Obvious Manipulations

Essentially stable matchings

“…Second, just because a mechanism is not strategyproof does not necessarily imply that it will be manipulated in practice. Building on the recent work of Li (2017) on obviousness in mechanism design, Troyan and Morrill (2019) argue that the existence of some manipulations may be tolerable, so long as these manipulations are not obvious manipulations. More formally, given a student i with true preferences P i , Troyan and Morrill (2019) define a manipulation P i as obvious if either (i) the worst possible outcome from reporting P i is strictly better than the worst possible outcome from P i or (ii) the best possible outcome from P i is strictly better than the best possible outcome from P i .…”

“…This points to a trade-off among essential stability, Pareto efficiency, and strategyproofness: a mechanism exists to obtain any two of these properties, but no mechanism achieves all three. Nevertheless, strategyproofness is a demanding criterion, and recent work by Troyan and Morrill (2019) has investigated the severity of manipulations. Their results, when combined with our Theorem 2, imply that any essentially stable mechanism is not obviously manipulable (Proposition 5), and so the incentive problem may not be so severe.…”

Obvious Manipulability of Voting Rules

“…A mechanism is defined as obviously strategyproof if each agent's worst case outcome under a truthful report is strictly better than their best case outcome under any untruthful report. Troyan and Morrill [23] studied obvious manipulations in the context of matching problems. In particular, they showed that whereas the Boston mechanism is obviously manipulable, many stable matching mechanisms (including those that are not strategyproof) are not obviously manipulable.…”

“…This has motivated research toward alternative concepts of strategyproofness that may be able to capture such variations. One such notion is not obvious manipulability, recently theorized by Troyan and Morrill [23]. Whilst strategyproofness assumes agents have complete information over other agent preferences and the mechanism operation, not obvious manipulability assumes agents are 'cognitively limited' and lack such information.…”

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The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion.

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