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Increasing Increment Generalizations Of Rank-Dependent Theories

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  • R. Duncan Luce

Abstract

Empirical evidence from both utility and psychophysical experiments suggests that people respond quite differently--perhaps discontinuously--to stimulus pairs when one consequence or signal is set to `zero.' Such stimuli are called unitary. The author's earlier theories assumed otherwise. In particular, the key property of segregation relating gambles and joint receipts (or presentations) involves unitary stimuli. Also, the representation of unitary stimuli was assumed to be separable (i.e., multiplicative). The theories developed here do not invoke separability. Four general cases based on two distinctions are explored. The first distinction is between commutative joint receipts, which are relevant to utility, and the non-commutative ones, which are relevant to psychophysics. The second distinction concerns how stimuli of the form (x, C; y) and the operation of joint receipt are linked: by segregation, which mixes stimuli and unitary ones, and by distributivity, which does not involve any unitary stimuli. A class of representations more general than rank-dependent utility (RDU) is found in which monotonic functions of increments U(x)-U(y), where U is an order preseving representation of gambles, and joint receipt play a role. This form and its natural generalization to gambles with n > 2 consequences, which is also axiomatized, appear to encompass models of configural weights and decision affect. When joint receipts are not commutative, somewhat similar representations of stimuli arise, and joint receipts are shown to have a conjoint additive representation and in some cases a constant bias independent of signal intensity is predicted.

Suggested Citation

  • R. Duncan Luce, 2003. "Increasing Increment Generalizations Of Rank-Dependent Theories," Theory and Decision, Springer, vol. 55(2), pages 87-146, September.
  • Handle: RePEc:kap:theord:v:55:y:2003:i:2:p:87-146
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    Cited by:

    1. R. Luce, 2005. "Measurement analogies: comparisons of behavioral and physical measures," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 227-251, June.
    2. R. Luce & A. Marley, 2005. "Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations," Journal of Risk and Uncertainty, Springer, vol. 30(1), pages 21-62, January.
    3. R. Luce & C. Ng & A. Marley & János Aczél, 2008. "Utility of gambling I: entropy modified linear weighted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 1-33, July.

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