WHEN WILL THEY EVER MAKE UP THEIR MINDS? THE SOCIAL STRUCTURE OF UNSTABLE DECISION MAKING

Abstract

French (1977), Harary (1959), and Abelson (1964) initiated a prominent line of social influence models to explain social norms or collective decisions from the structure of influence networks. These models fail to generate unstable decision dynamics, a phenomenon that can be observed in collective decision-making. To capture instability, we assume that decision-makers raise their level of salience to reduce expected losses from decision-outcomes. Our model generates persistently unstable outcome patterns under conditions related to the social network and to intolerance for expected losses. A 6-actor example reveals stable outcomes for low intolerance, complex oscillations for intermediate levels of intolerance, and simple and regular oscillation for high intolerance. We discuss implications for the predictability of collective decision-making.

Keywords:

• Opinion formation
• Social networks
• Collective decision-making
• Non-linear behavior
• Chaos theory

∗Author names are chosen in alphabetical order based on equal contributions to this work. We thank Patrick Doreian, Frans Stokman and two anonymous reviewers for their useful suggestions. The research of Andreas Flache has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. Earlier versions of this paper were presented at the ISA XIII World Congress of Sociology, Bielefeld, Germany, July 18–23, 1994; at the International Conference on Collective Decision and Policy Making, Groningen, The Netherlands, June 21–22, 1999; and at the 4th Summer School on Polarization and Conflict, San Sebastián, Spain, July 23–27, 2001.

Notes

¹We use the concepts of “group norm” and “decision-outcomes” as well as the concepts of “opinions” and “policy positions” interchangeably throughout this paper. Group norms and opinions refer to the interpretation of influence models in terms of opinion formation, whereas policy positions and decision-outcomes refer to the interpretation of influence models in terms of collective decision making.

²With the exception of particular degenerate cases, for example, the case in which at least two group members can influence each other, but none of them is able to influence himself. This would imply that they permanently cycle forth and back between each other's opinions. To avoid this complication, we exclude throughout this paper the case that group members have no self influence.

³This is different for the more recent influence model proposed by Friedkin (1999, 2001), who assumes that in adopting a new opinion, group members with self-influence take into account their initial opinion throughout the entire influence process. As a consequence, the Friedkin model predicts that some level of disagreement will remain as long as group members have self-influence and disagree initially, even in a fully connected network.

⁴A second motivation to move towards a more backward-looking model of opinion change is the recent criticism of game theoretic “reflexive rationality of actors anticipating each other's choices” (Scharpf 1990, 71). Authors such as Simon contend that this is a model of cognition that is at best a prescriptive model of how choices ought to be made, but one that bears little resemblance to actual decision-making, even by business firms where this forward-looking calculated rationality seems most plausible (Simon 1992, 36).

⁵Substantively, the central assumptions of our model are also compatible with Abelson's approach. However, there is a technical difference. Following French and Harary, we conceive of social influence as a time-discrete process. Abelson instead assumes a continuous process, using a differential equation model.

⁶If the opinions in the standard model are interpreted as policy positions, the model would predict an outcome of group decision making which is the average position of all group members, of course under the condition that the influence weights y _ij all are equal. In fact, the average policy position is used in models of collective decision making as a variant to Duncan Black's median voter theorem. For example, the two-stage model of collective decision making developed by Stokman and Van den Bos (1991) is functionally equivalent to French's standard model of opinion formation.

⁷In fact, Abelson incorporates into the standard model the concepts of (a) actor preferences and (b) their interests in substantive policy issues. Abelson acknowledges the personal advice of James Coleman who, at that moment, was working on models of political exchange.

⁸The intolerance parameter corresponds with Stokman and Stokman's (1995) parameter r for a “risk taking propensity” (294).

⁹Our analysis generalizes to “stubborn subgroups” which are fully connected subgraphs that can not be accessed from their complement in the network but who contain at least one member that has influence upon a node in the complement. For simplicity, we identify in the following “stubborn subgroups” with stubborn actors.

¹⁰The only exception occurs when every actor with access to the extreme positions is simultaneously fully satisfied with the outcome. In that case, they have either already adopted the extreme positions or at least some of these actors will be pulled towards the extreme positions, which in turn changes the outcome and increases their frustration in the next round.

¹¹For this it would be necessary to obtain an analytical proof that for the given parameters the system will never converge. A more general analytical proof would shed light on the question whether indeed a discontinuity occurs between τ = 3 and τ = 4 despite the fact that our system is very simple. Such a result still eludes us.

¹²More precisely, below τ = 2.8 the dynamics of opinion formation are characterized by unstable polarization, where opinions stabilize into an stable individual opinion within 20 influence rounds.