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The Gibbard-Satterthwaite theorem established that no non-trivial voting ruleis strategy-proof, but that does not mean that all voting rules are equallysusceptible to strategic manipulation. Over the past fifty years numerousapproaches have been proposed to compare the manipulability of voting rules interms of the probability of manipulation, the domains on which manipulation ispossible, the complexity of finding such a manipulation, and others. In theclosely related field of matching, Pathak and Sonmez pioneered a notion ofmanipulability based on case-by-case comparison of manipulable profiles. Theadvantage of this approach is that it is independent of the underlyingstatistical culture or the computational power of the agents, and it has provenfruitful in the matching literature. In this paper, we extend the notion ofPathak and Sonmez to voting, studying the families of $k$-approval andtruncated Borda scoring rules. We find that, with one exception, the notiondoes not allow for a meaningful ordering of the manipulability of these rules.

Comparing the Manipulability of Approval Voting and Borda