Characterizing Paretian Preferences

A characterization of a property of binary relations is of type M if it can be stated in terms of ordered M-tuples of alternatives. A characterization of finite type provides an easy test of whether preferences over a large set of alternatives possesses the property characterized. Unfortunately, there is no characterization of finite type for Pareto representability in R..2. A partial result along the same lines is obtained for Pareto representability in R..k, k .. 2.