Strategic Manipulation in Voting Systems

In this thesis, we are going to study the strategic manipulation of voting rules, mostly scoring rules. In the first part, we focus on naive manipulation, where we have a coalition of manipulators and the other voters vote sincerely. In Section 1.4 we introduce a new measure of manipulability of voting rules, which reflects both the size and the prevalence of the manipulating coalitions and is adaptable to various concepts of manipulation. We place this measure in a framework of probabilistic measures that organizes many results in the recent literature. We discuss algorithmic aspects of computation of the measures and present a case study of exact numerical results in the case of 3 candidates for several common voting rules. In Section 1.5 we study manipulability measures as power indices in cooperative game theory. In Chapter 2, we study the asymptotic behaviour of a model of manipulation called safe manipulation for a given scoring rule under the uniform distribution on voting situations. The technique used is computation of volumes of convex polytopes. We present explicit numerical results in the 3 candidate case. In the second part of the thesis, we adopt a game-theoretic approach to study strategic manipulation. We try to explore more behavioural assumptions for our voters. In Chapter 3, we have an introduction to voting games and different factors such as the available amount of information, voters’ strategies and