On the ultrafilter representation of coalitionally strategy-proof social choice functions

By means of a simple new characterization of ultrafilters, we elementarily prove, in the case of finitely many alternatives and arbitrarily large societies, that every coalitionally strategy-proof social choice function with at least three alternatives in its range is given by an ultrafilter. This provides an alternate and simple proof of results in Mihara (Soc Choice Welf 17:393–402, 2000). In case there are only two alternatives in the range of a coalitionally strategy-proof social choice function, we describe its structure, supplementing the work of Barberà et al. (Int J Game Theory 41:791–808, 2012).