Spatial Power Indices with a Finite Number of Issues

M. Josune Albizuri (), Alex Goikoetxea () and Jose M. Zarzuelo ()
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M. Josune Albizuri: University of the Basque Country
Alex Goikoetxea: University of the Basque Country
Jose M. Zarzuelo: University of the Basque Country

Mathematical Methods of Operations Research, 2025, vol. 101, issue 3, No 1, 373-394

Abstract: Abstract The Owen-Shapley spatial power index measures the power in a voting situation taking into account the ideological location of the voters. This spatial index assumes that voters face a continuum of issues, and these issues have the same relevance, and therefore are equally likely. In this work, we introduce a family of spatial power indices, where each member of the family is a modified version of the Owen-Shapley spatial power index. Unlike the case of the Owen-Shapley index, in this paper, we consider a more realistic assumption, namely, that voters face a finite number of issues and that these issues may have different relevance. Additionally, we provide an axiomatic characterization of this family using three basic axioms: equal power change property, anonymity, and dummy player property. Furthermore, we prove that these axioms are independent. Finally, an application for the Basque Parliament after the 2020 elections is also provided to study the distribution of power among the parties.

Keywords: Power indices; Spatial games; Spatial power indices; Owen-Shapley spatial power index.; 391A12; 91A80; 91B72 (search for similar items in EconPapers)
JEL-codes: C71 D72 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00895-2

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