By Michael D. Resnik
An creation to what's known as "Choice Theory" in Economics.
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Additional info for Choices: An Introduction to Decision Theory
Given any two-act problem in which the maximum for A \ is greater than that for A^ while the minimum for A\ is less than that for A-i, we can "rationalize" the choice of either act by appropriately moving our optimism index closer to 1 (to justify A\) or to 0 (to justify A2). Finally, let us also note that the optimism-pessimism rule presupposes an interval utility scale. To see this consider decision table 2-23. Letting the opti- 2-23 A, 0 4 A2 2 1 mism index be 1/2, the rule picks A\. But now let us hold the optimism index constant and apply an ordinal transformation to obtain table 2-24.
To take an illustration well known to decision theorists, suppose you sat down in an apparently seedy restaurant and were offered a choice between hamburger and roast duck. Ordinarily you prefer roast duck but you fear that this cook will ruin it. So you silently opt for the hamburger. Then the waiter returns to tells you that today you can also have frog legs sauteed in wine. The thought revolts you, but the new choice informs you that the cook has skill; so you change your mind and order the duck.
Thus Luce and Raiffa refers to the book Games and Decisions by R. D. Luce and H. Raiffa. When I cite two works by the same author, I will either use a brief title or give the author's name and the publication date of the work in question. The classic general treatise on decision theory is Luce and Raiffa. It not only surveys several of the topics not covered in this book but also contains an extensive bibliography. The reader wishing to do more advanced study in decision theory should begin with this work.