Impossibility theorems with countably many individuals

Abstract

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.

Keywords

• Arrow’s impossibility theorem
• The Gibbard–Satterthwaite theorem
• Infinite society
• Continuity