Customer Reviews

Probability and the Art of Judgment (Cambridge Studies in Probability, Induction and Decision Theory)

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Richard Jeffrey(RJ)has written an excellent book for the specialist reader.Such a reader needs to have already covered material equivalent to a bachelor's degree in philosophy plus have some familiarity with decision theory applied from a Bayesian perspective,loosely defined.The only objection I have about this book is the practically nonexistent treatment of the contributions to decision theory made by J M Keynes in 1921 in his pathbreaking work A Treatise on Probability(TP).RJ either ignores or is simply unaware of Keynes's original work on interval estimates done in chapters 5,10,15,17 and Part III of the TP.Keynes is the first scholar in history to provide an indepth analysis of an interval estimate approach.Unfortunately,Keynes called his interval estimates "nonnumerical " or "nonmeasurable" probabilities.Keynes's reasoning in using these terms is impeccable.Given that a numerical estimate of probability refers to the use of a single numeral or number,nonnumerical means that one numeral or number ,alone,is not sufficient to specify the probability relationship.In general, two numbers,not one,must be used in order to measure a probability.Naturally, if the interval estimates overlap,problems of noncomparability,nonrankability and incommensurability will occur,greatly complicating an analysis of probabilities.However, it should be clear that interval estimates are quantitative in nature.Unfortunately,F P Ramsey completely botched his two reviews of Keynes's TP in 1922 and 1926,coming up with the strange conclusion that Keynes's nonnumerical probabilities were "mysterious" entities that used NO numbers at all.It is possible that RJ is implicitly relying on these two reviews,since he quotes portions of Ramsey's two reviews at different places in his book.RJ also ignores Keynes's specification of an index,defined on the unit interval[0,1],to measure the completeness of the evidence upon which to base an estimate of a probability.Keynes's called his variable, w ,the weight of the evidence,where 0<=w<=1.Finally,RJ ignores Keynes's conventional coefficient of risk and weight,c. c incorporates nonlinear probability preferences and weight of the evidence(also called the ambiguity,vagueness,or uncertainty of the evidence)into a clearcut decision rule. Keynes's rule specifies that the decision maker seek to maximize cA,where A is the outcome.Again,Keynes was the first scholar in history to specify such a decision rule.RJ needs to include this material in a future revised edition of the present volume.