Preference aggregation is a challenging task: Arrow's famous impossibility theorem [1] tells us that there is no perfect voting rule. One of the best-known ways to circumvent this difficulty is to assume that voters' preferences satisfy a structural constraint, such as, e.g, being single-peaked. Indeed, under this assumption many impossibility results in social choice disappear. Restricted preference domains also play an important role in computational social choice: for instance, there are voting rules that are NP-hard to compute in general, but admit efficient winner determination algorithms when voters' preferences belong to a restricted domain. However, restricted domains that have nice social choice-theoretic properties are not necessarily attractive from an algorithmic perspective, and vice versa. In this note, we will discuss some domain restrictions that have proved to be useful from a computational perspective, and compare the use of restricted domains in computational and classic social choice theory.
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