[Journal:] SERIEs - Journal of the Spanish Economic Association [ISSN:] 1869-4195 [Volume:] 9 [Year:] 2018 [Issue:] 3 [Pages:] 333-350
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.
Arrow's impossibility theorem The Gibbard-Satterthwaite theorem Infinite society Continuity