Are weighted games sufficiently good for binary voting?

TL;DR

This paper investigates whether modeling binary voting systems as weighted games is practically sufficient by comparing power distributions, finding that deviations are generally small.

Contribution

It introduces a comparison of weighted games with a broader class of voting rules using power indices to assess practical adequacy.

Findings

Deviations in power distributions are relatively small.

Weighted games are often a good approximation for more complex voting rules.

The study provides evidence supporting the use of weighted games in practical decision-making.

Abstract

Binary yes-no decisions in a legislative committee or a shareholder meeting are commonly modeled as a weighted game. However, there are noteworthy exceptions. E.g., the voting rules of the European Council according to the Treaty of Lisbon use a more complicated construction. Here we want to study the question if we lose much from a practical point of view, if we restrict ourselves to weighted games. To this end, we invoke power indices that measure the influence of a member in binary decision committees. More precisely, we compare the achievable power distributions of weighted games with those from a reasonable superset of weighted games. It turns out that the deviation is relatively small.