This paper discusses how a subject's judgments about his actions, uncertainties and values may be improved by seeking out and reconciling inconsistences between related judgments. Decision theory tells us that there are relationships between coherent judgments, such as between a prior, likelihood and posterior, but does not tell us how a subject is to reconcile his own, possibly incoherent, views. The role of coherence in improving judgments is not clear. This paper discusses whether there is a unique, best reconciliation of (...) incoherent judgments and how such reconciliation could improve decision-making. The basic principles of the coherent view are explained and a language developed in which the problem of reconciliation can be discussed. The practical importance of the problem is emphasized, illustrated by several examples and possible solutions are explored. (shrink)

An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s axiom” after the French philosopher’s (...) fable of the ass that starved out of indifference between two bales of hay. To satisfy this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility. We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of utility theory. (shrink)