Election Score Can Be Harder Than Winner

06/22/2018

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by   Zack Fitzsimmons, et al.

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Election systems based on scores generally determine the winner by computing the score of each candidate and the winner is the candidate with the best score. It would be natural to expect that computing the winner of an election is at least as hard as computing the score of a candidate. We show that this is not always the case. In particular, we show that for Young elections for dichotomous preferences the winner problem is easy, while determining the score of a candidate is hard. This complexity behavior has not been seen before and is unusual. For example, a common slight variant of Young has a hard winner problem for dichotomous preferences, and natural versions of Dodgson and Kemeny for dichotomous preferences have easy score and winner problems.