Algebraic and Stochastic Models of Structures Arising in Utility Theory and Psychophysics

University Of California-Irvine, Irvine CA

Investigators

Abstract

This research continues and extends earlier theoretical work of the investigator and of collaborator A. A. J. Marley on the measurement of psychological attributes such as the utility of goods and the subjective intensity of physical signals such as lights or sounds. The research will describe the underlying structure of independent variables that affect the attribute in such algebraic terms as (1) the ordering by "subjectively greater than," (2) operations like being presented with two goods or stimuli at once or in quick succession, (3) treatments of stimuli as deviations from the status quo in utility or from threshold in psychophysics, and (4) use of judgements of "ratios of intervals" similar to those found in magnitude production methods. This project will account for violations of dominance, such as the utility of gambling per se, peculiarities of mixed gambles of gains and losses, and various principles to extend the theory from binary gambles to general ones. The project also will attempt to generalize some of the algebraic theories to probabilistic versions. Utility models are extensively used in providing advice to decision makers and subjective expected utility also is a key part of Bayesian statistical methods. Sensory measurement is used widely in a variety of industrial settings. Yet these applications are based primarily on empirical generalizations whose theoretical basis has recently been brought into doubt. This project will advance theory and methods in many application areas. It also will further the development of a probabilistic version of fundamental measurement theory, thereby expanding the value of this approach for many social and behavioral science inquiries.