Elections and Fair Division: An Introduction to Social Choice Theory

This graduate textbook introduces to social choice theory, with a specific focus on elections and fair division, supported by mathematical theories and practical implications.

Part I sheds light on the complexity of fair elections, and presents classical results from social choice theory, including May’s, Arrow’s, and Gibbard-Satterthwaite’s theorems, and how they impact the organization of fair elections. They also discuss the measurement of voting power in such elections via the Penrose-Banzhaf index and the Shapley-Shubik index. Besides these more or less classical topics, the authors introduce Balinski and Laraki’s transformative Majority Judgment framework. Moreover, Part I concludes by critically addressing flaws in contemporary Western democracies and proposing an alternative political system.

In Part II, the book dissects claims-based and preference-based fair division, explaining that the focus will be on the former. In particular, the focus will be on models that can elaborate on and make precise the thought that fairness requires that claims are satisfied in proportion to their strength’, as advocated for in the philosophical literature. The authors scrutinize various formal models, ranging from (weighted) bankruptcy problems to cooperative games, assessing their alignment with this claims-based conception of fairness. Part II concludes with a brief overview of preference-based fair division.

This textbook is a crucial resource for graduate and advanced undergraduate students and scholars, bridging the worlds of mathematics, philosophy, political theory, and social justice.

Harrie de Swart is a Professor Emeritus of Logic and Analysis of Language at the Faculty of Philosophy of Tilburg University, The Netherlands. He studied Mathematics and Physics at the Catholic University of Nijmegen, The Netherlands, with a specialization in logic, foundations, and philosophy of mathematics. De Swart holds a PhD in mathematical logic from the same university. After 50 years of experience with teaching logic and 25 years of teaching social choice theory, he authored a book on ＂Philosophical and Mathematical Logic＂ (Springer, 2018) and another book on Social Choice Theory, together with Stefan Wintein.

Stefan Wintein is an Associate Professor in Theoretical Philosophy at the Faculty of Philosophy of the Erasmus University Rotterdam, The Netherlands, and a member of the Erasmus Institute for Philosophy and Economics. He holds a PhD in logic from Tilburg University, The Netherlands, an MSc in Econometrics, and a MA in Philosophy. His research focuses on philosophical logic (self-referential truth, many-valued logics) and formal ethics (fairness, distributive justice). He teaches social choice theory, logic, and philosophy to economics students.