History
Ragnar Frisch was the first to write preference relations using the mathematics of axioms, in 1926. Up to then, economists had developed an elaborated theory of demand that omitted primitive characteristics of people. This changed at the end of the 19th and the beginning of the 20th century, when logical positivism started to affect economics through the notion that any theoretical concept used in a theory should be related to observables. Whereas economists in the 18th and 19th centuries felt comfortable theorizing about utility, with the advent of logical positivism in the 20th century, they felt that it needed more of an empirical structure. Because binary choices are directly observable, it instantly appealed to economists. The search for observables in microeconomics is taken even further by revealed preference theory.
Since the pioneer efforts of Frisch in the 1920s, one of the major issues which has pervaded the theory of preferences is the representability of a preference structure with a real-valued function. This has been achieved by mapping it to the mathematical index called utility. Gérard Debreu, influenced by the ideas of the Bourbaki group, championed the axiomatization of consumer theory in the 1950s, and the tools he borrowed from the mathematical field of binary relations have become mainstream since then. Even though the economics of choice can be examined either at the level of utility functions or at the level of preferences, to move from one to the other can be useful. For example, shifting the conceptual basis from an abstract preference relation to an abstract utility scale results in a new mathematical framework, allowing new kinds of conditions on the structure of preference to be formulated and investigated.
Another historical turnpoint can be traced back to 1895, when Georg Cantor, proved in a theorem that if a binary relation is linearly ordered, then it is also isomorphically embeddable in the ordered real numbers. This notion would become very influential for the theory of preferences in economics: by the 1940s prominent authors such as Paul Samuelson, would theorize about people actually having weakly ordered preferences.
Read more about this topic: Preference (economics)
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