# Strategy-proof Cardinal Decision Schemes

Working paper

Issue number:

722

Publisher:

University of Warwick

Year:

2005

We construct an example to show that the random dictatorship result no longer holds when individual utility functions satisfy this additional restriction. We then analyze the consequences of gradually reducing the grid size. That is, we consider an arbitrary sequence of strategy-proof and unanimous decision schemes deﬁned on a sequence of decreasing grid sizes approaching zero. We obtain a ‘limit’ random dictatorship result in the sense that the sequence of such decision schemes must converge to a random dictatorship for all proﬁles for which the limit exists.