Universal Voting Protocol Tweaks to Make Manipulation Hard
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Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are
manipulable. One could try to avoid manipulation by using voting protocols where determining a beneﬁcial manipulation is hard computationally. A number of recent papers study the complexity of manipulating existing protocols. This paper is the ﬁrst work to take the next step of designing
new protocols that are especially hard to manipulate. Rather than designing these new protocols from scratch, we instead show how to tweak existing protocols to make manipulation hard, while leaving much of the original nature of the protocol intact. The tweak studied consists of adding one
elimination preround to the election. Surprisingly, this extremely simple and universal tweak makes typical protocols hard to manipulate! The protocols become NP-hard, #P-hard, or PSPACE-hard to manipulate, depending on whether the schedule of the preround is determined before the votes
are collected, after the votes are collected, or the scheduling and the vote collecting are interleaved, respectively. We prove general sufﬁcient conditions on the protocols for this tweak to introduce the hardness, and show that the most common voting protocols satisfy those conditions. These are the ﬁrst results in voting settings where manipulation is in a higher complexity class than NP (presuming PSPACE =6 NP).