An alternative proof of Gibbard's random dictatorship result

By using a line of reasoning similar to the one used by Gibbard (Gibbard A (1973) Econometrica 41: 587-601) in the deterministic framework, we provide a more transparent and intuitive proof of the following random dictatorship result in the probabilistic framework, which is a corollary credited to H. Sonnenschein of the more general result of Gibbard (Gibbard A (1977) Econometrica 45: 665-681): A decision scheme is Pareto optimific ex post and strategy proof if and only if it is a random dictatorship.