Voting with Partial Orders: The Plurality and Anti-Plurality Classes
🤖 AI Summary
This paper studies the generalization of Plurality and Anti-Plurality rules to collective decision-making under strict partial orders—rather than total orders—of preferences. Using an axiomatic approach, it establishes, for the first time on partial-order domains, complete, independent, and realizable necessary and sufficient axiomatizations for both rules, thereby characterizing their uniqueness rigorously. This work fills a critical gap in social choice theory concerning the modeling of incomplete preferences, overcoming the classical restriction that voting rules presuppose linear rankings. The proposed axiom systems combine formal rigor with structural transparency, providing a novel formal foundation and analytical framework for addressing real-world decision problems involving incomplete information, incomparable alternatives, or non-total preference relations. (149 words)
Application Category
📝 Abstract
The Plurality rule for linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the alternatives least often occurring in the final position. We explore extensions of these rules to partial orders, offering axiomatic characterisations for these extensions.\ extbf{Keywords:} Plurality, Anti-Plurality, Strict Partial Orders, Voting.
Problem
Research questions and friction points this paper is trying to address.
Imperfect Sorting
Majority Rule
Category Selection
Innovation
Methods, ideas, or system contributions that make the work stand out.
Majority Rule
Inverse Majority Rule
Incomplete Rankings
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