Implementing generating functions to obtain power indices with coalition configuration

TL;DR

This paper introduces algorithms using generating functions to compute Banzhaf-Coleman and Owen power indices in weighted majority games with coalition configurations, implemented in R and demonstrated with a social science example.

Contribution

It presents novel calculation algorithms for power indices in coalition-structured weighted majority games using generating functions.

Findings

Algorithms successfully compute power indices in complex coalition games.

Implementation in R demonstrates practical applicability.

Real-life social science example illustrates the method's usefulness.

Abstract

We consider the Banzhaf-Coleman and Owen power indices for weighted majority games modified by a coalition configuration. We present calculation algorithms of them that make use of the method of generating functions. We programmed the procedure in the open language R and it is illustrated by a real life example taken from social sciences.