TY - JOUR

T1 - Triadic judgment models and Weber's law

AU - Sheu, Ching Fan

N1 - Funding Information:
I am most grateful to Jean-Claude Falmagne, whose guidance over the years has been invaluable. I am indebted to Geoffrey Iverson for a number of useful discussions and for sketching out a version the proof of Proposition 2. John Miyamoto, David Allbritton, Tony Marley and Ragnar Steingrimsson made extensive editorial comments on previous drafts of this paper. Their assistance is greatly appreciated. This work is supported, in part, by Grant NSC94-2413-H-194-028 from the National Science Council of Taiwan.

PY - 2006/6

Y1 - 2006/6

N2 - Let a, b, c, with a {greater than or slanted equal to} b {greater than or slanted equal to} c, be positive real numbers indicating the intensities of physical stimuli in a psychophysical experiment; let Pabc be the probability that b is judged to be more similar to a ("closer to") a than to c. This paper investigates the following representation and its subcases for triadic judgments{A formula is presented}where u is a real-valued, strictly increasing, continuous function and F is continuous, strictly decreasing in the first variable, and strictly increasing in the second variable. In addition to elucidating the connections between the representation and models of discrimination and bisection paradigms, this paper examines the mathematical consequences of Weber's law on subcases of the representation, demonstrating that the resulting analytic forms of these triadic models are very limited. The results constitute partial solutions to questions raised in Falmagne [(1985). Elements of psychophysical theory. New York: Oxford University Press] concerning the impact of Weber's law on probabilistic measurement models for triadic judgments.

AB - Let a, b, c, with a {greater than or slanted equal to} b {greater than or slanted equal to} c, be positive real numbers indicating the intensities of physical stimuli in a psychophysical experiment; let Pabc be the probability that b is judged to be more similar to a ("closer to") a than to c. This paper investigates the following representation and its subcases for triadic judgments{A formula is presented}where u is a real-valued, strictly increasing, continuous function and F is continuous, strictly decreasing in the first variable, and strictly increasing in the second variable. In addition to elucidating the connections between the representation and models of discrimination and bisection paradigms, this paper examines the mathematical consequences of Weber's law on subcases of the representation, demonstrating that the resulting analytic forms of these triadic models are very limited. The results constitute partial solutions to questions raised in Falmagne [(1985). Elements of psychophysical theory. New York: Oxford University Press] concerning the impact of Weber's law on probabilistic measurement models for triadic judgments.

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U2 - 10.1016/j.jmp.2005.12.001

DO - 10.1016/j.jmp.2005.12.001

M3 - Article

AN - SCOPUS:33646887855

VL - 50

SP - 302

EP - 308

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

IS - 3

ER -