18 September 2009, Computational Social Choice Seminar, Ulle Endriss
Most voting procedures will not always return a single election winner, but instead occasionally produce a tie, in which case the election outcome will be a set of candidates. Therefore, when we want to analyse the incentives of voters participating in an election operating under such a voting procedure, we need to be able to reason about their preferences over sets of candidates, rather than just over individual candidates. This is why the question of what constitutes appropriate principles by which to extend a preference order defined on a set to its powerset is an important one in social choice theory.
In this talk, I want to do three things: (1) present some of the axioms proposed in the literature for formalising principles for extending preferences from sets to their powersets and discuss their appropriateness in various contexts; (2) go through the proof of Kannai and Peleg's seminal result in the area; and (3) show how accepting certain combinations of the aforementioned axioms can allow us to rule out insincere voting under the system of approval voting.