Anonymity in large societies

Abstract

In a social choice model with an infinite number of agents, there may occur "equal size" coalitions that a preference aggregation rule should treat in the same manner. We introduce an axiom of equal treatment with respect to a measure of coalition size and explore its interaction with common axioms of social choice. We show that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom is the natural extension of the concept of anonymity, and in particular plays a similar role in the characterization of preference aggregation rules. JEL D71, C69 * We would like to thank Rajat Deb, John Duggan, Rabee Tourky, and participants at the

Computability of simple games: A characterization and application to the core

“…The decision has to be made before a state is realized and identified. (This idea is formalized by Gomberg et al (2005), who introduce "n-period coalition space," where n is the number of persons. )…”

“…be a countable set of (the names of) players. Any recursive (algorithmically decidable) subset of N is called a (recursive) (1997a), Fey (2004), and Gomberg et al (2005).…”

“…See Remark 5. 11 Detailed studies of anonymous rules based on infinite simple games includeMihara (1997a),Fey (2004), andGomberg et al (2005).12 Banks (1995),Truchon (1995), andAndjiga and Mbih (2000) are recent contributions to this literature. (Earlier papers on acyclic rules can be found inTruchon (1995) and Austen-Smith andBanks (1999).)…”

The possibility of Paretian anonymous decision-making with an infinite population

“…Mihara (1997) and Lauwers and Van Liedekerke (1995) are remarkable examples of earlier works that impose anonymity axioms in addition to the standard Arrow axioms. Recently, many works have tried to clarify various anonymity axioms, or to introduce some other requirements, such as continuity (Gomberg et al 2005;Torres 2005;Salonen and Saukkonen 2005). Kirman and Sondermann (1972) and Hansson (1976) characterize the power structure behind social choice.…”