10 Development of a clinical prediction model for an ordinal diagnostic outcome

Abstract

For choice with deterministic consequences, the standard rationality hypothesis is ordinality, i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann-Morgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage’s sure-thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behavior in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behavior violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments.