A Quantitative Approach to Incentives: Application to Voting Rules (Job Market Paper)

We present a general approach to quantifying a mechanism’s susceptibility to strategic manipulation, based on the premise that agents report their preferences truthfully if the potential gain from behaving strategically is small. Susceptibility is defined as the maximum amount of expected utility an agent can gain by manipulating. We apply this measure to anonymous voting rules, by making minimal restrictions on voters’ utility functions and beliefs about other voters’ behavior. We give two sets of results. First, we offer bounds on the susceptibility of several specific voting rules. This includes considering several voting systems that have been previously identified as resistant to manipulation; we find that they are actually more susceptible than simple plurality rule by our measure. Second, we give asymptotic lower bounds on susceptibility for any voting rule, under various combinations of efficiency, regularity, and informational conditions. These results illustrate the tradeoffs between susceptibility and other properties of the voting rule. Thanks to (in random order) Ben Golub, Alex Wolitzky, Anton Kolotilin, Mihai Manea, Nathan Hendren, Yusuke Narita, Pablo Querubin, Lirong Xia, Abhijit Banerjee, Jing Chen, Rakesh Vohra, Pablo Azar, Jim Schummer, Iván Werning, Robert Akerlof, Glenn Ellison, Daron Acemoglu, Horacio Larreguy, Jim Snyder, Xiao Yu Wang, Jonathan Weinstein, and Parag Pathak for discussions and advice. This work was partially supported by an NSF Graduate Research Fellowship.

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