Two simplified proofs for Roberts' theorem

Roberts (1979) showed that every social choice function that is ex-post implementable in private value settings must be weighted VCG, i.e. it maximizes the weighted social welfare. This paper provides two simplified proofs for this. The first proof uses the same underlying key-point, but significantly simplifies the technical construction around it, thus helps to shed light on it. The second proof builds on monotonicity conditions identified by Rochet [11] and Bikhchandani et. al. [2]. This proof is for a weaker statement that assumes an additional condition of “player decisiveness”.