Elections with Limited Information; A Fulfilled Expectations Model Using Contemporaneous Poll and Endorsement Data as Information Sources

Abstract

"This paper is one of several papers in which we develop and test models of 2 candidate elections under extremely decentralized and incomplete information conditions. We assume candidates do not know voter utility functions, and that most voters do not observe the policy positions adopted by the candidates. We assume that uninformed actors (voters and candidates alike ) have 'beliefs' about parameters of which they are uninformed, and that they attempt to inform these belief s on the basis of readily observable variable s endogenous to the system. Specifically, in this paper, we assume that uninformed actors inform their beliefs, and hence condition their behavior, on the basis of contemporaneous poll and (binary) endorsement data. An equilibrium is defined to be a set of strategies , together wit h a set of beliefs, such that all actors are maximizing expected utility subject to their beliefs, and such that no actor wants to revise his beliefs conditional on the information he does observe. This paper develops the above model only for the case of a one dimensional policy space with symmetric single peaked preferences. When the electorate is modeled as being infinite, with the cumulative density of ideal points for both informed and uninformed voters being invertible, we show that regardless of the number of informed voters in an equilibrium , the candidates behave exactly as if all voters had information. They respond to the preferences of the uninformed as well as the informed voters, ending up at the median ideal point of the entire electorate. Further, we show that regardless of candidate behavior, if voters are in equilibrium , their votes will extract all available information, in the sense that all voters, informed and uninformed alike, will vote as if they had perfect information about candidate positions. Finally, we give a dynamic for convergence of voting behavior, which shows that the model implies a 'bandwagon' effect, with the speed of convergence depending on the ratio of the density of informed to uninformed voters at the true candidate midpoint. In addition to the theoretical results, we run some experiments to test the implications of the model. The experiments show a moderate degree of support for the model."