Hollow Victory: The Minimum Winning Coalition

Abstract

The proof of Riker's size principle is inadequate for the general class of zero-sum bargaining games (whether symmetric or asymmetric), and the principle is valid only for a very restricted class of games—the supersymmetric games and their asymmetric counterparts. Butterworth's modification of the size principle (the maximum number of positive gainers principle) can be extended to cover games which are only approximately symmetric. Roll-call voting in the United States House of Representatives overwhelmingly violates the size principle; hence, the House does not generally play a supersymmetric zero-sum bargaining game. More generally, both Butterworth's and Riker's principles seem inapplicable to large bodies.