Self-interest and fairness in coalition formation: A social utility approach to understanding partner selection and payoff allocations in groups

Abstract

In this chapter we present a social utility approach to coalition formation. The central tenet of our approach is that outcome allocations and partner selection in multiparty situations are affected by self-interest and fairness. Inspired by the social utility model we argue that the relative weight assigned to both components is affected by structural aspects of the situation and individual characteristics of the negotiators. We first investigate how coalition bargainers substantiate their coalition demands. We show that bargainers are self-serving in their choice of allocation rules, indicating that perceptions of fairness can be coloured by self-interest. Second, we investigate how the alignment of self-interest and fairness fosters the formation of coalitions that maximise the payoffs of its members. Finally, we present a series of experiments that expands the notion of being fair to those who are excluded from a coalition. We show that bargainers are reluctant to benefit themselves when this harms the outcomes of others and that this is dependent on personal factors (e.g., social value orientations), situational factors (e.g., the valence of outcomes), and whether bargainers negotiate in an interindividual or in an intergroup setting.

Keywords:

• Coalition formation
• Fairness
• Multiparty negotiation
• Social exclusion

Acknowledgments

This research was supported by a Veni grant NWO-451-04-069 from the Netherlands Organisation for Scientific Research awarded to Ilja Van Beest. We would like to thank Colett van Laar for proofreading our manuscript.

Notes

¹In all studies participants were informed that their experimental pay was based on bargaining performance. In many experiments we instructed participants that obtaining a good bargaining outcome maximised their chances of winning 50 euros in a lottery that would be held after the experiment was completed (Van Beest, Andeweg, Koning, & Van Lange, in press; Van Beest et al., 2004a, Experiment 2; Van Beest et al., 2004b, Experiment 1 to 3; Van Beest, Wilke, & Van Dijk, 2003, Experiment 2). In some studies we did not use a lottery, and after the experiment ended we informed participants that they would get a flat fee instead (Van Beest, Van Dijk, De Dreu, & Wilke, 2005, Experiment 1; Van Beest et al., 2004a, Experiment 1; Van Beest et al., 2003, Experiment 1). Finally in Experiment 2 of Van Beest et al. (2005) participants got exactly what they obtained during bargaining. Given that these differences in incentive schemes did not alter the way participants negotiated, we feel safe in assuming that participants do not bargain differently when they bargain about points that are translated into chances of winning a bonus, or when they bargain about real money.

²Minimum resource theory (Gamson, 1961) is based on two assumptions. The first assumption is that players want to maximise their share of the reward. The second assumption is that players will allocate the reward in proportion to resources. Combining both assumptions, the theory predicts the formation of a coalition that minimises the total number of resources of its members, because it maximises the reward of its members. Minimum power theory (Gamson, 1964) is based on an extension of Shapley and Shubik's (1954) index of pivotal power. A player's pivotal power is defined as the relative frequency with which his or her resources, when added to the resources of other players, convert a non-winning coalition (a non-winning coalition is a coalition that does not control at least a majority of the resources) into a winning coalition. This measure equals P/N!, where N! is the total number of permutations (all possible orders of entry of players into a coalition) and P is the number of permutations in which a player is pivotal. Similar to minimum resource theory, players are assumed to maximise their share of the reward, but this time it is assumed that players allocate the reward in proportion to their pivotal power. As a result, the coalition that minimises the sum of pivotal power indices is most likely to form. The weighted probability model is a refinement of minimum power (Komorita, 1974). The basic assumption of the weighted probability model is that large coalitions (in terms of number of players) are more difficult to form than small coalitions. The theory assumes that the probability of a coalition is an inverse function of its size, and predictions of reward allocation among the coalition members are based on the probability of an individual being included in a coalition. A player's probability of being included is equal to the number of times he or she can be a member of a coalition.

³A more specific example of such an allocation problem is the 1998 general elections in the Netherlands. In this year three parties wanted to form a government but learned that the number of available seats in cabinet was not enough to satisfy the demands of all the parties. After some haggling, the smallest party threatened to break up the negotiation if they did not get the number of seats they felt they were entitled to. In the end the problem was solved by creating a new seat in cabinet.

⁴We are aware that coalitions are sometimes formed with the explicit purpose of reducing the outcomes of others. For insights on these situations we refer the reader to research on revolutionary coalitions that investigates how low-status members may form revolutionary coalitions to hurt the payoffs of high-status members (e.g., Lawler, 1995; Michener & Lawler, 1971).

⁵Similar to other research comparing individual and group behaviour, we used dyads to manipulate groups and not triplets or more. One reason was that previous research on the discontinuity effects established that competitiveness increases greatly as one moves from one-on-one interaction to two-on-two interactions, but slightly as one moves from two-on-two interaction to three-on-three interaction (Wildschut et al., 2003). Another reason was that we did not want to complicate our research by using a nested coalition design. Using triplets or more as a group manipulation has the disadvantage that party members may form within-party coalitions to establish what course of action to take. That is, if more than two party members are involved one has to establish a majority decision rule, whereas in the current version all members had to agree about what decision they wanted to make.