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Register a new userAlgorithmic Techniques for Necessary and Possible Winners
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Added by
Vishal Chakraborty
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm of Xia and Conitzer. In the case of the possible winners, where the problem is NP-hard, we give a natural reduction to Integer Linear Programming (ILP) for all positional scoring rules and implement it in a leading commercial optimization solver. Further, we devise optimization techniques to minimize the number of ILP executions and, oftentimes, avoid them altogether. We conduct a thorough experimental study that includes the construction of a rich benchmark of election data based on real and synthetic data. Our findings suggest that, the worst-case intractability of the possible winners notwithstanding, the algorithmic techniques presented here scale well and can be used to compute the possible winners in realistic scenarios.
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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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