Chapter 10
Decision Analysis
10.1 Beliefs and Actions
It is early morning, you are about to set off for the day and you wonder whether to wear the light coat you took yesterday, or perhaps a heavier garment might be more suitable. Your hesitation is due to your uncertainty about the weather; will it be as warm as yesterday or maybe turn cooler? We have seen how your doubts about the weather can be measured in terms of your belief that it will be cooler, a value that has been called probability, and we have seen how uncertainties can be combined by means of the rules of the probability calculus. We have also seen how probabilities may be used, for example in changing your beliefs in the light of new information, as a scientist might do in reaction to an experimental result, or a juror on being presented with new evidence, or as you might do with the problem of the coat by listening to a weather forecast. But there is another feature of your circumstances beyond your uncertainty concerning the weather, which involves the consequences that might result from whatever action you take over the coat. If you take a heavy garment in warm weather, you will be uncomfortably hot and maybe have to carry it; whereas a light coat would be more pleasant. If you wear the light coat and the weather is cold, you may be uncomfortably cold. In this little problem, you have to do something, you have to act. Thinking about the act involves not only uncertainty, and therefore probability, but also the ...
