Biomedical subjects

R Duncan Luce

Publications and source records attributed to R Duncan Luce.

3 recordsLinked to original sources

PubMed2004

Symmetric and asymmetric matching of joint presentations.

The global psychophysical theory of summation and magnitude production of R. D. Luce (2002) had joint presentations of pairs of intensities (measured above threshold) being matched asymmetrically, with 1 component being 0 intensity and the other the matching intensity. For loudness, an intensity pair to the 2 ears is matched by an intensity in just 1 ear. Realizing this experimentally has been difficult, and so, this article extends the theory to the use of symmetric matches with the same intensity being used in both components. In addition, the representational aspect is much improved; a new formulation of the results of the earlier theory is presented; the theory for symmetric matches is outlined; and it is shown that if 1 form of segregation, right or left, holds for asymmetric matches and 1 for symmetric ones, then all forms of segregation hold.

Humans↗

PubMed2002

Two functional equations preserving functional forms.

Two functional equations are considered that are motivated by three considerations: work in utility theory and psychophysics, questions concerning when pairs of degree 1 homogeneous functions can be homomorphic and calculating their homomorphisms, and the link of the latter questions to quasilinear mean values. The first equation is h(σ(y)x + [1 - σ(y)]y) = τ(y)h(x) + [1 - τ(y)]h(y) (x ≥ y ≥ 0), where h maps [0, ∞[into a subset of [0, ∞[and is strictly increasing and continuously differentiable; the functions σ and τ map [0, ∞[continuously into [0,1], σ(y) > 0 for y > 0 but σ is not 1 on]0, ∞[. The solutions are fully determined. (Recently Zsolt Páles has eliminated the differentiability assumption.) The second equation is h[y + f(x - y)] = h(y) + g[h(x) - h(y)] (x ≥ y ≥ 0), where h maps [0, ∞[onto a subinterval of positive length of [0, ∞[and is strictly increasing and twice continuously differentiable, f and g map [0, ∞[onto[0, ∞[and are twice differentiable, and either f"(0) ≠ 0 or g"(0) ≠ 0. The solutions are fully determined under these conditions. When f"(0) = g"(0) = 0 and h" is not identically zero, we determine the solutions under the added assumption of analyticity. It remains an open problem to find the solutions in the latter case under the assumption of only second order differentiability. A more general open problem is to eliminate all differentiability conditions for the second equation.

Journal Article↗

PubMed2002

A psychophysical theory of intensity proportions, joint presentations, and matches.

Empirically testable assumptions relate 3 psychophysical primitives: presentations of pairs of physical intensities (e.g., pure tones of the same frequency and phase to the 2 ears or 2 successive tones to both ears); a respondent's ordering of such signal pairs by perceived intensity (e.g., loudness); and judgments about 2 pairs of stimuli being related as some proportion (numerical factor, as in magnitude production). Explicit behavioral assumptions lead to 2 families of psychophysical functions, one corresponding to unbiased joint presentations and the other to biased ones. Under an invariance assumption, the psychophysical functions in the unbiased case are approximate power functions, and those in the biased case are exact power functions. A number of testable predictions are made. The mathematics involved draws from publications in utility theory and mathematics but with a reinterpretation of the primitives.

Humans↗