The interaction of value and subjective probability in decision making under risk

Crozier, WR

Abstract

In a class of decision making situations known as risky situations subjects are presented with information concerning payoffs which are dependent on the occurrence of some events and the likelihood of achieving these payoffs, and are asked to make decisions or judgments in terms of these payoffs and probabilities. The question of whether subjects' judgments of the likelihood of achieving these payoffs are independent of the value of the payoffs is an important one for the understanding of decision making behaviour and has attracted some attention, but these investigations have not resulted in any unequivocal answers.
The difficulty of answering this question was seen as bound up with the difficulty of making inferences about subjective probability or about changes in subjective probability from responses which are not probability estimates but are decisions which reflect both the Probabilities and the payoffs in the situation.
This study was concerned with asking what kind of experiment could overcome these inference problems to provide unambiguous evidence about such change in subjective probability. Two kinds of experimental design were considered.
In the first, a distinction which had been made in the literature between outcomes dependent on response (D.O.) and outcomes dependent only on the occurrence of an event (I.O.) was maintained. Changes in subjective probability were to be inferred from changes in the value of D.O. selected by subjects. Three experiments showed no evidence of change in these responses while one did show evidence of change in choice of D.O. Closer examination of individual protocols suggested that it was difficult to separate change in subjective probability from changes in decision strategy following the introduction of I.O.
In the second kind of experiment the dependent variable was the evaluation of the worth of a gamble composed of payoffs and probabilities of achieving them. In one experiment a prediction about the independence of payoffs and probabilities in such evaluations was derived from expectation models and tested; in another two dependent variables were included and probabilities inferred from evaluations were compared with those probabilities directly estimated by subjects. In general there was little evidence of change in subjective probability, but different response measures gave different results and it seemed that what was lacked was any clear idea of how subjective probability entered into these evaluations, and that expectation models might not be adequate as models from which subjective probability could be inferred.
From these experiments it was concluded that the kind of experiment required to investigate the interaction of value and subjective probability would be one which would include two dependent variables - inferred probabilities and direct estimates, in an examination of the role that subjective probability played in any one kind of decision situation.

Citation

Crozier, W. (1974). The interaction of value and subjective probability in decision making under risk