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 , 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 , where k also does not depend on n. Received: 10 February 2000/Accepted: 19 October 2000