Determining Possible And Necessary Winners Under Common Voting Rules Given Partial Orders

Abstract

Usually a voting rule or correspondence 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 profile of partial orders and a candidate <i>c</i>, two important questions arise: first, is <i>c</i> guaranteed to win, and second, is it still possible for <i>c</i> to win? These are the <i> necessary winner</i> and <i> possible winner</i> problems, respectively.