Abstract
How is information integrated across the attributes of an option when making risky choices? In most descriptive models of decision under risk, information about risk, and reward is combined multiplicatively (e.g., expected value; expected utility theory, Bernouli, 1738/1954; subjective expected utility theory, Savage, 1954; Edwards, 1955; prospect theory, Kahneman and Tversky, 1979; rank-dependent utility, Quiggin, 1993; decision field theory, Busemeyer and Townsend, 1993; transfer of attention exchange model, Birnbaum, 2008). That is, (some transform of) probability is multiplied by (some transform of) reward to give a value for a risky prospect, and the prospect with the maximum value is then chosen.
Highlights
I argue that information integration in risky decision-making may be additive
Valuations of risky prospects show multiplicative integration of risk and reward, integration is additive for judgments of attractiveness and, if risky decisions are based on attractiveness rather than valuation, integration in risky choice may be additive
Implications for the assessment of the stability of risky preference are profound – stable parameters in the multiplicative model will correspond with different stable parameters in the additive model and, further, the mode of integration itself may vary from time to time or context to context
Summary
How is information integrated across the attributes of an option when making risky choices? In most descriptive models of decision under risk, information about risk, and reward is combined multiplicatively (e.g., expected value; expected utility theory, Bernouli, 1738/1954; subjective expected utility theory, Savage, 1954; Edwards, 1955; prospect theory, Kahneman and Tversky, 1979; rank-dependent utility, Quiggin, 1993; decision field theory, Busemeyer and Townsend, 1993; transfer of attention exchange model, Birnbaum, 2008). Tversky found that there was a p by x interaction when predicting price but not logarithm of price and Tverksy rejected the additive model and concluded that his data were well described by a subjective expected utility model with a power law utility function and a subjective probability function This finding has been replicated with more complicated gambles of the form “p chance of gaining x and q chance of loosing y” (Anderson and Shanteau, 1970), when risks and rewards were presented as verbal phrases (e.g., “a somewhat likely chance to win a watch”) rather than as numbers (Shanteau, 1974), and for strength-of-preference judgments for pairs of gambles (Mellers et al, 1992a). The valence V(pi, xi) of a simple risky outcome Gi of the form “pi chance of xi otherwise nothing” is given by www.frontiersin.org
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