The cost of getting local monotonicity

TL;DR

This paper examines the implications of the Public Good index's failure to satisfy local monotonicity, highlighting its advantages and drawbacks in the context of dividing public goods.

Contribution

It analyzes the cost of local monotonicity violation in the Public Good index and discusses its impact on cooperative game theory.

Findings

The Public Good index does not satisfy local monotonicity.

Local monotonicity violation can be seen as a drawback or an advantage.

The paper explores the implications of this property in public good division.

Abstract

Manfred Holler introduced the Public Good index as a proposal to divide a public good among players. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback or as an advantage.