1. Avoiding legal risks

Badger Enterprises publishes a satirical magazine which specializes in publishing embarrassing details of the private lives of politicians. The editors are aware of a scandalous rumor about a member of Congress and wish to proceed with the story in a manner that maximizes expected net income.

The risk of an expensive libel action cannot be ignored and the editors estimate that the effects of such an action will be a cost of $125,000 net if lost (taking into account possible fines, legal costs, effects on future sales, and so on), and zero if won. These costs, and the probability of losing, estimated to be 0.2, are, they believe, independent of whether or not the rumor is true.

However, the probability of the politician suing does depend on whether the rumor is true and they estimate that the probability of his taking legal action is 0.3 if the rumor is true and 0.9 if it is not. They currently estimate the probability of the rumor being true at 0 5.

They have three possible courses of action:

(1) Dropping the story,

(2) Publishing immediately, or

(3) Hiring a private detective to investigate the rumor further so that after his report they could take a decision on whether or not to publish.

The private detective they have in mind would cost $10,000, and he is good but not infallible. The probability of his saying the rumor is true is 1.0 if indeed it is true and 0.2 if it is false. He will definitely answer in one direction or the other, but the probability of being sued depends only on whether the rumor is true or not.

They estimate extra net income (gross of any costs of legal activity) from increased circulation if they publish to be $50,000, and this would be independent of the truth of the story.

What should they do? How much should they be prepared to pay for a report from an infallible private detective?