Princeton University

School of Engineering & Applied Science

Quantitative Analysis of Strategic Voting in Anonymous Voting Systems

Tiance Wang
Engineering Quadrangle B327
Tuesday, November 10, 2015 - 11:30am to 1:00pm

Democratically choosing a single preference from three or more candidate options is not a straightforward matter. The behavior of voters voting dishonestly in order to gain better outcomes for themselves is known as strategic voting, or manipulation. For example, a voter realizing that her favorite candidate probably cannot win may instead cast the vote for her second favorite. Strategic voting undermines the credibility of the election outcome and turns voting into a game. People are thus interested in finding voting rules that are resistant to strategic voting. However, the Gibbard-Satterthwaite theorem implies that no fair voting system (equality among voters and equality among candidates) is completely immune to strategic voting. This dissertation is a quantitative analysis of strategic voting from a geometric perspective.
Anonymous voting rules, where all voters are equal, can be viewed as a partition of a high dimensional polytope into different regions. It is revealed that the orientation of the partition boundaries determines whether strategic voting is possible. This result helps measuring the vulnerability to strategic voting of different voting rules, as well as designing voting rules resistant to strategic voting. We show that Condorcet methods (where a candidate wins the "pairwise match" against any other candidate) are categorically more resistant to strategic voting than many other popular voting systems, including plurality and Borda count, due to their maximal use of pairwise comparisons to determine the winner. We verify our results on voting data we collected through an online survey on the 2012 US President Election.
We also explore how public opinion shifts as a result of strategic voting. Assuming all voters want to manipulate and have the right to change their votes for many times, we conclude that strategic voting in effect transforms plurality into instant run-off voting, and transforms Borda count to a Condorcet method.