Timing contradictions in von Neumann and Morgenstern's axioms and in savage's ?sure-thing? proof

Abstract

At the point of choice, let N be the delay in learning the outcome. Then von Neumann and Morgenstern's postulates contradictorily imply that N = 0 and N > 0. As a consequence, Savage's 'sure-thing' proof, which has bestowed on expected utility theory most of its normative appeal, depends on inconsistent assumptions. Further, the validity of Savage's proof cannot be retrieved by minimizing N > 0, by making the delay a mere moment or so. The historical origins of these contradictions are traced to (i) von Neumann and Morgenstern inadvertently limiting their risk model to the certain period, that is the period after gamblers learn the outcome(s), and (ii) Savage's use of the sure-thing principle for analysing "atemporally but also quite formally" compound gambles [Savage, 1954, p. 23].

Expected utility versus the changes in knowledge ahead

“…This error introduces the contradiction that the outcomes of sure contracts (those with the outcome known at t ¼ 0), and risky contracts, those with the outcome unknown at this time, had their outcomes known simultaneously, Pope (1985). The error of omitting the pre-outcome period creates a corresponding timing fallacy in the definition of risky acts in EUT under which as in e.g.…”

Managed Floats to Damp World-Wide Exchange Rate Liquidity Shocks Like 1982-5, 2006-9: Field and Laboratory Evidence for the Benefits of a Single World Currency

“…Upon making a risky choice, the chooser goes through what may be termed a pre-outcome period, a period of uncertainty, of ignorance of the final segment of his outcome flow. During this period, since the risk is still unresolved, there can be an interdependence of the mutually exclusive outcomes in the chooser's mind [54]. The chooser can hate or love the excitement of the tension created by wondering whether the good or bad outcome will occur, i.e.…”

“…a certain future. This precludes getting a non-contradictory set of axioms detailing the actual delays that precede resolution of risk, and blurs the distinction between real time risk effects that must enter the satisfactions (utility) mapping with atemporal aggregation effects that are outside time [50,54]. Such a false simultaneity postulate precludes understanding the distinction between the chooser's anticipated possible cause effect chains of an act, and how the chooser integrates (aggregates) these into a single value of an act.…”

Book Review

“…They left to future researchers finding the higher level of analysis that would overcome this contradiction, which they discerned must be pseudo. Pope (1985) showed that the contradiction vanishes once a stages of knowledge ahead framework is employed to divide up the future.…”