  The Gibbard-Satterthwaite Impossibility Theorem 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 house matching, 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 (OSP), recently
introduced by Li (2015).
  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. Indeed, the only OSP-implementable quantile rules choose
either the minimal or the maximal ideal point. For house matching, 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.
