The stability of multi-dimensional rules

Sébastien Courtin, Bertrand Tchantcho and Rodrigue Tido Takeng

Mathematical Social Sciences, 2025, vol. 137, issue C

Abstract: In this paper, we give a definition of the dominance relation in the context of “multi-dimensional rules” introduced by Courtin and Laruelle (2020). The decision process in a multi-dimensional rule is modeled as follows: (i) there are several individuals; (ii) there are several dimensions; (iii) each individual expresses a binary choice (“Yes” or “No”) on each dimension; (iv) a decision process maps each choice to a final decision (“accept” or “reject”). A necessary and sufficient condition for the non-emptiness of the core of such rules is provided with an application to weighted multi-dimensional rules. This result is an extension of Nakamura’s theorem (Nakamura, 1979) when the condition of monotonicity is added.

Keywords: Multi-dimensional rules; Dominance; Core; Nakamura (search for similar items in EconPapers)
JEL-codes: C71 D71 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:137:y:2025:i:c:s0165489625000605

DOI: 10.1016/j.mathsocsci.2025.102445

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