Characterization of certain orders using their associated choice functions

Abstract

Binary relation and choice functions define two different languages for describing the decision maker's (DM's) preferences over a finite set of alternatives. The study of normal choice functions establishes a link between these two languages. The existence of this kind of function demonstrates the compatibility between the DM's local choices (paired comparisons or binary choices) and the DM's global choices. In this paper, we explore this kind of linkage in depth by studying characterizations of special binary relations (total order, weak order, partial order and quasi order) using certain properties of their associated choice functions.