Vulnerability of Voting Paradoxes As a Criteria For Voting Procedure Selection

Abstract

Correct aggregation of individual preferences into collective one is central problem of nowadays Social Choice theory. After the Arrow’s and Gibbard–Satterthwaite impossibility theorems it became clear that our desire to justify an electoral procedure is doomed to failure. At the same time a lot of scholars continued exploring different properties of existing voting rules and constructing the new ones. Contemporary research in this area explore two main properties of aggregation procedures — their degree of manipulability and computational complexity of manipulation. Quantitative evaluations of these properties tend to be main criteria of voting procedure selection. But last decades it turned out that another threat for theory of voting is incompatibilities and unexpected outcomes of different kind, usually called paradoxes. This article provides complete systematization of voting paradoxes known for today. We also presented an attempt to formulate a complete proof of the (in)stability of seven most common used voting rules to paradoxes of any type, which had not been undertaken before. Our results show that different voting procedures are qualitatively different in the sense of vulnerability to voting paradoxes which makes reasonable to propose additional criteria of voting procedure selection and opens the gate for further quantitative research.