Stump COMPUTATIONAL ASPECTS OF APPROVAL VOTING AND DECLARED - STRATEGY VOTING

COMPUTATIONAL ASPECTS OF APPROVAL VOTING AND DECLARED-STRATEGY VOTING by Robert Hampton LeGrand III ADVISOR: Professor Ron K. Cytron December, 2007 St. Louis, Missouri Designing a protocol for collective decision-making is made difficult by the possibility of manipulation through insincere voting. The traditional plurality system suffers from this problem; approval voting addresses it by allowing voters to approve of both compromise and favorite alternatives. However, the specific nature of rational approval strategies has not been adequately studied. This research explores three different aspects of strategy under approval-voting systems, from chiefly a computational viewpoint. Declared-Strategy Voting (DSV) aims to minimize manipulation opportunities by capturing rational voters’ strategic thinking and applying it according to their preferences over the available alternatives. When rational strategies are employed on behalf of the voters, the playing field is leveled for all voters. Approval voting is a natural fit for use with DSV, but, unlike plurality voting, there is no extant theory regarding the most effective approval strategies in a DSV context. We propose such a theory. The minimax procedure is a multiwinner form of approval voting that aims to maximize the satisfaction with the outcome of the least satisfied voter. Unfortunately, computing the minimax winner set is computationally hard. We propose an approximation algorithm for this problem, a framework for polynomial-time heuristics that perform very well in practice, and a preliminary analysis of strategic voting under minimax. When there is only one alternative, for which each voter has an ideal final average approval level, a rational voter’s approval or disapproval will sometimes be insincere so as to move the result in a desired direction. A nonmanipulable protocol would allow indication of a voter’s ideal outcome and would never reward an insincere such indication. We present two such nonmanipulable protocols, one motivated by the DSV concept, and we propose to analyze and extend them to outcome spaces of higher dimension.