On Critical Threshold Value for Simple Games

TL;DR

This paper proves that for any simple game with n players, the critical threshold value does not exceed n/4, confirming a previously conjectured bound.

Contribution

It establishes a universal upper bound of n/4 for the critical threshold value in simple games, verifying a conjecture by Freixas and Kurz.

Findings

Critical threshold value is at most n/4 for all simple games.

The conjecture of Freixas and Kurz is confirmed.

Provides a bound that applies universally to simple games.

Abstract

In this note, we show that for every simple game with n players the critical threshold value is at most n/4. This verifies the conjecture of Freixas and Kurz.