As we noted in the introduction, we do not propose to discuss possible implications for the real world of democratic politics that may be drawn from the highly stylized models of vote buying that we have analyzed in this paper. To the extent that economic, legal, or moral thresholds prevent the emergence of the purchase and sale of votes among persons who initially possess property rights in the collective franchise, our whole analysis is simply inapplicable. If, however, such thresholds serve only to inhibit but not to prevent totally the emergence of such markets, there should be some value in an analysis that embodies the zero transactions costs assumption.