Decision theory begins with a suspiciously simple question: given several possible actions and an uncertain world, what should a rational person choose? Okay maybe that's hard.

Michael D. Resnik turns that question into a careful introduction to the mathematical and philosophical machinery beneath choice—probability, preference, utility, risk, ignorance and the rules by which competing outcomes are compared. It is less interested in everyday decision-making folklore than in exposing the assumptions concealed inside the word rational.

Resnik moves through decisions made under certainty, risk and incomplete knowledge, examining approaches such as expected utility, maximin and minimax regret. The useful friction comes from cases where apparently sensible rules produce unstable or counterintuitive results: an irrelevant alternative changes the preferred choice; probabilities depend on how evidence is understood; or a method designed to minimise regret creates fresh reasons for regret. The equations matter, but so do the philosophical questions surrounding them—what preferences represent, whether rationality can be formalised, and how much uncertainty a decision procedure can honestly absorb.

Originally written as a rigorous introduction for readers in philosophy, mathematics, economics and the social sciences, Choices remains a strong gateway into the subject for anyone interested in how formal systems try to convert uncertainty into action. Not beach reading, unless your beach holiday has become a hostile optimisation problem.

University of Minnesota Press, 1987; tenth printing, 2014. Paperback with rubbing, edge wear and small surface marks; internally clean.