Voting is a popular method of selecting a political leader or representatives in peoples social lives. Social choice theory systematically studies such preference aggregation methods. One of the problems that social choice theorists care most about is voter manipulation. The Gibbard-Satterthwaite impossibility theorem states that there is no reasonable social choice function that is free from voter manipulation. In an election it is not only voters who can think strategically, but also the candidates. In this thesis, we study the strategic behaviors of a candidate in two scenarios: voting with partial information, and open-list proportional representation.

Traditional social choice theory assumes that voters preferences are total orders on the set of candidates. Voting with parti...[ Read more ]

Voting is a popular method of selecting a political leader or representatives in peoples social lives. Social choice theory systematically studies such preference aggregation methods. One of the problems that social choice theorists care most about is voter manipulation. The Gibbard-Satterthwaite impossibility theorem states that there is no reasonable social choice function that is free from voter manipulation. In an election it is not only voters who can think strategically, but also the candidates. In this thesis, we study the strategic behaviors of a candidate in two scenarios: voting with partial information, and open-list proportional representation.

Traditional social choice theory assumes that voters preferences are total orders on the set of candidates. Voting with partial information studies what happens before an election when voters' preferences are given by partial orders, and the outcome of the election may still be open. In this case, a candidate may be interested in knowing if it is still possible for him to win, and if so, how. To address these problems, we consider various forms of queries where candidates can query voters to elicit their preferences and a minimal sets of such queries to ask in order to determine the outcome of the election with respect to the candidate. Our main technical results are that for pair-wise comparison queries, there is a unique minimal set and to compute such a minimal set, is in general, computationally hard.

Another setting is open-list proportional representation, where candidates or political parties need to think strategically. In this thesis we consider open-list proportional representation used in the context of the Hong Kong Legislative Council Geographical Committee election. In this election, voters vote on lists of candidates. The strategies of the parties are to make up lists of candidates, either on their own or with other parties so as to win the maximum number of seats. In this thesis we consider the simple case of just two parties, and model the election as a competitive game between the two parties, characterizing their strategies and analyzing the equilibrium of the game. Our main results are that this game has a pure strategy Nash equilibrium, but to compute this equilibrium is in general intractable.