The roll call interpretation of the Shapley value

TL;DR

This paper characterizes the conditions under which the Shapley value can be interpreted as the probability of a player being pivotal in a voting sequence, emphasizing exchangeability of votes.

Contribution

It provides a characterization of joint probability distributions that allow the roll call interpretation of the Shapley value, focusing on exchangeable voting patterns.

Findings

Shapley value equals the probability of pivotality under certain distributions.

Votes can be interdependent but must be exchangeable for the interpretation to hold.

The paper clarifies the conditions for the roll call interpretation in cooperative game theory.

Abstract

The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e., to bring about the required majority or to make this impossible for others. We characterize the joint probability distributions over cooperation patterns that permit this roll call interpretation: individual votes may be interdependent but must be exchangeable.