By Michael D. Resnik
An creation to what's known as "Choice Theory" in Economics.
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Extra resources for Choices: An Introduction to Decision Theory
This is considered a definite disadvantage of the minimax regret rule. ) There is another feature of the minimax regret rule that disadvantages it in comparison with the maximin rules. It is illustrated in tables 2-13 through 2-13 2-14 Decision Table Regret Table Ai 0 10 4 Al 5 0 6 A2 5 2 10 A2 0 8 0 2-15 2-16 Ai 0 10 4 Ai 10 0 6 A2 5 2 10 A2 5 8 0 A, 10 5 1 A3 0 5 9 2-16. Tables 2-15 and 2-16 have been obtained by adding a new act, AI. In the first set AI is the minimax regret act, in the second A2 is.
But that rule surely would have few adherents. Still, perhaps the heavy conservatism of the maximin rule could be lightened by combining it with the maximax rule. The former operates only on the minimum of each act, the latter only on the maximum. Because these are represented by numbers, it is possible to "compromise" between them by using numbers that themselves fall between the two extremes. For example, if the maximum for an act is 10 and the minimum is zero, then 32 DECISIONS UNDER IGNORANCE 5 can represent a halfway compromise, 8 can represent one favoring the maximum, and 3 one favoring the minimum.
For instance, if you know that you can have your first choice for dessert, you need not completely rank ice cream, cake, fruit, and pie against each other. It is enough that you decide that cake, say, is better than all the rest. You can leave the rest unconnected or with failed transitivities, since, as far as getting dessert goes, the effort of ranking them is wasted. If an agent's preferences meet conditions O1-O8, items ordered by his preferences divide into classes called indifference classes.
Choices: An Introduction to Decision Theory by Michael D. Resnik