In defense of exclusionary deliberation: Communication and voting with private beliefs and values

We analyze strategic communication and voting when agents do not necessarily have common beliefs and values. The potential for some pairs of participants to have opposed preferences makes truthful revelation difficult to support. Nonetheless, truthful equilibria are shown to exist for some parameterizations in which non-common values are likely. Truthful equilibria exist if and only if participants of all possible preference types are optimistic that a majority of the group has their preference type. In settings in which truthful equilibria exist for all population sizes, asymptotic efficiency attains. The probability that the collective choice corresponds to that which a majority would choose with full-information approaches one as population size tends to infinity. In many settings, however, truthful equilibria exist only for small groups. In these cases, we characterize a natural partially revealing equilibrium; asymptotic efficiency fails in these equilibria. Interestingly, we find that larger groups need not outperform smaller groups as truthful equilibria are easier to support with small deliberative bodies. Thus, the design of deliberative institutions involves a trade-off between the statistical benefit of more participants and the difficulty in supporting information transmission in larger settings. For many reasonable cases, the latter effect is dominant and excluding randomly chosen participants is desirable.