By Sven Ove Hansson
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Furthermore, several different decision rules should be tried and compared. 59 9. Decision-making under ignorance By decision-making under ignorance is commonly meant decision-making when it is known what the possible states of affairs are, but no information about their probabilities is available. 1. Situations are not uncommon in which information is lacking not only about the probabilities of the possible states of nature, but also about which these states of affairs are. 2. 1 Decision rules for "classical ignorance" The following is a variant of the umbrella example that has been used in previous sections: You have participated in a contest on a TV show, and won the big prize: The Secret Journey.
The conclusion for applied studies should be that methodological pluralism is warranted. Different measures of incomplete probabilistic information should be used, including binary measures, second-order probabilities and fuzzy measures. Furthermore, several different decision rules should be tried and compared. 59 9. Decision-making under ignorance By decision-making under ignorance is commonly meant decision-making when it is known what the possible states of affairs are, but no information about their probabilities is available.
Ellsberg's index. Daniel Ellsberg proposed the use of an optimism-pessimism index to combine maximin expected utility with what is essentially reliability-weighted expected utility. He assumed that there is both a set Y0 of possible probability distributions and a single probability distribution y0 that represents the best probability estimate. "Assuming, purely for simplicity, that these factors enter into his decision rule in linear combination, we can denote by r his degree of confidence, in a given state of information or ambiguity, in the estimated distribution [probability] yo, which in turn reflects all of his judgments on the relative likelihood of distributions, including judgments of equal likelihood.