Individual Choice Behavior: A Theoretical Analysis

by R. Duncan Luce

This influential treatise presents upper-level undergraduates and graduate students with a mathematical analysis of choice behavior. It begins with the statement of a general axiom upon which the rest of the book rests; the following three chapters, which may be read independently of each other, are devoted to applications of the theory to substantive psychophysics, utility, and learning.
Applications to psychophysics include considerations of time- and space-order effects, the Fechnerian assumption, the power law and its relation to discrimination data, interaction of continua, discriminal processes, signal detectability theory, and ranking of stimuli. The next major theme, utility theory, features unusual results that suggest an experiment to test the theory. The final chapters explore learning-related topics, analyzing the stochastic theories of learning as the basic approach with the exception that distributions of response strengths are assumed to be transformed rather than response probabilities. The author arrives at three classes of learning operators, both linear and nonlinear, and the text concludes with a useful series of appendixes."

Unknown Binding

First published September 25, 1979

About the author

R.Duncan Luce is Distinguished Research Professor of Cognitive Science and Research Professor of Economics at the University of California, Irvine.

From Wikipedia:
Robert Duncan Luce (born May 16, 1925) is the Distinguished Research Professor of Cognitive Science at the University of California, Irvine.

Luce received a B.S. in Aeronautical Engineering from the Massachusetts Institute of Technology in 1945, and PhD in Mathematics from the same university in 1950. He began his professorial career at Columbia University in 1954, where he was an assistant professor in mathematical statistics and sociology. Following a lecturership at Harvard University from 1957 to 1959, he became a professor at the University of Pennsylvania in 1959, and was awarded the Benjamin Franklin Professorship of Psychology in 1968. After visiting the Institute for Advanced Study beginning in 1969, he joined the UC Irvine faculty in 1972, but returned to Harvard in 1976 as Alfred North Whitehead Professor of Psychology and then later as Victor S. Thomas Professor of Psychology. He was elected to the National Academy of Sciences in 1972 for his work on fundamental measurement, utility theory, global psychophysics, and mathematical behavioral sciences. In 1988 Luce rejoined the UC Irvine faculty as Distinguished Professor of Cognitive Sciences and (from 1988 to 1998) director of UCI's Institute for Mathematical Behavioral Sciences. He received the 2003 National Medal of Science in behavioral and social science for his contributions to the field of mathematical psychology.

Contributions for which Luce is known include formulating Luce's choice axiom formalizing the principle that additional options should not affect the probability of selecting one item over another, defining semiorders, introducing graph-theoretic methods into the social sciences, and coining the term "clique" for a complete subgraph in graph theory.