A characterization of two-agent Pareto representable orderings

Partial orders defined on a nonempty set X admitting a two-agent Pareto representation are characterized. The characterization is based upon the fulfillment of two axioms. The first one entails the existence, for any point x & ISIN; X, of a very particular decomposition of the points which are incomparable to x. The second one encodes a separability condition. Our approach is then applied to show that if the cardinality of X is, at most, 5, then a two-agent Pareto representation always exists whereas this need not be the case otherwise. The connection with the concept of the dimension of a poset is also discussed. Certain examples are also presented that illustrate the scope of our tools.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).