Measurement of Incompleteness and Indecisiveness of a Preference Relation

Ramses H. Abul Naga () and Mauro Papi
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Ramses H. Abul Naga: Departamento de Teoría e Historia Económica, Universidad de Málaga and Faculté de Gou- vernance, sciences économiques et sociales, Université Mohammed VI Polytechnique.
Mauro Papi: Business School, University of Aberdeen.

No 2026-01, Working Papers from Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center

Abstract: In a deterministic setting, we examine the problem of ordering decision-makers exhibiting incomplete preferences over finite sets of alternatives. We provide an axiomatic characterization of three novel metrics: a decisiveness metric, an incompleteness metric, and a third metric that captures aspects of both indecisiveness and incompleteness. The proposed metrics, while being logically independent, are nonetheless founded on two key properties: (i) the concept of order extension and (ii) an invariance property related to the graph theoretic structure of a decision-maker’s preferences (Hasse-diagram invariance). We further dwell on how the metrics introduced in this paper relate to existing approaches in the literature, and on their potential use in empirical work.

Keywords: Incomplete preferences; measurement of indecisiveness; measurement of incompleteness. (search for similar items in EconPapers)
Pages: 40 pages
Date: 2026-09
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