# The Impossibility of Individually Rational, Pareto-efficient, and Strategy-proof rules for Fractional Matching

The Impossibility of Individually Rational, Pareto-efficient, and Strategy-proof rules for Fractional Matching

For a model of fractional matching with linear utility, interpreted as probabilistic matching, we show that strategy-proofness, ex post Pareto-efficiency, and ex ante individual rationality are incompatible. This result is robust to whether, or to what extent, transfers are possible. Since we prove this impossibility for the domain of preferences with linear utility representations and since ex post Pareto-efficiency is weaker than Pareto-efficiency from the ex ante perspective, it implies an incompatibility for more general fractional matching applications as well.