Handbook of Social Choice and Voting
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Handbook of Social Choice and Voting

Edited by Jac C. Heckelman and Nicholas R. Miller

This Handbook provides an overview of interdisciplinary research related to social choice and voting that is intended for a broad audience. Expert contributors from various fields present critical summaries of the existing literature, including intuitive explanations of technical terminology and well-known theorems, suggesting new directions for research.
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Chapter 14: Arrow’s Theorem and its descendants

Elizabeth Maggie Penn

Extract

The mathematical study of voting systems is motivated by the fact that any group seeking to make collective decisions must choose some method of translating the preferences of the group into social choices. The question of how the multiple and competing preferences of a diverse population can be aggregated is the foundation of a branch of economics and political science termed social choice theory (or, sometimes, collective choice theory). While the comparison of alternative voting schemes can be traced to ancient times, the publication of Kenneth Arrow’s monograph Social Choice and Individual Values in 1951 established social choice theory as a field. This work, for which Arrow received the Nobel Memorial Prize in Economic Sciences in 1972, sets out Arrow’s famous ‘impossibility theorem’, demonstrating that, when voters have three or more alternatives from which to choose, no voting system is capable of simultaneously meeting certain minimal conditions of fairness and sensibility. The significance of Arrow’s contribution lies not only in his surprising result, but also in his pioneering use of an axiomatic approach to studying the problem of voting system design.

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