Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules

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, if 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 and providing new many-one reductions, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voter...

• Type: Conference
• Year: 2009
• Where: MFCS
• Authors: Nadja Betzler, Britta Dorn
• Keywords: Linear Order, MFCS 2009, POSSIBLE WINNER, Scoring Rule