Partial-conjugates and Dimensionality of Posets

2014/02/18 by Shaofang Qi, Qi, Shaofang
Computer Science · Decision Sciences · #Advanced Algebra and Logic #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #FOS: Mathematics #Game Theory and Applications

paper · pdf · doi:10.48550/arxiv.1402.4351

openalex publication_date 2014/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to investigate the dimension of the partial order. We provide a characterization of a partial order having dimension n in general.

Related

• A Partial Order on Preference Profiles
• Distances Between Partial Preference Orderings
• Finding Preference Profiles of Condorcet Dimension k via SAT
• Existence of Richter-Peleg Representation for General Preferences
• The Complexity of the Partial Order Dimension Problem - Closing the Gap