Structured Voting for Structured Committees

TL;DR

This paper explores structured voting methods for committees with a partitioned, multi-level organization, using representation theory to develop and categorize various points-based voting systems that respect the committee's structure.

Contribution

It introduces a framework for structured voting on partitioned committees, utilizing representation theory to identify and classify diverse points-based voting methods.

Findings

Catalogs various structured voting methods based on representation theory

Highlights the use of weights depending on relations between committees

Extends traditional voting models to structured, multi-part committees

Abstract

There has been much recent work on multiwinner voting systems. However, sometimes a committee is highly structured, and if we want to vote for such a committee, our voting method should be more structured as well. We consider committees consisting of representatives for disjoint parts of a collective; for instance, n departments of an organization might each have m possible representatives to choose from. However, in our model the entire population still gets to vote on the committee, and we need to respect that symmetry, which we do by building on earlier work of Barcelo et al. using representation theory of wreath products. The main thrust of this paper is to advertise and catalog the surprising variety of possible points-based (linear) voting methods in this framework. For instance, if a voter ranks all possible structured committees, it may be reasonable to use weights which depend on the relations between the ranked committees, and not just their order as in 'traditional' voting frameworks!