Group Decision-Making in the Shadow of Disagreement

A model of group decision-making is studied, in which one of two alternatives must be chosen. While group members differ in their valuations of the alternatives, everybody prefers agreement to disagreement. Our model is distinguished by three features: private information regarding valuations, varying intensities in the preference for one outcome over the other, and the option to declare neutrality in order to avoid disagreement. We uncover a variant on the ‘tyranny of the majority’: there is always an equilibrium in which the majority is more aggressive in pushing its alternative, thus enforcing their will via both numbers and voice. Under general conditions, however, an aggressive minority equilibrium inevitably makes an appearance, provided that the group is large enough. The notable exception is the special case of unanimity rule: we show that aggressive minority equilibria may never exist irrespective of group size. Aggressive minority equilibria invariably display a ‘tyranny of the minority’: it is always true that the increased aggression of the minority more than compensates for smaller numbers, leading to the minority outcome being implemented with larger probability than the majority alternative. We fully characterize the asymptotic behavior of this model as group size becomes large, and show that all equilibria must converge to one of three possible limit outcomes.