Strategy-proof voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences

We consider voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences. Assuming continuity, γ-strategy-proofness—meaning that coalitions of size smaller or equal to a small number γ cannot manipulate—and unanimity, we show that such rules are decomposable into one-dimensional rules. Requiring, additionally, anonymity leads to an impossibility result. The paper can be seen as an extension of the model of Border and Jordan (1983) to a continuum of voters. Contrary, however, to their finite case where single voters are atoms, in our model with nonatomic voters even a small amount of strategy-proofness leads to an impossibility.