Rational Decisions (The Gorman Lectures in Economics)
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It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds.
The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies.
Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making.
else whatever—including sex and food. It is therefore unsurprising that a modern school of behavioral economists have reverted to this classical understanding of the nature of utility. A more specialized group devote their attention specifically to what they call happiness studies. However, the theory of revealed preference remains the orthodoxy in economic theory (Mas-Collel et al. 1995). 1.5.1 Freeing Economics from Psychology Economists after Bentham became increasingly uncomfortable,
to (7.5) to go through with gambles like a of figure 7.1 replaced by gambles like b. As before, the constants A and B are independent of , but now they depend on and F as well as E. Nor is it true that B = 0 in this new situation. Setting = yields that . Hence the Von Neumann and Morgenstern utility for gamble b in figure 7.1 is Similar reasoning also leads to the equation It follows from (7.7) and (7.8) that Since the left-hand side is independent of and the right-hand side is
ordinary people and Bayesian statisticians learn from experience is irrelevant. To take the argument forward, I want to draw an analogy between how a Bayesian learns while using the massaging methodology I have attributed to Savage, and how a child learns arithmetic. When Alice learns arithmetic at school, her teacher doesn’t know what computations life will call upon her to make. Among other things, he therefore teaches her an algorithm for adding numbers. This algorithm requires that Alice
already have anticipated what her reaction would be if she were to learn F. She will therefore have no reason to alter prob(E|F) should F occur. On the other hand, if she hasn’t carried through some analogue of the massaging process, there is no particular reason why she should be consistent at all. It may be that the occurrence of F inspires her with a whole new worldview. She may previously have been using Bayes’ rule to update her probabilities from a prior derived from her old worldview, but
94, 116, 124, 134 random, 101 randomizing box, 104 randomizing device, 96 rational choice theory, 21 rationalism, 1 Rawls, John, 39, 52, 62, 69 Riley, John, 52 Rios, S., 90, 125, 164 risk, 94 risk neutral, 53 Robbins, Lionel, 15, 67 Rubin, Herman, 161 Rumsfeld, Donald, 139 Ryan, Matthew, 168 sample space, 76 Samuelson, Larry, x Samuelson, Paul, 7, 38 Savage, Leonard, ix, 2, 22, 95, 116, 154, 163 Schervish, Mark, 2 Schmeidler, David, 1, 89, 92, 93 Seidenfeld, Teddy, 2, 88