Manipulative voting dynamics

In AI, multi-agent decision problems are of central importance, in which independent agents aggregate their heterogeneous preference orders among all alternatives and the result of this aggregation can be a single alternative, corresponding to the groups collective decision, or a complete aggregate ranking of all the alternatives. Voting is a general method for aggregating the preferences of multiple agents. An important technical issue that arises is manipulation of voting schemes: a voter may be to make the outcome most favorable to itself (with respect to his own preferences) by reporting his preferences incorrectly. Unfortunately, the Gibbard-Satterthwaites theorem shows that no reasonable voting rule is completely immune to manipulation, recent literature focussed on making the voting schemes computationally hard to manipulate. In contrast to most prior work Meir et al. [40] have studied this phenomenon as a dynamic process in which voters may repeatedly alter their reported preferences until either no further manipulations are available, or else the system goes into a cycle. We develop this line of enquiry further, showing how potential functions are useful for showing convergence in a more general setting. We focus on dynamics of weighted plurality voting under sequences made up various types of manipulation by the voters. Cases where we have exponential bounds on the length of sequences, we identify conditions under which upper bounds can be improved. In convergence to Nash equilibrium for plurality voting rule, we use lexicographic tie-breaking rule that selects the winner according to a fixed priority ordering on the candidates. We study convergence to pure Nash equilibria in plurality voting games under unweighted setting too. We mainly concerned with polynomial bounds on the length of manipulation sequences, that depends on which types of manipulation are allowed. We also consider other positional scoring rules like Borda, Veto, k-approval voting and non positional scoring rules like Copeland and Bucklin voting system. This thesis is dedicated to my family specially my parents, my grandfather and my uncle who have always stood by me and supported me throughout my life. They have been a constant source of love, concern, support and strength all these years. I warmly appreciate their generosity and understanding.