  Social choice becomes easier on restricted preference domains such as
single-peaked, single-crossing, and Euclidean preferences. Many impossibility
theorems disappear, the structure makes it easier to reason about preferences,
and computational problems can be solved more efficiently. In this survey, we
give a thorough overview of many classic and modern restricted preference
domains and explore their properties and applications. We do this from the
viewpoint of computational social choice, letting computational problems drive
our interest, but we include a comprehensive discussion of the economics and
social choice literatures as well. Particular focus areas of our survey include
algorithms for recognizing whether preferences belong to a particular
preference domain, and algorithms for winner determination of voting rules that
are hard to compute if preferences are unrestricted.
