Social choice in its modern guise is a young subject that can be dated back to the end of the 1940s and the beginning of the 1950s in the works of Duncan Black (1948), Kenneth Arrow (1950, 1951) and Georges- Theodule Guilbaud (1952).

This is nowadays consid­ered as a rebirth, the (first) birth being generally attributed to Jean-Charles de Borda (1784) and Marie-Jean-Antoine-Nicolas Caritat de Condorcet (1785).

Social choice is concerned with the selection of options on the basis of the opinions of individuals over these options. Note that there is an analogy with the choice by an individual of, say, an object, in the presence of multiple criteria. However, this entry is restricted to the multi-individual framework. The selection procedures have been studied either from a rather abstract point of view or from a more practical point of view. In the former, one considers notions such as aggregation functions, social choice functions and their properties, and in the latter one considers voting rules, voting games, and so on. It is interesting to note that this dichotomy has a historical origin, the abstract aspect being generally associated with the utilitarian tradition from Jeremy Bentham to Abram Bergson and Paul Samuelson, and with welfare economics and the practical aspect being associated with questions related to elections, be they elections in small committees or in larger organizations.

The precursors (this phrase will be used for authors living before the eighteenth century) dealt mostly with voting. The eighteenth century saw also an upsurge of inter­est under both aspects in the contributions of Borda and Condorcet. It is surprising that during the nineteenth century the interest in voting rather faded away in spite of the emergence of democratic societies. However, there has been some work on proportional representation (or the equivalent apportionment methods) by European scholars redis­covering what some founding fathers of American democracy previously did, with the brilliant exception to this lack of interest of Charles Lutwidge Dodgson, better known as Lewis Carroll.

The rebirth of social choice theory in the twentieth century offers the same dichotomy. Although both Black and Arrow are economists, the former obviously belongs to the voting tradition and the latter to the welfare economics tradition. Even though voting aspects are not absent in the founding book by Arrow, Social Choice and Individual Values (1951), a significant part is devoted to discussions of the compensation tests debate between John Hicks, Nicholas Kaldor and Tibor Scitovsky and of the Bergson-Samuelson social welfare functions. A large part of this entry will be devoted to Arrow’s theorem and its descendants and to other major results that form the cornerstone of the domain.