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Smallest quasi-transitive extensions

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  • Bossert, Walter
  • Cato, Susumu
  • Kamaga, Kohei

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.

Suggested Citation

  • Bossert, Walter & Cato, Susumu & Kamaga, Kohei, 2024. "Smallest quasi-transitive extensions," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    • Handle: RePEc:eee:mateco:v:112:y:2024:i:c:s0304406824000454
    DOI: 10.1016/j.jmateco.2024.102983
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    References listed on IDEAS

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