Existence of Richter-Peleg Representation for General Preferences

Leandro Gorno and Paulo Klinger Monteiro

Papers from arXiv.org

Abstract: This paper provides a general characterization of preferences that admit a Richter-Peleg representation without imposing completeness or transitivity. We establish that a binary relation on a nonempty set admits a Richter-Peleg representation if and only if it is "strongly acyclic" and its transitive closure is "separable". Strong acyclicity rules out problematic cycles among indifference classes, while separability limits the structural complexity of the relation. Our main result has two significant corollaries. First, when the set of alternatives is countable, a binary relation admits a Richter-Peleg representation if and only if it is strongly acyclic. Second, a preorder admits a Richter-Peleg representation if and only if it is separable. These findings have important implications for decision theory, particularly for obtaining maximal elements through scalar maximization in the presence of indecisiveness.

Date: 2025-08
New Economics Papers: this item is included in nep-mic
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2508.08980 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2508.08980

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().