On asymptotic strategy-proofness of the plurality and the run-off rules

In this paper we prove that the plurality rule and the run-off procedure are asymptotically strategy-proof for any number of alternatives and that the proportion of profiles, at which a successful attempt to manipulate might take place, is in both cases bounded from above by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$K/\sqrt n$$</EquationSource> </InlineEquation>, where n is the number of participating agents and K does not depend on n. We also prove that for the plurality rule the proportion of manipulable profiles is asymptotically bounded from below by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$K/\sqrt n$$</EquationSource> </InlineEquation>, where k also does not depend on n. Copyright Springer-Verlag Berlin Heidelberg 2002