Impossibility theorems with countably many individuals - Uuganbaatar Ninjbat (SERIEs - Journal of the Spanish Economic Association, 2018)
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: D70; D71; 330; Arrow's impossibility theorem; The Gibbard-Satterthwaite theorem; Infinite society; Continuity