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ACC544: Statistics Assignment- Charles Sturt University

Internal code- MAS546

Statistics Assignment

Questions

Most of the rules for decision making under uncertainty express a different degree of decision maker´s optimism.
We will describe the most used rules for the choice of the best alternative supposing that the decision criterion expresses the requirement of maximization
The maximax rule is appropriate for extreme optimists that expect the most favorable situation (they choose the alternative that could result in the maximum payoff). Under this rule, the decision maker will find the largest payoff in the decision matrix and select the alternative associated with it (the largest payoff is determined for each alternative and then the largest payoff from these values is selected; therefore “maximax”).
The maximin rule (Wald criterion) represents a pessimistic approach when the worst decision results are expected. The decision maker determines the smallest payoff for each alternative and then chooses the alternative that has the best (maximum) of the worst (minimum) payoffs (therefore “maximin”).
The Hurwicz-criterion represents a compromise between the optimistic and the pessimistic approach to decision making under uncertainty. The measure of optimism and pessimism is expressed by an optimism – pessimism index . The more this index is near to 1, the more the decision maker is optimist. By means of the index, a weighted average of the best payoff and the worst payoff (its weight  is computed for each alternative and the alternative with the largest weighted average should be chosen The principle of insufficient reason (Laplace criterion) assumes that all states of nature are equally likely. Under this assumption, the decision maker can compute the average payoff for each row (the sum of the possible consequences of each alternative is divided by the number of states of nature) and, then, select the alternative that has the highest row average.

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