This chapter discusses results about committees that use majority rule, some related results about majority rule as a social choice rule (that is, without referring to a specific context where majority rule is used), and results about electoral competitions where the winner is selected by...

This chapter surveys the literature on strategy proofness from a historical perspective. While I discuss the connections with other works on incentives in mechanism design, the main emphasis is on social choice models.

Ever since Sen crystallized the logical conflict between the welfaristic value of the Pareto principle and the nonwelfaristic value of individual libertarian rights into what he christened the impossibility of a Paretian liberal, there have been many attempts in social choice theory to...

Fuzzy set theory has been explicitly introduced to deal with vagueness and ambiguity. One can also use probability theory or techniques borrowed from philosophical logic. In this chapter, we consider fuzzy preferences and we survey the literature on aggregation of fuzzy preferences. We restrict...

We review the theory of fairness as it pertains to concretely specified problems of resource allocations. We present punctual notions designed to evaluate how well individuals, or groups, are treated in relation to one another: no-envy, egalitarian-equivalence, individual and collective lower or...

Many distributive issues involve situations in which initial characteristics make individuals unequal. In view of prevailing moral sentiments, some of these characteristics call for compensating transfers, and some do not. We study the literature on this problem of compensation. This literature...

This paper reexamines key results from the measurement of opportunity freedom, or the extent to which a set of options offers a decision maker real opportunities to achieve. Three cases are investigated: no preferences, a single preference, and plural preferences. The three corresponding...

Economists have used the term “nonbinary” to describe both choice functional nonbinariness (choice functions that cannot be rationalized as the maximizing outcome of a binary preference relation) and structural nonbinariness (the structure of the model dictates that pairs of alternatives do...

It is shown how simple geometry can be used to analyze and discover new properties about pairwise and positional voting rules as well as for those rules (e.g., runoffs and Approval Voting) that rely on these methods. The description starts by providing a geometric way to depict profiles, which...