Gibbard-Satterthwaite Success Stories and Obvious Strategyproofness

The Gibbard-Satterthwaite Impossibility Theorem [Gibbard, 1973, Satterthwaite, 1975] holds that dictatorship is the only Pareto optimal and strategyproof social choice function on the full domain of preferences. Much of the work in mechanism design aims at getting around this impossibility theorem. Three grand success stories stand out. On the domains of single-peaked preferences, of object assignment, and of quasilinear preferences, there are appealing Pareto optimal and strategyproof social choice functions. We investigate whether these success stories are robust to strengthening strategyproofness to obvious strategyproofness, a stronger incentive property that was recently introduced by Li [2015] and has since garnered considerable attention. For single-peaked preferences, we characterize the class of OSP-implementable and unanimous social choice functions as dictatorships with safeguards against extremism -- mechanisms (which turn out to also be Pareto optimal) in which the dictator can choose the outcome, but other agents may prevent the dictator from choosing an outcome that is too extreme. Median voting is consequently not OSP-implementable. Moreover, even when there are only two possible outcomes, majority voting is not OSP-implementable, and unanimity is the only OSP-implementable supermajority rule. For object assignment, we characterize the class of OSP-implementable and Pareto optimal matching rules as sequential barter with lurkers -- a significant generalization over bossy variants of bipolar serially dictatorial rules. While Li [2015] shows that second-price auctions are OSP-implementable when only one good is sold, we show that this positive result does not extend to the case of multiple goods. Even when all agents' preferences over goods are quasilinear and additive, no welfare-maximizing auction where losers pay nothing is OSP-implementable when more than one good is sold. Our analysis makes use of a gradual revelation principle, an analog of the (direct) revelation principle for OSP mechanisms that we present and prove, and believe to be of independent interest. An integrated examination, of all of these negative and positive results, on the one hand reveals that the various mechanics that come into play within obviously strategyproof mechanisms are considerably richer and more diverse than previously demonstrated and can give rise to rather exotic and quite intricate mechanisms in some domains, however on the other hand suggests that the boundaries of obvious strategyproofness are significantly less far-reaching than one may hope in other domains. We thus observe that in a natural sense, obvious strategyproofness is neither "too strong" nor "too weak" a definition for capturing "strategyproofness that is easy to see," but in fact while it performs as intuitively expected on some domains, it "overshoots" on some other domains, and "undershoots" on yet other domains.