Impossibility theorems with countably many individuals

• Main Author: Uuganbaatar Ninjbat
• Format: Article
• Language: English
• Published: SpringerOpen 2018-07-01
• Series: SERIEs: Journal of the Spanish Economic Association
• Subjects: Arrow’s impossibility theorem; The Gibbard–Satterthwaite theorem; Infinite society; Continuity
• Online Access: http://link.springer.com/article/10.1007/s13209-018-0182-4

Abstract The problem of social choice is studied on a domain with countably many individuals. In contrast to most of the existing literature which establish either non-constructive possibilities or approximate (i.e. invisible) dictators, we show that if one adds a continuity property to the usual set of axioms, the classical impossibilities persist in countable societies. Along the way, a new proof of the Gibbard–Satterthwaite theorem in the style of Peter Fishburn’s well known proof of Arrow’s impossibility theorem is obtained.