Choice under uncertainty

 

Choice under uncertainty

The area of choice under uncertainty represents the heart of decision theory. Known from the 17th century (Blaise pascal invoked it in his famous wager, which is contained in his pensees, published in 1670), the idea of expected values is that, when faced with a number of actions, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that will result from each course of action, and multiply the two to give an "expected value", or the average expectation for an outcome; the action to be chosen should be the one that gives rise to the highest total expected value. In 1738, Daniel bournouli  published an influential paper entitled Exposition of a New Theory on the Measurement of Risk, in which he uses the st, petersburg to show that expected value theory must be normatively wrong. He gives an example in which a Dutch merchant is trying to decide whether to insure a cargo being sent from Amsterdam to St Petersburg in winter. In his solution, he defines a utility functions and computes expected utility rather than expected financial value.

In the 20th century, interest was reignited by Abrahams wald's 1939 paper pointing out that the two central procedures of sampling distributions-based statistical-theory, namely hypothesis testing and parameter estimations, are special cases of the general decision problem. Wald's paper renewed and synthesized many concepts of statistical theory, including loss functions, risk functions, admiessable decision , antecedent procedures, Bayesein procedures, and minimax procedures procedures. The phrase "decision theory" itself was used in 1950 by E.L .Lehmann

The revival of subjective probability theory, from the work of Frank ramsay, Bruno le fenetti, Leonard savage and others, extended the scope of expected utility theory to situations where subjective probabilities can be used. At the time, von Neumann and Morgenstern's theory of expected utility proved that expected utility maximization followed from basic postulates about rational behavior.

The work of Maurice allice and Daniel ellesberg showed that human behavior has systematic and sometimes important departures from expected-utility maximization.The prospect theory by daniel khanemann and Amos tvarsky renewed the empirical study of economic behavior with less emphasis on rationality presuppositions. It describes a way by which people make decisions when all of the outcomes carry a risk. Kahneman and Tversky found three regularities – in actual human decision-making, "losses loom larger than gains"; persons focus more on changes in their utility-states than they focus on absolute utilities; and the estimation of subjective probabilities is severely biased by anchoring.