Democracy likes to present voting as a clean translation of collective preference into political choice. Mathematics is less obliging.

George G. Szpiro traces the long history of attempts to design a voting system that can reliably determine what “the people” want, following the problem from ancient Greece through medieval thought, the Enlightenment, the American and French revolutions, and modern electoral politics. Along the way, apparently sensible methods repeatedly produce contradictory, manipulable or simply impossible results. 

Szpiro builds the history through the thinkers who tried to solve it: Plato, Ramon Llull, Condorcet, Borda, Laplace, Jefferson, Hamilton, John von Neumann and Kenneth Arrow, among others. The mathematics is explained through political problems rather than presented as abstract machinery—majority cycles, strategic voting, proportional representation and the allocation of seats all become arguments about what fairness actually means. An accessible and destabilising book for readers interested in democracy, mathematics and the awkward fact that counting votes is never merely counting.

Princeton University Press hardcover, 2010 first edition and first printing. Light shelfwear to dust jacket; boards and pages clean, binding firm.