Coherence Brian
نویسنده
چکیده
A very rich and reliable bookie posts odds on a horse race. He values a contract which pays a pound of gold if Stewball wins at one ounce of gold. He values a contract which pays a pound of gold if Molly wins at one ounce of gold. He will buy or sell these contracts in any quantity at what he considers the fair price or better. Suppose that he also deals in contracts which pay a pound of gold if either Stewball or Molly win, and that he values these at four ounces of gold. If you had two ounces of gold, you could then buy separate contracts for Stewball and Molly for a net outlay of two ounces of gold and sell back a disjunctive contract on Stewball or Molly winning for four ounces of gold. With these you can now buy two seperate contracts each on Stewball and Molly, and sell back two disjunctive contracts, etc. If you don't have two ounces of gold, perhaps your banker will lend them to you on the strength of your prospects. You are able to make a Dutch Book against the bookie-a finite number of bets whose net gain is positive no matter what the outcome of the race-because his evaluation of the disjunctive contract does not cohere with his evaluation of the seperate contracts on its disjuncts. Coherence requires that if the bookie values the seperate contracts at one ounce of gold each, he values the disjunctive contract which pays off exactly as holding both seperate contracts together would, at two ounces of gold. Coherence also requires that a contract that pays a pound of gold no matter what is worth a pound of gold; and that a contract that pays off a pound of gold in some circumstan
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