Voting problems with a continuum of voters and finitely many alternatives are considered. Since the Gibbard–Satterthwaite theorem persists in this model, we relax the non-manipulability requirement as follows: are there social choice functions (SCFs) such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the SCF? Such SCFs are called exactly and strongly consistent. The paper extends the work of Peleg (Econometrica 46:153–161, 1978a) and others. Specifically, a class of anonymous SCFs with the required property is characterized through blocking coefficients of alternatives and through associated effectivity functions.An erratum to this article can be found at http://dx.doi.org/10.1007/s00355-006-0174-3
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