R. Duncan Luce, a UC Irvine mathematical psychologist who received the National Medal of Science in 2005 for his pioneering scholarship in behavioral sciences, died Aug. 11 at his home in Irvine after a brief illness, the university announced. He was 87.

In 1988, Luce founded and became director of UC Irvine's Institute for Mathematical Behavioral Sciences. He was later named distinguished research professor in cognitive sciences and economics.

His work, according to the university, combined formal math models with psychological experiments to try to understand and predict human behavior, including how individuals and groups make decisions. His studies of decision making and game theory have been applied to the fields of economics, social sciences, psychology and other disciplines.

Luce explained that in his studies he assigned numerical values to psychological experiences and sensory events to allow researchers to accurately measure and compare the occurrences to one another.

For example, light perception can be described in varying degrees from dim to brilliant, with each stage receiving its own numerical figure. Other human experiences could be treated similarly.

"When you can represent these numerically, then you can start writing equations and using the kind of mathematics the physical sciences have generated," Luce said in a 1989 interview with the Orange County Register.

Robert Duncan Luce was born May 16, 1925, in Scranton, Pa., and majored in aeronautical engineering while enrolled in the Navy's accelerated V-12 training program at the Massachusetts Institute of Technology. After World War II, he returned to MIT and switched to mathematics for his doctorate.

"I remember telling my parents I decided to go to graduate school in mathematics," Luce said in the 1989 interview. "My father shook his head and reminded me of the PhDs who were selling apples on the street during the Depression. He thought it was very ill-advised and not a good way to make money. Later on, things turned out reasonably well and he changed his view."

Luce did research at MIT, Columbia University, the University of Pennsylvania and the Institute for Advanced Study at Princeton before joining UC Irvine's social sciences department in 1972. A few years later he left for Harvard University, where he became chairman of the psychology department. Irvine lured him back in 1988.

Among his academic publications are "Individual Choice Behavior," widely used as a college textbook, and "Games and Decisions," a 1957 study of game theory written with Howard Raiffa.

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R. Duncan Luce dies at 87; UC Irvine mathematical psychologist