The Mathematics of voting

Michel Balinski's “ Fair majority voting (or how to eliminate gerrymandering)” [Am. Math. Mon. 115, No. 2, 97-113 (2008; Zbl 1151.91036)] describes a new method, Fair Majority Voting, to avoid the effects of disproportion. Check the review of Marcus Pivato for a detailed discussion.

Naturally, the books “Mathematics and democracy. Designing better voting and fair-division procedures.” [Princeton, NJ: Princeton University Press (2008; Zbl 1151.91001)] of Steven J. Brams and “Mathematics and politics. Strategy, voting, power and proof.” [2nd ed., Berlin: Springer (2008; Zbl 1151.91005 Zbl 1151.91005 of Alan D. Taylor and Allison M. Pacelli take a broader approach. The first, Zbl 1151.91005 in the words of the reviewer Klaus Ehemann, “tries to show how mathematics can be used to illuminate 2 essential features of democracy, the aggregation of the individual preferences to give a social choice or election outcome that reflects the interests of the electorate, and the division of public and private goods in a way that respects due process and the rule of law.” ; the second, to quote the reviewer Giacomo Bonnano, “ covers six main topics in twelve chapters: social choice, yes-no voting, political power, conflict, fairness and escalation...with no college-level mathematical or social science pre-requisites. ”