Paradoxes of Rationality, Probability, and Utility

This unique anthology reflects the author’s analyses and/or resolutions of some of the most perennially perplexing and widely discussed problems arising in rational choice theory, probability theory, and utility theory. It spans 25 years of his research and publications in these related fields. Part One features treatments of the Prisoner’s Dilemma, illustrating why there is no objectively “best strategy” in nature and nurture alike. Part Two treats Newcomb’s problem, along with potential failures of misguided “collective” rationality in non-cooperative multi-player games. Part Three examines pillars and pitfalls of the widely applied and often mis-applied Principle of Indifference, while resolving Bertrand’s notorious random chord paradox, the Sleeping Beauty Problem, and the Two Envelopes Problem Part Four models a thorny moral dilemma debated by Hobbes, Spinoza, and Kant, namely, the ethics of redeeming oneself from a highway robber via the expedient of lying. Part Four then introduces a “reverse Turing test” that leads to a refutation of the Strong AI thesis. It concludes with a methodological comparison of solutions by an engineer, a physicist, and a mathematician to an old Cambridge challenge puzzle, while shedding new light on a humorous but ontologically impossible solution by Dirac.