Most Expected Winner: An Interpretation of Winners over Uncertain Voter Preferences
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It remains an open question how to determine the winner of an election given incomplete or uncertain voter preferences. One solution is to assume some probability space for the voting profile and declare the candidates having the best chance of winning to be the (co-)winners. We refer to this as the Most Probable Winner (MPW). In this paper, we propose an alternative winner interpretation for positional scoring rules - the Most Expected Winner (MEW), based on the expected performance of the candidates. This winner interpretation enjoys some desirable properties that the MPW does not. We establish the theoretical hardness of MEW over incomplete voter preferences, then identify a collection of tractable cases for a variety of voting profiles. An important contribution of this work is to separate the voter preferences into the generation step and the observation step, which gives rise to a unified voting profile combining both incomplete and probabilistic voting profiles.
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