  Our work revisits the design of mechanisms via the learning-augmented
framework. In this model, the algorithm is enhanced with imperfect
(machine-learned) information concerning the input, usually referred to as
prediction. The goal is to design algorithms whose performance degrades gently
as a function of the prediction error and, in particular, perform well if the
prediction is accurate, but also provide a worst-case guarantee under any
possible error. This framework has been successfully applied recently to
various mechanism design settings, where in most cases the mechanism is
provided with a prediction about the types of the players.
  We adopt a perspective in which the mechanism is provided with an output
recommendation. We make no assumptions about the quality of the suggested
outcome, and the goal is to use the recommendation to design mechanisms with
low approximation guarantees whenever the recommended outcome is reasonable,
but at the same time to provide worst-case guarantees whenever the
recommendation significantly deviates from the optimal one. We propose a
generic, universal measure, which we call quality of recommendation, to
evaluate mechanisms across various information settings. We demonstrate how
this new metric can provide refined analysis in existing results.
  This model introduces new challenges, as the mechanism receives limited
information comparing to settings that use predictions about the types of the
agents. We study, through this lens, several well-studied mechanism design
paradigms, devising new mechanisms, but also providing refined analysis for
existing ones, using as a metric the quality of recommendation. We complement
our positive results, by exploring the limitations of known classes of
strategyproof mechanisms that can be devised using output recommendation.
