Smallest quasi-transitive extensions

Walter Bossert, Susumu Cato and Kohei Kamaga

Journal of Mathematical Economics, 2024, vol. 112, issue C

Abstract: Quasi-transitivity is a weakening of transitivity that has some attractive features, such as the important role it plays in the context of path-independent choice. However, the property suffers from the shortcoming that it does not allow for the existence of a closure operator. This paper examines the question to what extent an alternative operator can be defined that may then be used to ameliorate some of the limitations of quasi-transitivity imposed by the absence of a well-defined closure. To do so, we define the concept of a smallest quasi-transitive extension. A novel weakening of quasi-transitivity turns out to be necessary and sufficient for the existence of such a smallest extension. As an illustration, we apply the notion of a smallest quasi-transitive extension in the context of rational choice on arbitrary domains.

Keywords: Quasi-transitivity; Extensions; Rational choice (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:112:y:2024:i:c:s0304406824000454

DOI: 10.1016/j.jmateco.2024.102983

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