INTRODUCTION

Social choices, by which we mean group or collective decisions, are made in twoways. In political voting, collective decision is typically used to make “political” decisions, and in the market mechanism, collective decision is typically used to make economic decisions. In this chapter, we concentrate exclusively on the former. Collective action (or social [group] choices) should be based on the preferences of individuals (or agents) in society. Therefore, an important aspect of social choice theory is a description and analysis of the way preferences of individual members of a group are aggregated into a decision of the group as a whole (see Arrow 1950; and Taylor 2005). We are interested in aggregating preferences of the agents into a social decision, which essentially means that we consider social choice functions that, for each possible individual preference profile, picks an alternative for society from the set of alternatives. This approach is different from social welfare function (discussed in Chapters 2–6) that for each possible individual preference profile picks an ordering for society (not just an alternative like the social choice function).

Social choice methods can be subject to strategic manipulation in the sense that an agent, by misrepresenting his preference, may secure an outcome he prefers to the outcome which would have been obtained if he had revealed his preference sincerely. This issue was first addressed by Gibbard (1973) and Satterthwaite (1975). They consider a situation where a collective decision has to be made by a group of individuals regarding the selection of an outcome. The choice of this outcome depends on the preferences that each agent has over the various feasible outcomes. However, these preferences are known only to the agents themselves, that is, each agent knows only his preference. The Gibbard–Satterthwaite theorem states that under verymild assumptions, the only procedureswhich will provide incentives for each individual to report his private information truthfully is one where the responsibility of choosing the outcome is left solely to a single individual (the dictator).

The chapter is organized as follows. In Section 10.2, we consider the framework and we also provide the statement of the Gibbard–Satterthwaite theorem.