Nonanonymity and sensitivity of computable simple games

This paper investigates algorithmic computability of simple games (voting games). It shows that (i) games with a finite carrier are computable, (ii) computable games have both finite winning coalitions and cofinite losing coalitions, and (iii) computable games violate any conceivable notion of anonymity, including finite anonymity and measurebased anonymity. The paper argues that computable games are excluded from the intuitive class of gniceh infinite games, employing the notion of ginsensitivityh\-equal treatment of any two coalitions that differ only on a finite set.