Arrow's famous impossibility theorem (1951) states that there is no perfect voting rule: for three or more candidates, no voting rule can satisfy a small set of very appealing axioms. However, this is no longer the case if we assume that voters' preferences satisfy certain restrictions, such as being single-peaked or single-crossing. In this talk, we discuss single-peaked and single-crossing elections, as well as some other closely related restricted preference domains, and provide an overview of recent algorithmic results for these domains.
