  We propose a mechanism design framework that incorporates both soft
information, which can be freely manipulated, and semi-hard information, which
entails a cost for falsification. The framework captures various contexts such
as school choice, public housing, organ transplant and manipulations of
classification algorithms. We first provide a canonical class of mechanisms for
these settings. The key idea is to treat the submission of hard information as
an observable and payoff-relevant action and the contractible part of the
mechanism as a mapping from submitted scores to a distribution over decisions
(a score-based decision rule). Each type report triggers a distribution over
score submission requests and a distribution over decision rules. We provide
conditions under which score-based mechanisms are without loss of generality.
In other words, situations under which the agent does not make any type reports
and decides without a mediator what score to submit in a score-based decision
rule. We proceed to characterize optimal approval mechanisms in the presence of
manipulable hard information. In several leading settings optimal mechanisms
are score-based (and thus do not rely on soft information) and involve costly
screening. The solution methodology we employ is suitable both for concave cost
functions and quadratic costs and is applicable to a wide range of contexts in
economics and in computer science.
