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Towards a Dichotomy for the Possible Winner Problem in Elections Based on Scoring Rules (2010)
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@MISC{Betzler10towardsa,
author = {Nadja Betzler and Britta Dorn},
title = {Towards a Dichotomy for the Possible Winner Problem in Elections Based on Scoring Rules },
year = {2010}
}
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Abstract
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, k-approval, and Borda. Generalizing previous NP-hardness results for some special cases, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSIBLE WINNER is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2, 1,...,1, 0), while it is solvable in polynomial time for plurality and veto.
Keyphrases
scoring rule possible winner problem linear order computational complexity possible winner voting protocol joint decision unbounded number broad class distinguished candidate scoring vector partial order polynomial time partial vote previous np-hardness result pure scoring rule score value prominent example special case unweighted voter realistic setting
