By Irving John Good

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**Additional resources for Good Thinking: The Foundations of Probability and Its Applications**

**Example text**

But Peirce blew it. ] One implication of the "suggestion" that all types of judgments can be used is to encourage you to compare your "overall" judgments with your detailed ones; for example, a judgment by a doctor that it is better to operate than to apply medical treatment, on the grounds perhaps that this would be standard practice in the given circumstances, can be "played off" against separate judgments of the probabilities and utilities of the outcomes of the various treatments. (jii) Precision of judgments Most theories of subjective probability deal with numerically precise probabilities.

In America a jury may be satisfied with a lower threshold for condemning a black man for the rape of a white woman than vice versa (News-Chronicle 32815 [1951], 5). Such behavior is unreasonable when combined with democratic bodies of decisions. The importance of the jury's coming to a definite decision, even a wrong one, was recognized in law at the time of Edward 111 (c. 1350). At that time it was regarded as disgraceful for a jury not to be unanimous, and according to some reports such juries could be placed in a cart and upset in a ditch (Enc.

If the class of problems put to the expert have the property that the average value of p is x, then the factor 2 in the above formula for the fee should be replaced by x~x(\ — x}~(\~*} = b, say. " [But see p. ]) Another modification of the formula should be made in order to allow for the diminishing utility of money (as a function of the amount, rather than as a function of time). In fact if Daniel Bernoulli's logarithmic formula for the utility of money is assumed, the expression for the fee ceases to contain a logarithm and becomes c\[bp\ }k — 1| or —c(l — (b — bpl )&}, where c is the initial capital of the expert.