Review of 'The Mathematics of Voting and Apportionment' on 'Goodreads'
4 stars
This book is part of the "Compact Textbooks in Mathematics" series from Birkhhauser. It covers three related topics: social choice and voting theory, yes/no (motion) voting and power indices, and problems of apportionment.
The structure and coverage of content is excellent for the undergraduate level and the general layout of the text is appealing. The level of the text is noticeably above many similar texts dealing with voting theory as others are primarily aimed at the humanities student who is required by their institution to complete a STEM course of some kind.
The usual topics within Voting theory are discussed - various voting methods, Condercet and Borda, and Arrow's impossibility theorem - but uniquely it seems this book looks at MacGarvey's theorem and some graph theory, Social Welfare theory, and a more thorough look at manipulability of social choice. The yes/no voting is more traditional, following much the same path …
This book is part of the "Compact Textbooks in Mathematics" series from Birkhhauser. It covers three related topics: social choice and voting theory, yes/no (motion) voting and power indices, and problems of apportionment.
The structure and coverage of content is excellent for the undergraduate level and the general layout of the text is appealing. The level of the text is noticeably above many similar texts dealing with voting theory as others are primarily aimed at the humanities student who is required by their institution to complete a STEM course of some kind.
The usual topics within Voting theory are discussed - various voting methods, Condercet and Borda, and Arrow's impossibility theorem - but uniquely it seems this book looks at MacGarvey's theorem and some graph theory, Social Welfare theory, and a more thorough look at manipulability of social choice. The yes/no voting is more traditional, following much the same path as Taylor's book [b:Mathematics and Politics: Strategy, Voting, Power, and Proof|8413309|Mathematics and Politics Strategy, Voting, Power, and Proof|Alan D. Taylor|https://i.gr-assets.com/images/S/compressed.photo.goodreads.com/books/1340785584l/8413309.SX50.jpg|1173972] but with a bit more discussion of the combinatorics and power of voting blocks. Finally the apportionment chapter felt fresher because El-Helaly didn't make it feel like a discussion solely of the US federal system and the associated electoral college.
Generally I liked this book and will base some of my teaching around it. The presentation does expect a greater level of sophistication on behalf of the student - particularly with the use of formal logic in proofs where perhaps easier to understand versions could be used - but on the whole that sophistication here is what is lacking in the existing undergraduate texts. Recommended.