Decision Theory

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The Optimist Criterion

The optimist criterion attempts to describe the decision-making behavior of people who are perfectly optimistic in their expectations. An optimistic decision maker is attracted by large rewards and is willing to risk high losses in order to obtain them.

 

It is possible to model the optimist profile with the MAXIMAX decision rule (when the payoffs are positive-flow rewards, such as profits or revenue. When payoffs are given as negative-flow rewards, such as costs, the optimist decision rule is MINIMIM. Note that negative-flow rewards are expressed with positive numbers.)

 

Let's assume that ACME's managers are thoroughly optimistic. We would suppose they would therefore go for a large manufacturing facility in hopes of attaining the maximum profit. The psychological processes leading to such behavior can be captured by the two-step logic of the Maximax rule.

Maximax decision rule

1.  For each action alternative (matrix row) determine the maximum payoff possible.

2.  From these maxima, select the maximum payoff. The action alternative leading to this payoff is the chosen decision.

 

Using ACME's decision matrix defined previously:

"Maximax" is shorthand for "Maximum of the (row) maxima."

By convention, only one additional column is appended to the original matrix. The decision is shown by circling the maximax value, thus indicating the row of the chosen action alternative:

The Minimim decision rule applies when the payoff matrix consists of negative-flow rewards, such as costs. An optimistic decision maker would be attracted by the possibility of securing lower costs.

Critique of Maximax/Minimim
Maximax/Minimim is not a rationally acceptable decision rule because it excludes most of the information available in the payoff matrix. Notice that the Maximax column above shows only three numbers (15, 9, 3) from which to select the course of action. Six payoffs were excluded from consideration in the choice. This means that ~67% of the data for the problem were ignored. Neglecting available information in a decision problem cannot be said to be rational.

Decide for yourself
Consider the following situation: Would you risk getting nothing for a chance to obtain an extra $1 over a sure $99? Most people wouldn't.