Weighted Committee Games

TL;DR

This paper introduces weighted committee games to model multi-alternative decision-making, analyzing how different voting weights influence outcomes under various voting rules and highlighting differences in sensitivity across these rules.

Contribution

It extends the concept of weighted simple voting games to multi-alternative settings and compares the impact of weights across different voting rules.

Findings

Weight equivalence classes vary across rules.

Borda committees are more sensitive to weight changes.

Decisions are more affected by weights in Borda than in plurality or Copeland.

Abstract

Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of different voting weights (share-holdings, party seats, etc.) under plurality, Borda, Copeland, and antiplurality rule. The number and geometry of weight equivalence classes differ widely across the rules. Decisions can be much more sensitive to weights in Borda committees than (anti-)plurality or Copeland ones.