von Neumann-Morgenstern Utility Theorem
A von Neumann-Morgenstern Utility Theorem is a theorem that any individual with vNM utility function (u) and whose preferences satisfied four axioms then their individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility.
- Context:
- He became religious before dying of cancer (converted to Catholicism).
- See: von Neumann-Morgenstern Utility Function, Theory of Games and Economic Behavior, Expected Utility Hypothesis, Greatest Happiness Principle.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Von_Neumann–Morgenstern_utility_theorem Retrieved:2014-9-13.
- In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four [1] axioms has a utility function; such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility. That is, they proved that an agent is (VNM-)rational if and only if there exists a real-valued function u defined by possible outcomes such that every preference of the agent is characterized by maximizing the expected value of u, which can then be defined as the agent's VNM-utility (it is unique up to adding a constant and multiplying by a positive scalar). No claim is made that the agent has a "conscious desire" to maximize u, only that u exists.
Any individual whose preferences violate von Neumann and Morgenstern's axioms would agree to a Dutch book, which is a set of bets that necessarily leads to a loss. Therefore, it is arguable that any individual who violates the axioms is irrational. The expected utility hypothesis is that rationality can be modeled as maximizing an expected value, which given the theorem, can be summarized as “rationality is VNM-rationality”.
VNM-utility is a decision utility in that it is used to describe decision preferences. It is related but not equivalent to so-called E-utilities[2] (experience utilities), notions of utility intended to measure happiness such as that of Bentham's Greatest Happiness Principle.
- In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four [1] axioms has a utility function; such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility. That is, they proved that an agent is (VNM-)rational if and only if there exists a real-valued function u defined by possible outcomes such that every preference of the agent is characterized by maximizing the expected value of u, which can then be defined as the agent's VNM-utility (it is unique up to adding a constant and multiplying by a positive scalar). No claim is made that the agent has a "conscious desire" to maximize u, only that u exists.
- ↑ Neumann, John von and Morgenstern, Oskar, Theory of Games and Economic Behavior. Princeton, NJ. Princeton University Press, 1953.
- ↑ Kahneman, Wakker and Sarin, 1997, Back to Bentham? Explorations of experienced utility, The quarterly journal of economics.
1944
- (von Neumann & Morgenstern, 1944) ⇒ John von Neumann, and Oskar Morgenstern.(1944). “Theory of Games and Economic Behavior".