The asymptotic strategyproofness of scoring and Condorcet consistent rules

We calculate the proportion of preference profiles where “small” coalitions of agents may successfully manipulate any given scoring rule and show that it decreases to zero at a rate proportional to with the number of agents. If agents have to incur a small cost in order to decide how to manipulate the voting rule, our results imply that scoring rules are robust to such manipulation in large groups of agents. We present examples of asymptotically strategyproof and non strategyproof Condorcet consistent rules. We thank Eric Maskin and Shmuel Nitzan for useful discussions. We also thank seminar participants at Harvard, Haifa, and Technion universities for their comments. Neeman is grateful for the generous financial support of the NSF under grant SBR-9806832.