CHOICE FUNCTIONS AND UPPER CHOICE FUNCTIONS

Choice functions play an important role in political science. We present structure results of choice functions following an algebraic approach. It is logical that rational political actors are not able to perceive every alternative in a set of alternatives X. They may also choose to exclude some alternatives from consideration. Let S be a subset of X that some set of political actors are not able to perceive. Then the complement X\S is the set comprising those alternatives considered in the decision process. If C is a choice function on X, then C(X\S) are the alternatives chosen and X\C(X\S) are those that are not. We are thus led to the concept of an upper choice function. We define upper choice functions in terms of choice functions and we give relationships between them.