Domains of individual preferences for which the well-known impossibility Theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. First, we introduce necessary and sufficient conditions for a domain to admit non-dictatorial, Pareto efficient and either strategy-proof...

We consider voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences. Assuming continuity, gamma -strategy-proofnessmeaning that coalitions of size smaller or equal to a small number gamma cannot manipulateand unanimity, we show that such rules are...