Voting Systems for Social Choice

Abstract

Voting systems are ways of resolving conflicts, choosing candidates, selecting policy options as well as of determining winners or rankings of competitors in various contests. There are other methodological approaches to tackle these problems: conflict analysis methods (See the chapter by Kilgour and Hipel, this volume), group decision support systems (See the chapter by Ackerman and Eden, this volume), soft computing methods (See the chapter by Carlsson, this volume), multicriteria decision analysis (See the chapter by Salo and Hämäläinen, this volume) and game-theoretical tools (See the chapter by Kibris, this volume). Often voting systems are used in determining a just or fair distribution of costs and benefits among a number of participants. Also here other methods can sometimes be applied (See the chapter by Klamler, this volume). The basic motivation for the study of voting systems is the fact that different systems often produce different outcomes when applied to a given set of voter opinions. In some contexts we are able to single out plausible outcomes, e.g. candidates that – given a distribution of opinions in the electorate – ought to be elected for the system to be called reasonable or democratic in some specific sense. Social choice theorists have developed various plausibility criteria for the evaluation of voting systems. After discussing the classic paradoxes of social choice, we review the main criteria as well as the most important results in social choice theory. We also present some techniques for the analysis of opinion distributions. Our main focus is on systems that lead to one candidate being elected, but we also deal with multi-winner electoral systems. We also briefly touch upon the issue of which systems could be considered best in terms of the criteria discussed.

The author thanks D. Marc Kilgour and Colin Eden for comments on an earlier version. This work was supported by the Academy of Finland.