Chapter 3

Probability

3.1 Measurement

In this chapter the systematic study of uncertainty begins. Recall that there is a person “you”, contemplating an “event”, and it is desired to express your uncertainty about that event, which uncertainty is called your “belief” that the event is true. The tool to be used is reason (§2.1) or rationality, based on a few fundamental premises and emphasizing simplicity (§2.6). The first task is to measure the intensity of your belief in the truth of the event; to attach to each event a number that describes your attitude to the statement. Many people object to the assignment of numbers, seeing it as an oversimplification of what is rightly a complicated situation. So let us be quite clear why we choose to measure and what the measurement will accomplish. One field in which numbers are used, despite being highly criticized by professionals, is wine-tasting, where a bottle of wine is given a score out of 100, called the Parker score after its inventor, the result being that a wine with a high score such as 96 commands a higher price than a mere 90. Some experts properly object that a single number cannot possibly capture all the nuances that are to be found in that most delectable of liquids. Nevertheless, numbers do have a role to play in wine-tasting, where a collection of different wines is tasted by a group of experts, the object being to compare the wines, which naturally vary; variation, as we shall see in §9.1, gives rise to uncertainty. ...

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