Positive responsiveness and infinite electorates May 2, 2008
Posted by adrianmiroiu in work in progress.trackback
In a highly influential paper K. May characterized the simple majority rule on a finite group of voters in terms of three properties of aggregation functions: neutrality, anonymity and responsiveness. However, attempts to generalize May’s result to infinite sets of voters bring about difficulties one does not encounter in the finite case. Size is an example: all countable infinite sets are in one sense of the same ‘size’. As one may expect, size raises the question of interpreting May’s anonymity condition on infinite domains. In this context, May’s responsiveness property did not look to play a significant role. The paper argues that when the electorate is infinite, part of the import of responsiveness is that the set-theoretical Axiom of Choice holds.
