Inductive logic is risky. We need it when we are uncertain. Not just uncertain about what will happen, or what is true, but also when we are uncertain about what to do. Decisions need more than probability. They are based on the value of possible outcomes of our actions. The technical name for value is utility. This chapter shows how to combine probability and utility. But it ends with a famous paradox.
ACTS
Should you open a small business?
Should you take an umbrella?
Should you buy a Lotto ticket?
Should you move in with someone you love?
In each case you settle on an act. Doing nothing at all counts as an act.
Acts have consequences.
You go broke (or maybe found a great company).
You stay dry when everyone else is sopping wet (or you mislay your umbrella).
You waste a dollar (or perhaps win a fortune).
You live happily ever after (or split up a week later).
You do absolutely nothing active at all: that counts as an act, too. Some consequences are desirable. Some are not. Suppose you can represent the cost or benefit of a possible consequence by a number–so many dollars, perhaps. Call that number the utility of the consequence.
Suppose you can also represent the probability of each possible consequence of an act by a number.
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