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The Gibbard-Satterthwaite theorem established that no nontrivial voting rule is strategy-proof, but that does not mean that all voting rules are equally susceptible to strategic manipulation. Over the past fifty years numerous approaches have been proposed to compare the manipulability of voting rules in terms of the probability of manipulation, the domains on which manipulation is possible, the complexity of finding such a manipulation, and others. In the closely related field of matching, Pathak and Sönmez (2013) pioneered a notion of manipulability based on case-by-case comparison of manipulable profiles. The advantage of this approach is that it is independent of the underlying statistical culture or the computational power of the agents, and it has proven fruitful in the matching literature. In this paper, we extend the notion of Pathak and Sönmez to voting, studying the families of k-approval and truncated Borda scoring rules. We find that, with one exception, the notion does not allow for a meaningful ordering of the manipulability of these rules.

Strategic voting, or manipulation, is the process by which a voter misrepresents his preferences in an attempt to elect an outcome that he considers preferable to the outcome under sincere voting. It is generally agreed that manipulation is a negative feature of elections, and much effort has been spent on gauging the vulnerability of voting rules to manipulation. However, the question of why manipulation is actually bad is less commonly asked. One way to measure the effect of manipulation on an outcome is by comparing a numeric measure of social welfare under sincere behaviour to that in the presence of a manipulator. In this paper we conduct numeric experiments to assess the effects of manipulation on social welfare under scoring rules. We find that manipulation is usually negative, and in most cases the optimum rule with a manipulator is different to the one with sincere voters.

The Gibbard-Satterthwaite theorem established that no non-trivial voting rule is strategy-proof, but that does not mean that all voting rules are equally susceptible to strategic manipulation. Over the past fifty years numerous approaches have been proposed to compare the manipulability of voting rules in terms of the probability of manipulation, the domains on which manipulation is possible, the complexity of finding such a manipulation, and others. In the closely related field of matching, Pathak and Snmez (2013) pioneered a notion of manipulability based on case-by-case comparison of manipulable profiles. The advantage of this approach is that it is independent of the underlying statistical culture or the computational power of the agents, and it has proven fruitful in the matching literature. In this paper, we extend the notion of Pathak and Snmez to voting, studying the families of k-approval and truncated Borda scoring rules. We find that, with one exception, the notion does not allow for a meaningful ordering of the manipulability of these rules.