Leonard Jimmie Savage (1917–1971) was the architect of modern Bayesian decision theory. His 1954 book The Foundations of Statistics synthesized the insights of Ramsey, de Finetti, and von Neumann–Morgenstern into a unified axiomatic framework in which rational decision-making under uncertainty requires the use of personal (subjective) probabilities updated by Bayes' theorem. More than any other single work, Savage's Foundations provided the philosophical and mathematical justification that the Bayesian movement needed to challenge the dominant frequentist paradigm.
Early Life and Education
Born Leonard Ogashevitz in Detroit, Michigan, Savage later changed his surname. Despite severe visual impairment from childhood, he excelled academically, earning his PhD in mathematics from the University of Michigan in 1941 under the supervision of Sumner Myers. He worked at the Institute for Advanced Study, the Statistical Research Group at Columbia University during World War II, the University of Chicago, and finally Yale University, where he spent the last years of his career.
The Foundations of Statistics
Savage's masterwork, The Foundations of Statistics (1954), begins with a set of axioms governing a rational agent's preferences over acts—functions mapping states of the world to consequences. From these axioms, Savage derives both a unique subjective probability distribution over states and a utility function over consequences, such that the agent behaves as if maximizing expected utility. This framework, known as subjective expected utility (SEU) theory, remains the standard normative model of rational choice under uncertainty.
“According to the personalistic view, the role of the mathematical theory of probability is to enable the person using it to detect inconsistencies in his own real or envisaged behavior.”— L. J. Savage, The Foundations of Statistics (1954)
The Sure-Thing Principle
Among Savage's axioms, the most famous and controversial is the Sure-Thing Principle: if you would prefer act A to act B knowing that event E occurred, and you would also prefer A to B knowing that E did not occur, then you should prefer A to B regardless of whether E occurs. This seemingly innocuous principle, when combined with Savage's other axioms, is sufficient to generate the entire SEU framework. It was challenged by the Allais paradox and has been the subject of intense debate ever since.
Savage did not merely provide a theoretical foundation; he actively proselytized for the Bayesian approach. His influence extended through his students, his collaborators (including Dennis Lindley and I. J. Good), and his participation in key conferences and debates. The Bayesian renaissance of the 1960s and 1970s is directly traceable to the intellectual energy Savage generated.
Other Contributions
Beyond the Foundations, Savage made important contributions to the minimax theory of Abraham Wald, to the foundations of mathematical statistics more broadly, and to the study of elicitation of subjective probabilities. His 1962 monograph The Foundations of Statistical Inference, based on a discussion with other leading statisticians, remains a model of clarity in statistical philosophy.
Legacy
Savage died prematurely of a heart attack at the age of fifty-three. His influence, however, has only grown. The SEU framework is foundational in economics, artificial intelligence, and cognitive science, and The Foundations of Statistics is regarded as one of the most important books in twentieth-century statistics.
Born on 20 November in Detroit, Michigan, as Leonard Ogashevitz.
Received PhD in mathematics from the University of Michigan.
Worked at the Statistical Research Group, Columbia University, during World War II.
Published The Foundations of Statistics.
Professor at the University of Chicago.
Moved to Yale University as Eugene Higgins Professor of Statistics.
Died on 1 November in New Haven, Connecticut, aged fifty-three.