The average representation - a cornucopia of power indices?

TL;DR

This paper introduces two new power indices based on weighted representations that align more closely with relative weights, addressing the common disparity between power and weights in classical indices.

Contribution

It proposes novel power indices derived from weighted representations, expanding the family of indices with desirable proportionality and property-sharing features.

Findings

New indices are proportional to relative weights

They retain key properties of classical power indices

Potential for a broader family of indices with additional restrictions

Abstract

For the classical power indices there is a disproportion between power and relative weights, in general. We introduce two new indices, based on weighted representations, which are proportional to suitable relative weights and which also share several important properties of the classical power indices. Imposing further restrictions on the set of representations may lead to a whole family of such indices.