Evaluation of decision power in multi-dimensional rules

Sébastien Courtin

Mathematical Social Sciences, 2022, vol. 115, issue C, 27-36

Abstract: This work deals with the evaluation of decision power in multi-dimensional rules. Courtin and Laruelle (2020) introduced a decision process that specifies the collective acceptance or rejection of a proposal with several dimensions. The decision process is modeled as follows: (i) There are several individuals. (ii) There are several dimensions. (iii) Each of the individuals expresses a binary choice (“Yes” or “No”) on each dimension. (iv) A decision process maps each choice to a final binary decision (“Yes” or “No”). We extend and characterize six well-known power indices within this context: the Shapley–Shubik index (Shapley and Shubik, 1954), the Banzhaf index (Banzhaf, 1965), the Public good index (Holler, 1982), the Null individual free index (Alonso-Meijide et al., 2011), the Shift index (Alonso-Meijide and Freixas, 2010) and the Deegan–Packel index (Deegan and Packel, 1978).

Keywords: Multi-dimensional rules; Power index; Shapley–Shubik index; Banzhaf index; Public good index; Deegan–Packel index (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:115:y:2022:i:c:p:27-36

DOI: 10.1016/j.mathsocsci.2021.11.001

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