Rational choice based on vague preferences

This paper studies ‘vague preferences’. In contrast to the concept of fuzzy preferences, the more general notion of vague preferences does not entail the assumption that the different ‘degrees of preference’ are completely ordered. It is shown that the more general concept of a vague preference order arises very naturally in the context of aggregating a set of (exact) weak orders. Furthermore, necessary and sufficient conditions for the rationalizability of an exact choice function by means of a vague preference order are given. It turns out that in the general case these conditions are weaker than in the case where the ‘degrees of preference’ are completely ordered. Consequently, there exist choice functions which are rationalizable by a general vague preference order but which are not rationalizable by a fuzzy preference order, or more generally by any vague preference order which induces a complete ranking of the ‘degrees of preference’. Examples of such choice functions are provided.