Roughly Weighted Hierarchical Simple Games

TL;DR

This paper explores hierarchical simple games, focusing on their rough weightedness and how it relates to weighted majority games, with implications for secret sharing and social choice.

Contribution

It characterizes roughly weighted hierarchical simple games and identifies conditions under which they coincide with weighted majority games.

Findings

Characterization of roughly weighted hierarchical simple games

Identification of conditions where hierarchical and weighted games coincide

Insights into applications in secret sharing and social choice

Abstract

Hierarchical simple games - both disjunctive and conjunctive - are natural generalizations of simple majority games. They take their origin in the theory of secret sharing. Another important generalization of simple majority games with origin in economics and politics are weighted and roughly weighted majority games. In this paper we characterize roughly weighted hierarchical games identifying where the two approaches coincide.