A Conflict between Finite Additivity and Avoiding Dutch Book
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چکیده
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منابع مشابه
Countable Additivity and Subjective Probability
While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti’s central argument against countable additivity and provide a new Dutch book proof of the principle, to argue that if we accept the Dutch book foundations of subjective probability, countable additivity is a...
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Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of aut...
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The object here is to sketch the mathematics behind de Finetti’s (1931, 1937) argument for the Bayesian position. Suppose a bookie sets odds on all subsets of a set, accepting bets in any amount (positive or negative) on any combination of subsets. Unless the odds are computed from a prior probability, dutch book can be made: for some system of bets, the clever gambler wins a dollar or more, no...
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