On the threshold representation of partial orderings
Abstract
In this paper, we provide a constructive proof for threshold representations of partial orderings in a finite setting and extend the construction to arbitrary sets. This contributes to a long-standing open problem posed in Nakamura (2002) and Aleskerov et al. (2007). We identify and discuss aspects of our proof that do not directly generalize to an infinite setting and, for each, provide intuitive sufficient conditions.
Fields of Study & Subjects
Game Theory and Voting Systems
Advanced Combinatorial Mathematics
Advanced Algebra and Logic
Publication details
- Journal / source
- Mathematical Social Sciences
- Volume
- 140
- Pages
- 102516–102516
- Publication date
- 17 February 2026
- Language
- EN