Robert Duncan Luce was one of the most influential mathematical psychologists of the twentieth century. His work spanned choice theory, measurement theory, psychophysics, and the mathematical foundations of the behavioral sciences, earning him the National Medal of Science in 2003.
Major Contributions
Luce's 1959 book Individual Choice Behavior introduced the choice axiom (now called Luce's Choice Axiom or the IIA property), which became the foundation for probabilistic choice theory. His three-volume work Foundations of Measurement (with Krantz, Suppes, and Tversky) provided the most comprehensive axiomatic treatment of psychological measurement ever produced, establishing rigorous conditions under which psychological attributes can be represented numerically.
In psychophysics, Luce contributed to the theory of response times, proposed a near-miss to Weber's Law, and developed a comprehensive mathematical framework connecting various psychophysical laws. His work consistently emphasized the importance of axiomatic foundations — the idea that psychological measurement should be grounded in clearly stated, testable assumptions about qualitative empirical relations.