assumption is:
(A,) Each network
equally likely.
in the sample
space
of a power
structure
is
Under this baseline assumption, the probability of a particular R-network is simply the reciprocal
of the size of the sample space, i.e.
P(R,) = l/K.
Based on assumption
A,, Table 2 illustrates probability
distributions for power structure
S,. Because three networks are possible
under the (1, 2)-exchange
regimes for S,, the probability
of each
R-network in these regimes is $. Because only one network is possible
in the 3-exchange regime for S,, the probability of that network is 1.
Outcomes
of exchange networks
Fourthly, the outcome(s)
for each of the R-networks
in the sample
space is (are) determined.
The outcome may be some transparent
structural feature of the R-network: its density, diameter, connectivity
category, point centralities,
bundle sizes, and so forth; see Harary et
al. (1965) for the definitions of these and other structural features of
networks. The outcome also may be derived from a process model of
bargaining and concern features of the transactions
that occur in the
network.
In this paper, I focus on two outcomes of exchange transactions: (a>
the amount of resources acquired by each actor in a R-network and
(b) the particular division of resources for each of the transactions in a
R-network. I refer to the amount of resources that an actor acquires
N.E. Friedkin
/ Expected calue model
219
as the actor’s PAYOFF. The precise definition of PAYOFF differs
according to whether actors or exchanges are the units of analysis. (a)
For each actor, PAYOFF is the net amount of resources that the actor
acquires from the transactions
in a particular R-network: under {e 2
2}-exchange regimes, an actor’s PAYOFF may be comprised
of receipts from several transactions.
(b) For each exchange between actors
i and j, PAYOFF is the amount
of resources
that actor i (i <j>
acquires from the exchange; the convention of setting i <j allows an
unambiguous
indication of the exchange ratio for the transaction.
If
24 units of a resource are at stake and PAYOFF = 18 for an exchange
between actors 1 and 2, then the exchange ratio is 3 : 1 in favor of
actor 1.
The egalitarian
norm, that stipulates
an even split of available
resources among the parties to an agreement, is the obvious candidate
Table 2
H,, Outcomes
Sample
Rh
for power
space
P(R,)
(a) l-Exchange
structure
S,
PAYOFF
OUTCOMES
Actor
1
2
3
Exchange
1
2
4
2
3
2
4
regime:
R2
:
0
12
0
12
*
*
12
R,
i’
0
12
12
0
*
12
*
Rs
i’
E(PAYUFF)
(b) 2-Exchange
12
4
12
12
0
4
0
4
12
12
*
12
*
12
regime:
R4
7’
0
24
12
12
*
12
12
R,
f
12
24
0
12
12
*
12
R7
i’
12
8
24
24
12
8
0
8
12
12
12
12
*
12
12
12
36
36
12
12
12
12
12
12
12
12
12
12
E(PAYOFF)
(c) 3-Exchange
RX
1
E(PAYOFF)
regime:
H, =(A,, A,, A,, .44).
It is assumed
that 24 units of a resource are available for each transaction.
Actor PAYOFF is the amount of resources an actor receives from the transactions
in R,.
Exchange PAYOFF is the amount of resources actor i receives from the transaction
with actor j
(i < j).
The asterisk indicates that a transaction
between actors i and j does not occur in R,.
for a baseline approach to exchange outcomes:
(A,) If aij is the amount of resources that might be divided
between actors i and j, then a transaction between i and j will net
each actor one-half aJj.
Outcomes of this baseline assumption are illustrated in Table 2. Later
in the paper, I describe a promising alternative to this baseline
approach.
Given the set of baseline assumptions H,, = (A,, A,, A,, A,], the
final step in the approach is to compute the expected value(s) of the
outcome(s). An expectation is an indicator of the central tendency of
the distribution of outcomes for the set of R-networks that may arise
from the power structure; in the special case of a binary IO, 1)
outcome the expectation is simply the probability of the outcome. If
the sample space of the power structure contains relatively few
R-networks, then it is possible to carry out the computation exactly.
When the sample space of the power structure is large the expectations may be estimated from a suitable sample of R-networks.
Table 2 illustrates baseline expectations for PAYOFF. The expectation for an actor’s net receipts is:
where P(R,) is the probability of R, in a sample space comprised K
networks and P54Y0F~i, is the resource outcome for actor i in R,.
That is, for each R-network in the sample space a product is formed
of the probability of the R-network and the outcome, and these
products are summed to form the expectation of the ourcome.
For transactions, the relevant prediction is the amount of resources
actor i is expected to acquire in agreements with another actor j.
Conditional expectations are computed, wherein the PdYOFF of
actor i from a transaction with actor j is weighted by the relative
frequency of the R-network in which the transaction occurs among
that subset of R-networks that contain the particular transaction.
N.E. Friedkin / Expected value model
221
For power structure S, the predictions of the baseline H,, approach
are exceedingly simple. Actor 2 who appears in the central position of
the structure is expected to acquire more resources than the other
actors {1, 2, 4), and these other actors are expected to acquire similar
amounts of resources. The exchange regime affects the absolute
amount of resources acquired by the actors but does not affect the
rank order of their resource receipts. The exchange ratios are homogeneous as a consequence of the egalitarian agreements; nevertheless,
actor 2 benefits from a structural position that permits this actor to
participate in more transactions than other actors.
Table 3 gives the H,, predictions for each network in Fig. 1
predictions of an alternative (H,) set of assumptions also are presented in Table 3. Detailed comments on the table are postponed
until the H, assumptions have been introduced.
A refined model H,
The predictions of the baseline model H,, involve the assumption of
an egalitarian (50-50) split of available resources between the actors
who exchange. This assumption is modified in H,.
Building on the thesis that the size of actors’ offers are inversely
related to the relative frequency of their exclusion from social exchange, A, can be replaced with a more refined approach to the
bargaining process. The proposed refinement A,., involves a set of
assumptions dealing with (a) actors’ initial offers and (b) how actors
reconcile inconsistent offers. I use the notation A$‘,, A(zh, A’;!, . . . A(:!,
to refer to the constituent parts of A,.,.
The first of these constituent assumptions predicts actor i’s initial
offer to actor j as a function of the dependency of actor i on actor j:
(A’~~,)The amount of available resources initially offered by actor i
to actor j is governed by an asymptotic regression function
flj
=
aij
-
bij(
Cijyd,’
(2)
where aij > 1 is the amount of available resources, fij is the
amount of these available resources that actor i initially offers to
222
N.E. Friedkin
/ Expected
~due modd
actor j, 0 < bij < aij and 0 < c,~ < 1 are coefficients,
is the actor i’s dependency on actor j.
and 0 s dij I 1
(A(iT1) The dependency
of actor i on actor j is the probability that
actor i is excluded from an exchange and that the two actors do not
exchange with each other. ’
Thus, actor i is assumed to be dependent
on actor j on the basis of
the association between the exclusion of actor i from exchange and
actor i not exchanging with actor j. Under l-exchange
regimes, this
formulation
of an actor’s dependency
simplifies to the vulnerability
of
the actor to exclusion (i.e. the probability that the actor is excluded
from an exchange); hence, under this regime an actor makes the same
initial offer to all possible transaction
partners. Under multiple exchange regimes an actor’s dependency
and initial offers may vary for
different transaction
partners.
The curve [2] rises from ajj - bjj; i.e. when actor i is least dependent on actor j (dij = O), the predicted
initial offer of actor i is an
amount that is less than the available resources. As actor i’s dependency on actor j increases (i.e. as djj + 11, the predicted offer steadily
approaches
the asymptote ajj which is the total available resources.
A priori values for the coefficients
{bij, cjj} may be derived under
two assumptions:
(A(:,),) Actors who are minimally dependent
offer only one unit of
their available resources and (A’:!,) actors who are maximally dependent offer all but one unit of their available resources.
From the first assumption
ajj - b,j = 1. From
f,j = aij - 1 when dij = 1. Hence,
the second
assumption
’ Let maxfdeg,)
represent
the maximum
number
of exchanges
for actor i in any of the
R-networks.
Actor i is excluded from an exchange in R, if the number of the actor’s exchanges
in R, is less than maxtdeg,); let A indicate this event. Let B indicate the event that actor i and
actor j do not exchange with each other in R,. The dependency
of actor i on actor j is the
probability of the joint event d,, = PfAn B) in the sample space of the power structure. I settled
on this measure of dependency
after eliminating
several plausible alternatives
that performed
less well.
223
N.E. Friedkin / Expected unlue model
Table 3
E(PAYOFF)
s,
H,
H,
H,
H,
for Fig. 1 power structures
(e
(e
(e
(e
= 1)
= 1)
= 2)
= 2)
1
4
1
8
3
s,
Actors
H, (e = 1)
H, (e = 1)
H, (e = 2)
H,(e=2)
1
6
1
12
12
%
Actors
H, (e = 1)
H, (e = 1)
H, (e = 2)
H,(e=2)
1
4
1
8
3
2
12
22
24
39
3
4
1
8
3
4
4
1
8
3
2
12
17
24
24
3
12
17
24
24
4
6
1
12
12
12
12
2
12
5
(e = 1)
(e = 1)
(e = 2)
(e = 2)
12
9
4
12
12
12
12
3
12
12
H,
H,
H,
H,
(e = 1)
(e = 1)
(e = 2)
(e = 2)
2
12
19
24
39
3
4
1
8
3
4
12
17
20
15
12
12
2
12
5
5
8
3
12
12
H,
H,
H,
H,
(e
(e
(e
(e
=
=
=
=
1)
1)
2)
2)
1
4
1
9
3
S7
Actors
H,
H,
H,
H,
1
10
10
18
13
(e
(e
(e
(e
= 1)
= 1)
= 2)
= 2)
23
12
12
12
12
34
12
21
12
12
23
12
22
12
19
24
12
12
12
19
45
12
19
12
12
34
12
6
12
19
45
12
18
12
12
67
12
18
12
12
34
12
12
12
19
45
12
19
12
12
36
12
22
12
19
24
12
19
12
19
34
12
12
12
12
34
12
12
12
21
45
12
12
12
12
Exchanges
12
18
20
15
3
9
4
24
39
4
12
18
20
15
5
9
4
12
12
12
17
20
15
3
12
15
24
39
4
12
17
20
15
56
8
3
12
12
2
12
20
24
39
3
8
6
20
15
4
8
6
20
15
2
10
10
18
13
3
10
10
24
42
4
10
10
18
13
67
12
9
18
4
20 12
15 12
12
12
6
12
12
23
12
18
12
5
36
12
6
12
19
Exchanges
Actors
%
24
12
22
12
19
Exchanges
Actors
12
8
3
12
12
23
12
22
12
19
Exchanges
Actors
s‘l
H,
H,
H,
H,
Exchanges
Actors
4
1
8
3
12
12
5
12
12
23
12
12
12
5
Exchanges
12
12
2
12
5
23
12
19
12
19
Exchanges
5
10
10
18
13
12
12
12
12
12
23
12
12
12
3
13
12
12
12
3
35
12
12
12
21
224
N.E. Friedkin / Expected r>aluemodel
Table 3 (continued)
%
Actors
H,,(e=l)
H,(e=l)
H,,(e=2)
H,(e=2)
1
9
8
17
13
s,
Actors
H,,(e=l)
H,(e=l)
H,,(e=2)
H, (e = 2)
1
7
2
12
12
Exchanges
2
9
8
17
13
3
10
12
24
37
4
7
3
13
4
5
12
20
24
34
6
5
1
8
3
2
12
19
19
14
3
10
6
24
34
4
12
20
24
34
5
5
1
7
2
6
7
4
14
5
12
12
12
12
12
23
12
9
12
3
34
12
15
12
21
45
12
4
12
5
56
12
22
12
19
13
12
9
12
3
34
12
7
12
12
45
12
22
12
20
36
12
12
12
20
46
12
20
12
20
35
12
8
12
12
Exchanges
12
12
4
12
12
23
12
17
12
4
Si indicates the power structure.
e is the e-exchange regime.
H, indicates the set of assumptions
from which the predictions
are derived.
It is assumed that 24 units of a resource are available for each transaction.
Actor PAYOFF is the amount of resources an actor receives from the transactions
in R,
Exchange PAYOFF is the amount of resources actor i gets from a transaction
with actor j where
i < j.
For example, given 24 units of a resource,
predicted initial offers are:
fij
1
12
17
19
21
22
cji = 0.969 and some of the
23
Next we must consider what happens when two actors’ offers are
inconsistent;
the offers of two actors, i and j, are inconsistent
if their
personal claims on available resources (aij -fij and aij -fji, respectively) do not sum to the amount of the available resources:
(A$!,) If the sum of actors’ personal claims exceed the amount of
available resources, they split-the-difference
and settle on the average of their two offers. (A’,6!,) If both actors want less than one-half
of the available resources,
they evenly divide the available resources. (A’,7!,) Finally, there is the somewhat complex situation
where one actor wants one-half the resources or more, the other
wants less than one-half
the resources,
and the sum of their
personal claims is less than the amount of available resources; in
N.E. Friedkin / Expected value model
Table 4
Assumptions
225
of the models
Models:
Ha = (A,, A,, A,, A,)
H, =(A,, A,, A,, A,.,)
Assumptions:
A,
Rational actors
Structural
stability of power structure S
Al
A,
Maximal transaction
networks CR,, k = 1, K)
A,
Equally likely R,
A,
Transaction
outcomes
A 4.a Egalitarian
rule
A 4,, Alternative
model
A”’
Function for initial offers
4.1
A’3
Actor dependency
(vulnerability)
4.1
Bounds for initial offers
IA’:!, A$)1 1
{A’:‘,’>A(:!, 7A(i),) Reconciling
inconsistent
offers
this case, the unclaimed portion of the available resources is allocated to the actor with the lower of the two personal claims.
Summary
Table 4 gives an overview of the assumptions that have been introduced and the two models that are based on them. H, is the baseline
model which includes the assumptions (A,) of equally likely R-networks and (A,) of egalitarian (50-50) splits of resources in exchanges.
H, is the refined model constructed by replacing assumption A, with
the just introduced assumptions A,, = {A’,$, A$!,, . . . , A’&).
Predictions
A theoretical attraction of the expected value approach is that it
forwards quantitative predictions of actors’ resource receipts as opposed to the qualitative (rank order) predictions which have been a
characteristic of other approaches. Here, however, I emphasize the
qualitative features of the predictions in order to facilitate comparison
with predictions derived from other theoretical schemes.
226
N.E. Friedkin / Expected value model
With one exception, the two models (H, and H,) provide consistent
rank order predictions for the nine power structures; see Table 3.
Actors and transactions that are tied in rank order under z-i,, assumptions are sometimes distinguished under H, assumptions; for instance,
in S, (e = 1) actors 2 and 4 who are tied under H, are differentiated
under H,. The exception to the rank-order consistency occurs in S,
(e = 2) where the rank order of actors 1 and 6 are reversed under the
two models. Henceforth, I focus on the H, predictions; see Friedkin
(1991b) for an empirical evaluation of H, assumptions.
For the chain structure S,, and all other chains, the model predicts
that actors located at the terminal positions of the chain are the least
advantaged. Under the 2-exchange regime, actors located in the
interior positions of a chain are equally advantaged. Under the
l-exchange regime, the most advantaged actor(s) is (are) adjacent to
the terminal positions. Hence, in chains composed of five or more
actors the most central actors (Freeman 1979; Friedkin 1991a) are not
the most advantaged.
The predictions for the ‘T’ structures {S,, S,, S,, S,) also indicate
that actors in the most central positions are not necessarily the most
advantaged. While the central actors in S, and S, are the most
advantaged, such is not the case in S, and S,. This structural ‘anomaly’
appears only under the l-exchange regime; under the 2-exchange
regime, the central actors are always the most advantaged. In these ‘T
structures, actors located at the terminal positions are the least
advantaged.
The predictions for the ‘stem’ structure S, indicate that the central
actor is the most advantaged and that the actor in the stem is the least
advantaged under both exchange regimes. The predictions for two of
the ‘kite’ structures S, and S, are somewhat more interesting. In S,,
under the l-exchange regime no actor is relatively advantaged while
under the 2-exchange regime the central actor is more advantaged
than the others. The addition of a ‘tail’ to this structure, i.e. S,,
dramatically stratifies the actors.
The last structure S, is similar to S,; note that S, becomes S, with
the removal of the line between actors 4 and 6. In S, (e = 11 the
non-central actors 2 and 4 are more advantaged than the central actor
3; essentially the same rank order of actors occurs in S,. In S, (e = 2)
the central actor 3 is the most advantaged, while in S, (e = 21 actor 3
shares this advantaged status with another actor.
N.E. Friedkin / Expected value model
227
Rank order predictions suppress information on the magnitude of
the differences between actors. For example, in S, (e = 1) the noncentral actors 2 and 4 are the most advantaged; however, they are only
slightly more advantaged than the central actor 3. Hence, findings that
might show no significant difference between these non-central and
central actors must be assessed in terms of the statistical power of
methodology to detect the predicted small difference. Two other
illustrations are provided of the quantitative information that is being
advanced by the H, predictions.
Consider again the H, predictions for structures S, and S, under
the l-exchange regime. What is the consequence of the single line
(between actor 4 and 6) that distinguishes the two structures? The
resource expectations for actors 2, 3, and 4 are respectively 17, 15, and
17 units in S, and 19, 6, and 20 units in S,. While the expectations of
actors 2 and 4 are at essentially the same levels in both structures, the
expectation of actor 3 is 60% less in S, than in S,.
Consider again the ‘kite’ structures S, and S, under the l-exchange
regime. What is the consequence of the single line which distinguishes
the two structures? The resource expectations of actors 1, 2, and 3 are
approximately the same in both structures. The major difference is
that the additional line doubles the resource expectation of actor 5
and diminishes the resource expectation of actor 4 by 70%.
Discussion
The prevailing theoretical agenda of the recent work on network
exchange phenomena has been to construct a measure of pointcentrality that, when applied to a network of potential exchange
transactions, correctly predicts the resources actors acquire through
negotiated agreements. Substantial controversy has developed in the
pursuit of this agenda. In light of this controversy, the present expected value approach to social exchange outcomes has at least four
theoretical attractions.
First, from baseline assumptions, the model appears consistent with
available experimental evidence in locating those positions in a power
structure that tend to acquire the most resources through social
exchange; in particular, the model provides a simple account of the
experimental findings on certain power structures in which the seemingly most central actors do not acquire the most resources.
228
N.E. Friedkin / Expected IYAM model
Second, the approach
is not limited to rank-order
predictions:
it
predicts the expected amount of resources acquired by actors through
social exchange and the expected ratios of resource exchange. The
quantitative
predictions of the model allow new sorts of predictions to
be tested and a better calibration of experimental
designs to achieve
appropriate
levels of statistical power.
Third, the approach
easily accommodates
different
regimes of
social exchange: negative exchanges, positive exchanges, multiple exchanges, mixed exchanges, and resource flows (Cook et al. 1983: 277).
In treating these regimes as alternative
restrictions
on the sample
space of a power structure, the model provides a potentially integrative framework for their analysis.
Fourth, and finally, the model provides a convenient
schema in
which to cumulatively refine elementary
assumptions about the social
exchange process. By disentangling
major components
of the social
exchange process, the approach helps to clarify certain complex theoretical issues and points to areas where additional
formal development of social exchange theory might be undertaken.
Three avenues of future work appear especially important
to the
development
of the present
approach.
(1) Assumption
A, which
specifies equally likely R-networks
should be replaced with a more
refined approach
to the probability
distribution
of transaction
networks; while it is plausible that isomorphic
R-networks
are equally
likely, the problem of predicting the relative frequencies
of non-isomorphic networks is presently unsolved. (2) Assumption A,., regarding transaction
outcomes should be evaluated with data on the initial
offers of actors; and, as part of this evaluation,
alternative
specifications of interpersonal
dependency
(assumption A’fl,l should be examined. (3) Finally, the present approach not only ignores the sequences
of exchange
that give rise to a R-network,
but also ignores the
processes that link the development
of separate R-networks;
it might
be worthwhile to pursue a generalization
of the approach that takes
such sequential processes into account.
References
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N.E. Friedkin / Expected value model
229
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