Comparing two Rational Choice theories on Influence Strategies in
Collective Decision Making using Computer Simulation1
(Draft version)
Marjolein Achterkamp
Interuniversity Center for Social Science Theory and Methodology (ICS)
University of Groningen, the Netherlands
Abstract.
In the research on influence strategies used in collective decision making in policy domains
two main theoretical approaches can be distinguished: Conflict Resolution and Social
Exchange theory. Until now these approaches are compared by comparing the predictions of
two models of collective decision making which stem from these two approaches: the
Expected Utility model of Bueno de Mesquita and the Exchange model of Stokman and Van
Oosten. However, this has lead to two problems. Although much effort is put in collecting
data on collective decision-making situations, the available data sets are not yet sufficient to
answer the question in which collective decision-making situations the difference in
assumption on applied influence strategy lead to different predictions. Because of this, I
propose to use simulated data for a more structured search.
Furthermore, since the Expected Utility model and the Exchange model differ in more
respects than just applied influence strategy, it is questionable whether the differences in
results stem from the difference in applied influence strategy. To study the effect of applied
influence strategy, the Exchange model and Expected Utility model have to be modified in
such a way that they only differ in this respect. These modifications lead to the Iterative
Exchange model and the Challenge model, which are the models that will be compared.
A design for a structered search using simulated data is presented and the paper ends with
some (preliminary) results.
1 Influence strategies in Collective Decision Making
1.1 Introduction
In collective decision making the outcome of a decision is not the result of a choice of a
central authority, but depends on the partly simultaneous individual choices of the relevant
actors (Coleman 1990). For most policy domains, it holds that actors with voting power
determine the outcome by their voting behavior. However, all actors involved can influence
the outcome by influencing each other. Although this general insight is widely recognized,
1
Paper for the Workshop on Computational Sociology, TU Hamburg-Harburg, February 13 - 15, 1998.
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less consensus is found on the strategy actors (are assumed to) use to influence each other.
In my research project I compare influence strategies used in collective decision making. I
assume that all actors already made up their mind about their preferred outcome of the
collective decision. What are the strategies they use to change other actors’ votes? And is the
use of one influence strategy more effective than the use of another strategy?
1.2 State of research on Influence Strategies
In social psychology studies on decision making considerable attention is paid to influence
strategies. However, focus here is on influence strategies used in small groups and most
attention is paid on influence strategies in intimate relations. Various possible strategies are
identified, and these strategies are measured along several dimensions. Falbo and Peplau
(1980) use the dimensions directness (hidden strategies vs. open strategies) and
interactiveness (bilateral, i.e cooperation of both influencer and target is necessary vs.
unilateral, i.e cooperation of the target is not necessary). Johnson (1976, 1978) uses the
dimensions direct vs. indirect, helplessness vs. competence and personal vs. concrete. Other
researches like Kipnis et al. (1976), Cowan et al. (1984), and Howard et al. (1986) use the
dimension strong vs. weak. Hardly any attention is paid here on influence strategies in policy
networks.
The sociologist Parsons developed a classification of influence strategies in political
decision making (Parsons 1963). He recognizes two dimensions, channel (situational directed at the target’s situation, or intentional - directed at the target’s beliefs), and sanction
type (positive or negative) (see table 1).
Table 1. Parsons’ classification of influence strategies
Situational Channel
Intentional Channel
Positive Sanction
Inducement
Persuasion
Negative Sanction
Coercion
Activation of Commitments
In case of inducement ego improves, or promises to improve alter’s situation if alter does as
ego wants. In case of coercion, ego deteriorates, or threatens to deteriorate, alter’s situation if
alter does not do as ego wants. These strategies are directed at alter’s situation. The other two
strategies are directed at alter’s preferences (beliefs). Ego tries, without changing alter’s
situation, to change alter’s intention, i.e. ego tries to make alter see that it is a ‘good thing’
that ego wants him to do. He can do so by presenting alter reasons why doing what ego wants
would be good for alter (persuasion) or why not doing what ego wants would be bad
(activation of commitments). The distinction between situational channel and intentional
channel can be seen as a distinction between research traditions. In political science focus is
2
on the situational side. In the organizational studies attention is more on the intentional
aspects. For example, in the theory of Management of Meaning (March and Olson 1989;
Bouwen 1993) actors are open to the views of others. Actors change their preferences if an
other actor can persuade him to do so.
In political science studies of collective decision making focus generally is on meaning
and distribution of power (French and Raven 1959; Mokken and Stokman 1976; Marsden and
Laumann 1977; Lukes 1986). Researchers are mainly interested in collective outcomes of the
decisions and little attention is paid to the strategies actors use to influence other actors. The
game theoretical approach shows an even stronger focus on collective outcomes. The concept
of equilibrium points is used to predict collective outcomes, but how actors reach these points
gets little attention (Harsanyi 1977; Rasmusen 1989).
1.2 Social Exchange theory and Conflict Resolution
However, two main theoretical approaches on influence strategies in policy domains can be
distinguished: Social Exchange theory and Conflict Resolution. These are the theories that I
want to compare. In the Conflict Resolution approach a collective decision is viewed as a
conflict, with winners and losers (Lasswell 1958; Bueno de Mesquita et al. 1985). Actors try
to force other actors into changing their voting behavior by making use of their capabilities. In
the Social Exchange theory, influence in collective decision making is regarded as an
exchange (Coleman 1972). An actor (ego) can choose to act against his own preferences, in
favor of the preferences of another actor (alter) for one issue, in exchange for alter acting
according ego’s preferences for a second issue (‘logrolling’).
In terms of the social psychology classifications the conflict strategy is a unilateral strategy
and the exchange strategy is a bilateral strategy. Both can be considered as open and strong
strategies. Both influence strategies are directed at the voting position of the other actor, so at
the situational channel. According to Parsons’ classification, the conflict strategy is a typical
coercion strategy, whereas the exchange strategy can be considered as inducement. So
restricting myself to these two theories means (in terms of Parson) leaving out influence
strategies that are directed directly at the preferred positions of the voters. Both theories fit in
a rational choice frame. Both theories assume that the actors know their preferences, and try
(by influencing other actors) to maximize the utility they attach to the outcome of decisions
(i.e. to get an outcome as close to their preferred outcome as possible). These assumption
seem reasonable in the context of collective decision making in policy domains.
The general question of my research project is
In which collective decision making situations does the social exchange theory (the
assumption that actors exchange positions) provide a better description/explanation of the
decision making, and in which collective decision making situations does the theory of
conflict resolution (the assumption of challenging other actors’ positions) provide a better
description/explanation.
3
2 Models of Collective Decision making
2.1 Conflict versus Exchange in Models of Collective Decision Making
In the literature this question is researched by comparing the results of models of collective
decision making, each based on one of the influence strategies.
The question that these comparisons should answer is
To what extent does the relative predictive power of a model based on an Exchange
strategy and a model based on a strategy of Conflict Resolution, vary in different collective
decision-making situations2?
Both the Social Exchange theory and the theory of Conflict Resolution are used to develop
mathematical models of collective decision making. These models are used to predict the
outcome of collective decisions. However, only few of the models are based on assumptions
on the behavior at actor level, and that are the models of interest to me.
2.2 Models based on the theory of Conflict Resolution
The most important model of collective decision making that stems from the theory of
Conflict Resolution is the Expected Utility model of Bueno de Mesquita (Bueno de Mesquita
et al. 1985; Bueno de Mesquita 1994). This model is based on an influence strategy that I call
the Challenge strategy. According to this strategy actors estimate the expected utility of
challenging the voting position of another actor. This expected utility is dependent on the
utility gain of a shift in voting position of the challenged actor, and the chance that the
challenged actor gives in to the challenge. This chance is dependent on the power difference
between the actors. If challenged, the model assumes that actors have to decide whether to
(partly) give in to the challenge, or to withstand the challenge and engage in conflict. This
description shows that the Expected Utility model is based on assumptions on actor level. The
collective outcome is a direct result of simultaneously made individual choices of the actors.
The Expected Utility model is tested at collective level in numerous decision making
situations (Bueno de Mesquita et al. 1985; Bueno de Mesquita and Stokman 1994; Wu and
Bueno de Mesquita 1994; Baarda 1996; Bueno de Mesquita et al. 1996). The results are good.
2.3 Models based on the Social Exchange theory
All exchange models attribute to Coleman’s exchange model (1972). The Coleman model is
based on the variables Control, Events and Interest. Actors are interested in events that are
controlled by other actors (see table 2).
Table 2. Coleman’s model
2
With collective decision making situations I mean distributions over the actors of preferences, saliences, and
capabilities (see section 3.2).
4
are interested in
Actors
that are controlled by
Events
Actors
j=1..m
j=1..n
j=1..n
Events are supposed to be not dividable: actors have to approve or disapprove of an event.
Coleman assumes that the actors exchange control over the events. If actor j1 is interested in
event i1 that is controlled by actor j2, and actor j2 is interested in event i2 that is controlled by
actor j1, the actors can exchange control over the two events, and so are both better off. The
model predicts an equilibrium distribution of control based on the actors’ initial distributions
of control, interest and preferences (pro or contra), and the predicted collective decisions on
the events are then based on that equilibrim distribution.
The main critique on the Coleman model is directed at the lack of dividableness of the
events, and so of control over the events. The Coleman model has been modified by several
researchers (see for example Marsden and Laumann 1977; Laumann et al 1987; Stokman and
Van den Bos 1992; Pappi et al. 1995). For an overview of modifications of the original
model, see Knoke et al. (1996).
The Coleman model and most of its successors are not based on assumptions on behavior
at actor level. The model predicts the distribution of control in the equilibrium state, but it
does not describe which actors exchange control among each other. For this research, I am
interested in an exchange model that uses Coleman’s ideas, but is also based on actors’
choices to engage in an exchange with other actors. Stokman and Van Oosten (1994a)
developed such a model. The problem of dividableness of the exchange component (control
over event) in the Coleman model is treated here by assuming that not control, but voting
positions are exchanged. This enables predictions on decisions with a dichotomous outcome
space. According to the Exchange strategy in the Stokman and Van Oosten model, actors are
able to estimate which exchanges (on which two issues and with which other actor) are
worthwhile and they propose their preferred exchange to the other actor involved in this
exchange. After the proposals are made, the actors are assumed to accept the best proposed
exchange.
2.4 Results of the Expected Utility model and the Exchange model
Stokman and Van Oosten’s Exchange model does not only fit in the Social Exchange theory,
it can also be seen as a reaction to Bueno de Mesquita’s Expected Utility model. The
Exchange model is based on the same input variables as the Expected Utility model (the
preferred positions of the actors, the interest (salience) they have in the outcomes and the
capabilities they can use to influence the decision making). Both the Challenge strategy and
the Exchange strategy are directed at the voting position of other actors: both models assume
that an actor tries to influence the voting positions of other actors in such a way that the
collective outcome comes closer to the outcome she prefers. Furthermore, the two models
5
assume the same scheme of proposing and accepting new voting positions.
Since the Bueno de Mesquita’s Expected Utility model and Stokman and Van Oosten’s
Exchange model are based on the same input variables, it is straightforward to compare the
results of these models (Stokman 1993; Bueno de Mesquita and Stokman 1994; Rojer 1996).
The models, although based on different influence strategies, both appear to predict quite well.
However, the models do not always predict the same outcome. Furthermore, the prediction
errors are not correlated. This could indicate that there are certain differences between
collective decision making situations which determine what assumption about the applied
influence strategy leads to the best prediction.
However, these results also lead to new questions: If the model results are quite similar,
does this mean that it does not matter which strategy is used? How different are the models at
actor level? How different were the theories on which the models are based, if you look at the
actor level? When (in which collective decision-making situations) do the different strategies
lead to different shifts in voting positions?
To get more insight in the differences between the results of the models, we need a more
structured search for data configurations (distributions of preferences, salience and
capabilities) in which the models predict the same results and data configurations in which the
models predict very different results. Although much effort is already put in collecting data on
collective decision-making situations, the available data sets do not provide yet for such a
structured search. Because of this, I use simulated data3. Section 4 presents the research
design for this structured search with simulated data. But first, section 3 describes another
problem (and a solution to this problem) concerning the comparing of results of the Exchange
model and the Expected Utility model.
3 The Challenge model and the Iterative Exchange model
3.1 Introduction
Besides the lack-of-data problem, there is yet another problem concerning the comparing of
results of the Exchange model and the Expected Utility model: the differences in these results
do not have to stem from the difference in applied influence strategy, since the Expected
Utility model and Exchange model differ in more respects than just applied influence strategy.
The models differ is applied decision rule and applied utility function and in other, more
auxiliary assumptions. Because of this, I question whether comparing the results of these two
models is a good way to compare two theories on influences strategies. To study the effect of
the applied influence strategy, the Exchange model and the Expected Utility model have to be
modified in such a way that they only differ in this respect.
These modifications lead to the Iterative Exchange model and the Challenge model (for
3
Of course, computer simulations can only indicate in which collective decision-making situations the models
give different results. To get insight in the predictive power of the model, the predicted outcomes have to be
compared with real outcomes.
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these modifications and for more details, see Achterkamp 1997). The Iterative Exchange
model is an elaboration of Stokman and Van Oosten’s Exchange model, the Challenge model
is based on Bueno de Mesquita’s Expected Utility model. The Iterative Exchange model and
the Challenge model only differ in assumed influence strategy and both can be considered as
special cases of a General model of collective decision making.
3.2 Model variables and assumptions
Both the Iterative Exchange model and the Challenge model use the following input variables;
for every issue and for every actor: the actors’ preferred outcomes, or preferred positions; the
interest they have in the outcomes, or their saliences; and their potential power, or
capabilities.
Both models assume that actors are rational and aim at maximizing the utility these actors
attach to decision outcomes. They assume that (1) the issues are unidimensional and (2) actors
have a single-peaked utility function. The utility for an actor i of the expected outcome is
dependent on the distance between the expected outcome and the actor’s preferred position
and on the salience the actor attaches to this issue. Both models assume that actors can
influence the collective outcome by influencing each other. Actors try to force other actors to
change their voting position (that is the alternative they vote for) in such a way that the
expected outcome of the decision will move closer to the influencer’s preferred outcome. If
an influence attempt succeeds, the influenced actor has to leave his preferred position. The
voting position of actor i on issue a at time t is the position the actor is forced to or decides to
take at time t.
3.3 Algorithm
The algorithm of both models can be stated as follows: The actors estimate the expected
outcomes on the basis of their assessment of the voting positions, capabilities and saliences of
the other actors. They evaluate these expected outcomes, and then make use of their power
(capabilities times salience) in trying to influence other actors in such a way that those actors
will take a voting position closer to the influencer’s preferred position. The actors take their
new voting positions and estimate the new voting positions of the other actors, and re-estimate
the expected outcome. These steps are repeated until the differential change in expected
outcomes becomes marginal.
This algorithm fits in the scheme for models of collective decision making as stated by
Stokman and Van Oosten (1994b). This scheme divides models of collective decision making
into five steps:
1. Actor Decision Analysis: The actors determine their utility function.
2. Domain Evaluation: The actors interact to obtain information on the utility functions of
the other actors and use this information to estimate the expected collective outcome.
3. Proposal Utterance: The actors decide which actors they should influence in order to get
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a collective outcome closer to their preferred position and propose a change in voting
position to these actors.
4. Proposal Effectuation: The actors evaluate the proposals they got in the previous step.
They accept the proposals of which they expect the most positive (or least negative)
effects on the collective outcome and change their voting positions according these
proposals. The new expected collective outcome is estimated on the basis of the new
voting positions.
Step 3 and 4 are repeated until a model dependent criterion is fulfilled.
5. Decision Taking: A decision rule is used to determine the predicted collective outcome.
3.4 Step 3 and 4 in the Iterative Exchange model
The proposals in the Iterative Exchange model are exchanges of voting positions. Exchanges
involve two actors (say ego and alter) and two issues. The issue on which ego is willing to
give in at the exchange is labeled ego’s supply issue, and the issue on which ego hopes to gain
from a surrender by alter is labeled ego’s demand issue. The model assumes that an actor can
determine which exchanges are worthwhile, and that he proposes the exchange that provides
him the largest utility gain. An actor is free to accept the proposed exchange, so an exchange
is only possible if both actors are better off after the exchange. Actors accept the offer that
provides them with the highest utility gain. An accepted exchange means that both actors
change their voting position on their supply issue.
3.5 Step 3 and 4 in the Challenge model
The proposal assumed in the Challenge model is a challenge by ego of alter’s voting position.
The Challenge model is based on the assumption that actors will propose those challenges
from which they expect utility gain.
Ego’s expectation about the gain in utility resulting from a challenge depends on ego’s
estimation of the chance that alter will give in to the challenge without conflict, and the
chance that, if alter responds with a conflict, ego will win. If actors enter a conflict, the model
assumes that in estimating the probability of success, both actors take into account the support
of other actors for their proposal in comparison with their rival’s alternative proposal. If ego’s
expected utility of challenging alter is positive, ego regards it worthwhile to challenge alter on
this issue. If alter is challenged by ego, three options arise:
I. Conflict: A conflict occurs if alter also expects a gain in utility from challenging ego.
Neither of the actors is willing to change his voting position.
II. Give-in: A give-in situation occurs if alter expects no gain from challenging ego and is
willing to give in by adopting ego's voting position. This is the case when the expected
utility loss of alter on challenging ego is larger than the expected utility gain of ego on
challenging alter.
III. Compromise: A compromise situation occurs if alter expects no gain from challenging
ego, but is not willing to give in to ego’s wishes completely. This happens if the expected
8
utility loss of alter on challenging ego is smaller than the expected utility gain of ego. The
new voting position of alter lies between alter's old position and ego's position.
4 Comparing the Challenge model and the Iterative Exchange model using
computer simulations: design
4.1 Questions and models
The question that I want to answer using the computer simulations is
To what extent does the relative predictive power of the Iterative Exchange model and the
Challenge model vary in different collective decision-making situations?
However, since the models on which these models are based often predict similar outcomes, it
is also questionable whether the good model predictions of both models should be attributed
to ‘realistic’ modeling of an influence strategy or to the very detailed data. It could be that the
outcome is already comprised in the values of the variables preferences, salience and power.
So a question that should be answered before answering the research question is the question
to what extent the predictive power of a model that assumes an influence strategy differs from
a model that assumes no influence at all. The Iterative Exchange model and the Challenge
model should not only be compared to each other, but also to a base model (‘null model’) that
is based on the same input variables.
I compare the following models:
 Base model 1: Mean of preferred positions
 Base model 2: Weighted mean of preferred positions, weighted by capabilities
 Base model 3: Weighted mean of preferred positions, weighted by capabilities times salience
 Challenge model
 Iterative Exchange model
4.2 Dependent variable
I compare the predictions of these models. The dependent variable I use is the deviation-score
between predictions of two models (first: between a one-strategy model and a base model;
second: between models with different influence strategies).
I have to standardize for ‘maximal possible deviation’ on an issue. One idea is to use a
standardizing based on standard deviation or variance of the preferred positions. However,
such a standardizing is dependent on the distribution of the preferred positions, and might
conceal the effect of this distribution on the difference-score. So instead I use the following
standardizing.
 Let xla and xra be the extremes on the scale of preferred positions on issue a:
9
x la =
MIN ( x
ia
( t 0 ))
MAX ( x
ia
( t 0 ))
i=1..n
x ra =
(1)
i=1..n
 Let mdlk(Ya(T)) be the outcome as predicted by model mdlk.
 The difference-score on issue a I plan to use is
| mdl1 ( Y a (T)) - mdl 2 ( Y a (T))|
Da ( mdl1 , mdl 2 ) =
x ra - x la
(1)
A model predicts outcomes on all issues in the set. Since a change in (for example) salience
distribution on one issue will also have effects on the Iterative Exchange model’s outcome on
a second issue, I have to combine the differences per issue into a difference over all issues.
Since the number of issues in a set is also an independent variable, I cannot use the sum of the
scores.
The scores on the separate issues can be combined in several ways:
1. The mean of the scores on the seperate issues.
D( mdl 1 , mdl 2 ) =
2.
1
m
m
 D ( mdl
a
1
, mdl 2 )
(1)
a=1
The mean squared difference.
1
MSD( mdl 1 , mdl 2 ) =
m
m
 ( D ( mdl
a
1
, mdl 2 ))2
a=1
(1)
4.3 Issue classification
In the computer simulations the following will be varied:
 The distribution of salience and capability over preferred positions.
 Number of actors. (Note that the challenge model requires at least three actors.)
 Number of issues. (Note that the iterative exchange model requires at least two issues.)
Distributions
I restrict myself to the following types of distributions of salience and capability over the
preferred positions:
1. Homogeneous distribution
10
2. Increasing / decreasing value
3. One-top distribution
4. Two-top distribution
11
Note that
 to classify an issue, we need to indicate both a salience distribution and a capability
distribution;
 the positions of the q’s and x’s should be varied. The values of the x’s indicate the
distribution of preferred positions over the actors.
Table 1 stated the issue-types that I use. The table shows 18 types. Within these types the
values of the p’s and x’s have to be varied.
Table 1: Issue Classification
distribution of
saliences
capabilities
1/1
homogeneous
homogeneous
1/2
homogeneous
increasing
1/3
homogeneous
1/4
distribution of
saliences
capabilities
2/1
increasing
homogeneous
one-top
3/1
one-top
homogeneous
homogeneous
two-top
4/1
two-top
homogeneous
2a/2a
increasing
increasing
2a/2b
increasing
decreasing
decreasing
increasing
2/3
increasing
one-top
3/2
one-top
increasing
2/4
increasing
two-top
4/2
two-top
increasing
3/3
one-top
one-top
3/4
one-top
two-top
4/3
two-top
one-top
2b/2a
12
4/4
two-top
two-top
Number of actors
For a distribution of type 1 or 2 (homogeneous or decreasing/increasing) at least two actors
have to be involved in the decision making; type 3 (one-top) requires at least three actors;
type 4 at least five actors. A question is: What is the effect of an extra actor in a distribution?
Compare sets with 2 (only the exchange model is applicable), 3, 4, 5 and 10 actors.
Number of issues
The exchange model requires at least two issues. The challenge model treats the issues
separately. Compare sets with 2, 5 and 6 issues. (2 as minimum, 5 and 6 to study the effect of
an even or odd number of issues.) A set of issues can consist of issues of the same type, or
issues of different types.
5 Comparing the Challenge model and the Iterative Exchange model using
computer simulations: results
I am working on section of the paper.
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