Overview

February 18-19,2020
Voting systems

Mathematical research on voting systems dates back to the eighteenth century work of Borda and Condorcet. Starting from the work of Arrow in the 1950's, it has occupied a prominent role in economic theory. Actually, much of the subsequent research in economics and political science follows the classical Arrovian tradition, using a combination of optimization methods, game theory, and axiomatic analysis to identify the normatively appealing features of different voting systems. More recently, voting systems have attracted a growing interest from researchers in computer science (particularly artificial intelligence and theoretical computer science) and operations research. What distinguishes this research is that it places significant emphasis on computational concepts and algorithmic tools to analyze voting systems. Since the ultimate goal of this research is to implement voting systems that allow people to vote electronically (like Doodle polls or online surveys) or automated systems to perform distributed decision-making, the task is to identify voting systems whose outcomes can be computed efficiently. At the same time, economists and political scientists have taken a much more positive perspective on voting systems, increasingly using statistical techniques to analyze how different voting systems actually perform. The goal of this research is to determine what voting systems perform best in practice, when agents (whether they be people or computer systems) are bound by cognitive and computational constraints that prevent them from fully optimizing their decisions. Currently, the most important challenge in the field is to identify voting systems that not only exhibit appealing normative properties, but also have significant practical appeal — both in terms of computational efficiency and actual performance. Ultimately, this depends on collaboration among researchers in different fields who employ a variety of mathematical methodologies.