  Recent work has constructed economic mechanisms that are both truthful and
differentially private. In these mechanisms, privacy is treated separately from
the truthfulness; it is not incorporated in players' utility functions (and
doing so has been shown to lead to non-truthfulness in some cases). In this
work, we propose a new, general way of modelling privacy in players' utility
functions. Specifically, we only assume that if an outcome $o$ has the property
that any report of player $i$ would have led to $o$ with approximately the same
probability, then $o$ has small privacy cost to player $i$. We give three
mechanisms that are truthful with respect to our modelling of privacy: for an
election between two candidates, for a discrete version of the facility
location problem, and for a general social choice problem with discrete
utilities (via a VCG-like mechanism). As the number $n$ of players increases,
the social welfare achieved by our mechanisms approaches optimal (as a fraction
of $n$).
