Understanding, evaluating and selecting voting rules through games and axioms

Abstract

The dissertation entitled "Understanding, Evaluating and Selecting Voting Rules Through Games and Axioms" by Danilo Santa Cruz Coelho is composed of four chapters. The introduction is the first one and describes briefly the contents of the following chapters. In Chapter 2, in the context of a probabilistic voting model proposed by Rae (1969), the author investigates the consequences of choosing among threshold voting rules according to the maximin criterion. A threshold voting rule is given by the minimum number of votes needed to approve a proposal of change from the status quo. The author shows that the voting rules that satisfy the maximin criterion are different from the simple majority rule which is the one that maximizes the sum of voter's expected utilities. He provides a characterization of the threshold voting rules that satisfy this criterion as a function of the distribution of voters' probabilities to favour change from the status quo. In Chapter 3, two different game theoretical models that can be induced by the rule of k names are proposed and analysed. A characterization of the set of strong Nash Equilibrium outcomes of each of the games is provided. These characterizations enable the author to discuss the preferences of the players over different variants of the rule of k names. An important part of the rule of k names is the procedure used to screen out the k names to be proposed to the individual who takes the final decision. Six different screening rules which are used in reality by different decision bodies around the world are documented. In Chapter 4, he studies whether these screening rules satisfy stability. A screening rule is stable if it always selects a weak Condorcet set whenever such set exists. He shows that all of the six screening rules violate stability if the voters act not strategically. He then proposes two screening rules which satisfy stability. Finally, he provides two possible justifications for the widespread use of unstable screening rules.

Date of Award	8 Nov 2004
Original language	Undefined/Unknown
Supervisor	Salvador Barberà (Director)