Additivity, utility, and subjective probability

Abstract

The additive conjoint measurement model is applied to the study of decision making under certainty and risk. A data matrix is called additive if it is possible to rescale its cell entries such that their order is preserved and that every rescaled entry can be expressed as a sum of its row and column components. It is shown that the SEU model, according to which individuals attempt to maximize their subjectively expected utility, is equivalent to additivity for a specified class of risky choices. In the experimental study eleven prisoners bid for both risky and riskless offers. Additivity is confirmed by the data supporting the independence between utility and subjective probability. Two alternative variants of the SEU model are used to derive subjective probability and utility functions for each subject. In order to account for the data, one needs either (a) a positive utility for gambling or (b) subjective probability functions where complementary events do not sum to unity. Neither variant is compatible with classical utility theory but both are successful in predicting an independent set of data. Relationships to existing data and implications for future research are discussed.