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Thinking and Deciding

Thinking and Deciding

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Chapter 5<br />

Normative theory<br />

of probability<br />

O fortune<br />

Like the moon<br />

Everchanging<br />

Rising first<br />

Then declining;<br />

Hateful life<br />

Treats us badly<br />

Then with kindness<br />

Making sport with our desires,<br />

Causing power<br />

And poverty alike<br />

To melt like ice.<br />

Translation of anonymous twelfth- or thirteenthcentury<br />

Latin lyric, set to music by Carl Orff, to<br />

begin Carmina Burana, completed in 1936.<br />

Our theory of thinking is intended to help us choose among actions <strong>and</strong> beliefs.<br />

Making such choices obviously often involves estimating the likelihood that various<br />

events will occur in the future. Will it rain tomorrow? Will I get the job I applied<br />

for? Probability theory is a well-established normative theory that deals with such<br />

estimates.<br />

The ancient Egyptians played games of chance that involved calculation of probabilities,<br />

but the development of modern probability theory began only in the seventeenth<br />

century (Hacking, 1975). In part, this development was inspired by the<br />

practice of town governments raising money by selling annuities. Miscalculation of<br />

the chances of living to various ages left some towns bankrupt. One person who<br />

helped solve the problem of how to figure the price of annuities so that the seller<br />

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