[This paper proves that for majority voting over multidimensional alternative spaces, the majority rule intransitivities can generally be expected to extend to the whole alternative space in such a way that virtually all points are in the same cycle set. In other words, given almost any two points in the alternative space, it is possible to construct a majority path which starts at the first, and ends at the second. It is shown that for the intransitivities not to extend to the whole space in this manner, extremely restrictive conditions must be met on the frontier (or boundary) of the cycle set. Similar results are shown to hold for any social choice rule derived from a strong simple game. These results hold under fairly weak assumptions on individual preferences: individuals need only have continuous utility representations of their preferences such that no two individuals' preferences coincide locally. The results seem to rule out the possibility, at least in models of interest to economists, of using the transitive closure of the majority relation as a useful social choice function. They also imply that under any social choice rule meeting the conditions assumed here, it is generally possible to design agendas based on binary procedures which will arrive at virtually any point in the alternative space, even Pareto dominated points.]

[This paper considers the impact of certain types of policy related voting patterns on the existence and location of equilibrium strategies in the spatial model of two-candidate competition. In contrast to much of the previous literature, this paper makes a distinction between the aggregate level patterns of voting and the individual level variables which bring them about. By so doing the assumptions can focus on objects which have a more direct empirical referent, namely, the aggregate level support function and the distribution of ideal points. Using this approach, sufficient conditions are found for the existence of equilibrium which, although themselves strong, make considerably weaker demands on individuals than have been generally assumed in the literature. Thus, it is not necessary that each voter vote strictly with regard to policy but, rather, it is sufficient that in the electorate as a whole there is a moderate amount of policy related voting. Other results of the analysis are that policy related voting of any type seems to encourage candidates to converge towards the center, with support from extremists only accentuating this tendency. It is the candidate's most loyal supporters who seem to have the least influence over his policy position.]

This paper reports on an experimental study of-the way in which individuals make inferences from publicly available information. We compare the predictions of a theoretical model of a common knowledge inference process with actual behavior. In the theoretical model, "perfect Bayesians," starting with private information, take actions; an aggregate statistic is made publicly available; the individuals do optimal Bayesian updating and take new actions; and the process continues until there is a common knowledge equilibrium with complete information pooling. We find that the theoretical model roughly predicts the observed behavior, but the actual inference process is clearly less efficient than the standard of the theoretical model, and while there is some pooling, it is incomplete.

Previous analyses have shown that if a point is to be a core of a majority rule voting game in Euclidean space, when preferences are smooth, then the utility gradients at the point must satisfy certain restrictive symmetry conditions. In this paper, these results are generalized to the case of an arbitrary voting rule, and necessary and sufficient conditions, expressed in terms of the utility gradients of "pivotal" coalitions, are obtained.

This paper investigates the effect that common knowledge of public information has on individual beliefs. We assume that n individuals start with the same prior beliefs over a finite probability space, and then each observes private information. We prove that if an admissible statistic of their posterior probabilities of an event becomes common knowledge, then everyone's posterior probabilities for that event must be the same. The class of admissible statistics includes any statistic which is an invertible function of a stochastically monotone function. We also prove that if information partitions are finite, an iterative procedure of public announcement of the statistic-where the statistic is publicly announced and then individuals recompute posterior probabilities based on their previous information plus the announced value of the statistic-converges in a finite number of steps to the common knowledge situation described above. The result has applications to asymmetric information models in economics, where private information becomes incorporated into an aggregate, publicly observed statistic such as a price or quantity in a market.

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We provide a theorem giving a set of conditions under which public observation of an aggregate of individual expectations leads to consensus. The key concept unkerlying the result is that of common knowledge, as formalized by Aumann (1976)