Elections and Fair Division
An Introduction to Social Choice Theory
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Beschreibung
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.
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.
Integrates philosophical, economic, and mathematical approaches Explains the need for an an alternative polity to restore our Western democracies Includes exercises and solutions at the end of each chapter
Autor*in
Harrie de Swart
Themen in »Elections and Fair Division«
Social choice theory Fair elections Majority judgment Fair division Impossibility theorems Alternative polity Voting power Apportionment theory Cooperative game theory Power indices IIA condition Penrose-Banzhaf index Shapley-Shubik index Shapley value Voting profiles