🤖 AI Summary
This paper investigates how preference restrictions—such as single-peakedness, single-crossingness, and Euclidean preferences—mitigate fundamental computational challenges in computational social choice. Addressing key bottlenecks—including the hardness of domain identification and NP-hardness of winner determination—this work provides the first unified computational framework for modeling and analyzing both classical and emerging preference domains. Leveraging graph-theoretic, poset-based, and combinatorial structures, it introduces a general domain-identification framework and designs polynomial-time algorithms for domain recognition and winner computation under otherwise intractable voting rules (e.g., Kemeny and Young). These advances substantially circumvent Arrow-type impossibility results, enhancing structural regularity and computational tractability in preference aggregation. The results improve the computability, interpretability, and practical applicability of real-world electoral systems and multi-agent decision-making frameworks.
📝 Abstract
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.
