Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures

I enjoyed this book. Brams does provide mathematical proofs of his propositions in the chapter appendices, but overall, this is a fairly accessible and wide-ranging overview of Brams' current thinking on voting rules and fair-division procedures. One of the most interesting contributions of this book is the development of ranked approval voting systems, which combine many of the attractive features of Condorcet voting and simple approval voting. Brams also develops ways to implement proportional representation outside the party-list context, useful for professional societies, corporate boards, etc. seeking to elect multiple positions at once. I highly recommend this book to lay readers seeking to learn about the state of the art in normative voting-rule theory. With any luck, it will advance the cause of reform of voting rules in single-winner, political elections.