#reading-9-probability-concepts
The theorem’s name comes from the terminology of wagering. Suppose someone places a $100 bet on
X at odds of 10 to 1 against
X, and later he is able to place a $600 bet against
X at odds of 1 to 1 against
X. Whatever the outcome of
X, that person makes a riskless profit (equal to $400 if
X occurs or $500 if
X does not occur) because the implied probabilities are inconsistent. He is said to have made a
Dutch book in
X.
Ramsey (1931) presented the problem of inconsistent probabilities. See also
Lo (1999).
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