Strategic Choice in Hilbert Space

A small-but-growing number of social scientists have in recent years begun to explore the purchase of formalisms and a probability theory originally developed to accommodate nonclassical experimental results in particle physics. Motivated by the desire to explain empirical outcomes that do not fit comfortably with the axioms of rational choice theory—and that are thus related tenets of classical probability theory—these scholars have begun to examine and embrace the theory of probability namesaked for Max Born as a general framework for understanding and modeling choice. Born’s (1926) account of probability differs from the familiar, classical context of Kolmogorov both in terms of its mathematical exposition/foundation and with respect to its governing axioms. The Born theory is expressly geometric as opposed to set-theoretic. Its axioms are formalized in the (usually) complex planes of Hilbert spaces, where distances are most generally conceptualized as metrics between (sometimes high-dimensional) spaces as opposed to points. In this framework, certain of Kolmogorov’s set-theoretic axioms can be relaxed, and empirical results that do not agree with them can be systematically accommodated.