Proportional Algorithms for Democratic Decisions

Introduction

The project is set in the field of computational social choice.

Focus of the Project

We will focus on formal models describing scenarios where a group of individuals, called voters, disagrees on certain matters yet needs to make a collective decision. The decision must truly represent a compromise. We focus on group fairness understood as proportionality.

Real-life Applications

There are numerous real-life scenarios that involve collective (public) decisions, and where our solutions could be applied. Examples include:

• Elections of representative bodies (such as parliaments, faculty boards, etc.)
• Participatory budgeting elections (where citizens decide how to allocate a part of a municipal budget)
• Scenarios where certain local communities (say, housing cooperatives) make a series of decisions

In addition, proportional algorithms for making collective decisions can be used for:

1. Selecting nominees for an award
2. Constructing rankings of movies or books
3. Selecting validators in consensus protocols, such as the blockchain
4. Constructing rankings of web pages in response to user queries
5. Locating public facilities
6. Improving genetic algorithms

Project Goals

The goal of this project is to develop generic methods of reasoning about equity of treatment of voters and to design new algorithms that satisfy the most demanding criteria of proportionality.

Research Objectives

The new methods should be applicable to a number of specific models that concern public decisions. We will:

1. Prove theorems specifying whether and under which conditions our notions of proportionality are satisfiable.
2. Analyze various rules and algorithms with respect to our criteria of proportionality and other important desiderata that are commonly considered in social choice theory.
3. Determine the computational complexity of the problem of finding proportional public decisions.
4. Develop exact, approximation, fixed-parameter-tractable, and heuristic algorithms for this and related computational problems.