Reviewed by
Roman Seidl
Institute for Environmental Decisions
Social choice theory (or theory of collective choice) deals with group decisions by aggregating individ-ual preferences/decisions into a collective preference/decision in the form of votes and elections and with the resulting problems and paradoxes and their avoidance, probability and solution. Key problems of social choice theory are for instance, the problem of cyclic majorities (Condorcet paradox) and the method of paired voting (Condorcet method), the Borda election, and the paradox of liberalism.This is the realm of this handbook and the reader interested in these problems will find a solid source to investigate them. Since its publication year 2016 the book was cited 131 times and since 2017 alone 83 times according to google scholar (2018-3-16). This indicates quite some impact on the research community in a vibrant field of study.
The book is structured as follows: First, a succinct introduction to the field of social choice and computational social choice paves the way to the rest of the book by a detailed book outline. The actual content starts with a part on voting comprising nine chapters. Part II is devoted to fair allocation, part III on coalition formation. In part IV, appropriately termed “additional topics”, three chapters cover topics, which did not fit to one specific heading. Remarkably, there is also a bunch of topics not explicitly covered by this book (or better: explicitly not covered, as explained in detail by the introduction section 1.4). Among those topics are also ‘new problem domains for social choice’, such as group classification and crowdsourcing.
Moreover the introduction briefly covers basic concepts needed to understand the computational parts of the book (in particular the P/NP issue and linear and integer programming). However, the degree of formalisation and the number of terms and equations in the book require advanced knowledge. Most chapters are no easy read for beginners and hence this is no introductory text-book, but actually a hand book for the advanced researcher familiar with formal notation and the problem at hand.
The chapters cover an abundance of specific theoretical and computational themes such as simultaneous voting (chapter 9). The chapters are well structured in subchapters starting by detailing the question at hand, often reviewing historical approaches to solving the issue, and presenting state-of-the-art attempts.
There is much detail in the chapters due to their density, both concerning the problem description, problem formalisation and references. One example is given with the rationalisation of voting rules in chapter 8. Moreover, the respective authors hint on problems still waiting for (improved) solutions; see, for instance, chapter 7 on bribery.
If readers are looking for a short and concise introduction to (computational) social choice and for in-depth descriptions of essential theoretical problems and computational solutions covering a wide range of topics (voting, allocation, etc.), then this handbook may really be useful.
A plus is definitely that the book is available as PDF (http://procaccia.info/papers/comsoc.pdf), which enables the reader to search for terms and references.
To sum up: I can recommend the volume as a handbook one can consult on specific topics for help with background, suggestions and further reading.
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