We investigate the extent to which it is possible to evaluate the probability of a particular candidate winning an election, given imperfect information about the preferences of the electorate. We assume that for each voter, we have a probability distribution over a set of preference orderings. Thus, for each voter, we have a number of possible preference orderings-we do not know which of these orderings actually represents the voters' preferences, but we know for each one the probability that it does. We give a polynomial algorithm to solve the problem of computing the probability that a given candidate will win when the number of candidates is a constant. However, when the number of candidates is not bounded, we prove that the problem becomes #P-Hard for the Plurality, Borda, and Copeland voting protocols. We further show that even evaluating if a candidate has any chance to win is NP-Complete for the Plurality voting protocol, in the weighted voters case. We give a polynomial algorithm for this problem when the voters' weights are equal. Copyright © 2008, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.
CITATION STYLE
Hazon, N., Aumann, Y., Kraus, S., & Wooldridge, M. (2008). Evaluation of election outcomes under uncertainty. In Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS (Vol. 2, pp. 941–948). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).
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