Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders

Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a voting rule, a profile of partial orders, and an alternative (candidate) c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. Each of these two problems is further divided into two sub-problems: determining whether c is a unique winner (that is, c is the only winner), or determining whether c is a co-winner (that is, c is in the set of winners). We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We completely characterize the complexity of possible/necessary winner problems for the following common voting rules: positional scoring rules, Copel...

• Type: Conference
• Year: 2008
• Where: AAAI
• Authors: Lirong Xia, Vincent Conitzer
• Keywords: AAAI 2008, Intelligent Agents, Linear Order, Partial Orders, Voting Rules