On the Size of Winning Coalitions

A recent note by Robert Butterworth is critical of William Riker's size principle on several important grounds. There is, however, an important omission in his analysis which this present essay aims to correct. The author goes on to tie assertions about coalition structure in n-person zero-sum games to a solution theory for such games. In the appendix to this essay the general five-person game, of which Butterworth's game is a special case, is considered in some detail. The effect, with one reasonable solution theory, is a favorable appraisal of the size principle.