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Luce, R.

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Luce

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Luce, R.

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1986 - 19902

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Author's Publications: search.filters.isAuthorOfPublication.8006854d-6083-4b48-a878-2da711fd1a58

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    Uniqueness and Homogeneity of Ordered Relational Structures
    (Elsevier, 1986) Luce, R.
    There are four major results in the paper. (1) In a general ordered relational structure that is order dense, Dedekind complete, and whose dilations (automorphisms with fixed points) are Archimedean, various consequences of finite uniqueness are developed (Theorem 2.6). (2) Replacing the Archimedean assumption by the assumption that there is a homogeneous subgroup of automorphisms that is Archimedean ordered is sufficient to show that the structure can be represented numberically as a generalized unit structure in the sense that the defining real relations satisfy the usual numerical property of homogeneity (Theorem 3.4). The last two results pertain just to idempotent concatenation structures. (3) In a closed, idempotent, solvable, and Dedekind complete concatenation structure, homogeneity is equivalent to the structure satisfying an inductive property analogous to the condition for homogeneity in a positive concatenation structure (Theorem 4.3). Finally, (4) an axiomatization is given for an idempotent structure to be of scale type (2, 2), which has previously been shown to be equivalent to a dual bilinear representation. Basically two operations are defined in terms of the given one, and the conditions are that each must be right autodistributive and together they satisfy a generalized bisymmetry property. The paper ends listing several unsolved problems.
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    Rational Versus Plausible Accounting Equivalences in Preference Judgments
    (Blackwell Publishers, 1990) Luce, R.
    Subjective expected utility (SEU) embodies four distinct principles of rational behavior. Although all have been called into some question empirically, the least plausible and least studied is the property that formally equivalent gambles are treated as indifferent in preference. The paper describes some results that arise when this property is sharply weakened and to some degree replaced by alternative rational and not-so-rational-assumptions. The resulting utility representations, like SEU, are weighted averages of the utilities of consequences, but with the weights dependent on more than the underlying chance event. In rank-dependent cases, which arise from a restricted assumption about formally equivalent gambles, the weights depend on the rank position of the corresponding consequence. In ank-and sign-dependent models, they depend both on the rank position of the consequence associated to the event and on whether it is a gain or a loss. The theory giving rise to the latter involves an additional primitive, namely, joint receipt of gambles, in terms of which new rational and irrational assumptions are invoked. The result generalizes prospect theory to gambles with more than a single gain and a single loss.