The purpose of this paper is to give a systematic account of the significance that antagonism among opinions of individuals has on the theory of social choice. We define an "intensity" of antagonism among individuals and an index of "possibility" of constructing social welfare functions, and show that when there is less antagonism in a society, then there is more "possibility" of constructing social welfare functions. Since antagonism is an opposite concept to similarity, this relation can be viewed as a formal realization of Arrow's assertion [1, Ch. 7] that sets preference similarity as the basis of social welfare judgement.