This paper offers a modified version of the certainty equivalence (CE) theory of utility for uncertain prospects and a new set of axioms as its basis. It shows that the CE and the von Neumann-Morgenstern (NM) approaches to uncertainty are opposite in spirit: The CE approach represents a flight from the world of uncertainty to the rules of certainty while the NM approach represents a flight from the world of certainty to one of uncertainty. The two approaches differ even in (...) their treatment of compound prospects and their actuarially identical simple counterparts. (shrink)

We propose a theory that relates perceived evidence to numerical probability judgment. The most successful prior account of this relation is Support Theory, advanced in Tversky and Koehler. Support Theory, however, implies additive probability estimates for binary partitions. In contrast, superadditivity has been documented in Macchi, Osherson, and Krantz, and both sub- and superadditivity appear in the experiments reported here. Nonadditivity suggests asymmetry in the processing of focal and nonfocal hypotheses, even within binary partitions. We extend Support Theory by revising (...) its basic equation to allow such asymmetry, and compare the two equations’ ability to predict numerical assessments of probability from scaled estimates of evidence for and against a given proposition. Both between- and within-subject experimental designs are employed for this purpose. We find that the revised equation is more accurate than the original Support Theory equation. The implications of asymmetric processing on qualitative assessments of chance are also briefly discussed. (shrink)