Though deliberation is a critical component of democratic decision-making, existing deliberative processes do not scale to large groups of people. Motivated by this, we propose a model in which large-scale decision-making takes place through a sequence of small group interactions. Our model considers a group of participants, each having an opinion which together form a graph. We show that for median graphs, a class of graphs including grids and trees, it is possible to use a small number of three-person interactions to tightly approximate the wisdom of the crowd, defined here to be the generalized median of participant opinions, even when agents are strategic. Interestingly, we also show that this sharply contrasts with small groups of size two, for which we prove an impossibility result. Specifically, we show that it is impossible to use sequences of two-person interactions satisfying natural axioms to find a tight approximation of the generalized median, even when agents are non-strategic. Our results demonstrate the potential of small group interactions for reaching global decision-making properties.
The study of majority rule dynamics, which is an important part of deliberative decision-making, has also been a long-studied problem. A particular relevant experimental result analyzed the majority rule dynamic in groups of five and showed that the solution concept that performed best (out of 16 considered) was the majority rule equilibrium @cite_16 . Our work is a natural next step of this observation applied to the goal of scaling deliberative decision-making. Namely, given experimental evidence for the ability of small groups to come to consensus on the majority rule equilibrium, how can we use these small groups to make good decisions for larger groups?
@cite_16
2083307720
This article reports the findings of a series of experiments on committee decision making under majority rule. The committee members had relatively fixed preferences, so that the process was one of making decisions rather than one of problem solving. The predictions of a variety of models drawn from Economics, Sociology, Political Science and Game Theory were compared to the experimental results. One predictive concept, the core of the noncooperative game without side payments (equivalent to the majority rule equilibrium) consistently performed best. Significantly, however, even when such an outcome did not exist, the experimental results did not display the degree of unpredictability that some theoretical work would suggest. An important subsidiary finding concerns the difference between experiments conducted under conditions of high stakes versus those conducted under conditions of much lower stakes. The findings in the two conditions differed considerably, thus calling into question the political applicability of numerous social psychological experiments in which subjects had little or no motivation.