Decision, Probability and Utility : Selected Readings

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Summary: Gardenfors and Sahlin ignore Keynes's contributions.
Review: This book is a collection of the most important articles published in applied probability/decision theory through 1988.Some of the articles that are republished in this book are F Ramsey's "Truth and Probability",H Kyburg's" Bets and Beliefs",Kahneman and Tversky's "Prospect Theory...",Issac Levi's "Indeterminate Probabilities",Daniel Ellsberg's "Risk,Ambiguity and the Savage Axiom's",Gardenfors and Sahlin's "Unreliable Probabilities...",among others.This book is highly recommended for the specialist reader.The main criticism of the essays in this book is the complete absence of any discussion about J M Keynes's contributions to applied probability and decision science made in 1921 in his pathbreaking A Treatise on Probability(TP).Gardenfors and Sahlin(GS)make a major error in placing the 1926 Ramsey review of Keynes's TP as the book's first selection.Bertrand Russell was making an understatement when he stated that the Ramsey reviews of Keynes's TP had the least value of any of Ramsey's published or unpublished work.Ramsey completely misinterpreted Keynes's definitions of the word's"nonnumerical" and "nonmeasurable"in Keynes's introductory chapter 3 in the TP.Ramsey mistakenly assumed that Keynes was arguing that in general a decision maker would be unable to estimate probabilities using numbers (or numerals as Keynes called them).Ramsey thus talks about Keynes's "mysterious nonnumerical probabilities" and/or"mysterious degrees of belief".In fact,this reviewer can find no value at all in either of Ramsey's reviews with respect to his assessment of Keynes's TP.Contrary to Ramsey,Keynes is the first scholar in history to develop a systematic approach to estimating probabilities using intervals.Each interval has a lower bound and a upper bound.This requires two numerals,not one.Thus ,by nonnumerical Keynes meant that in general it would not be possible to estimate a probability using a single number(i.e.,nonnumerical meant "not by a single numeral").Of course ,this introduced the problem of overlapping interval estimates.Problems of noncomparability,nonrankability, and incommensurability would complicate the evaluations of probabilities.Ramsey overlooked Keynes's analysis contained in chapters5,10,15,17 and Part III of the TP.Unfortunately,so do all of the other contributors to this book.None of the articles mention that Keynes was the first scholar to specify an index to measure the weight of the evidence.Letting w equal the weight of the evidence,w is defined on the unit interval[0,1]as 0<=w<=1.w measures the completeness of the relevant potential evidence available to a decision maker in order to calculate an estimate of probability.Finally,all of the contributors to this volume of collected essays overlooked Keynes's major contribution to decision theory,his conventional coefficient of risk and weight,c.c incorporates variables needed to deal with nonlinear probability preferences and weight of the evidence problems(Ellsberg calls the problem ambiguity while GS call the problem unreliable probabilities).The goal of Keynes's decision theory is to maximize cA,as opposed to the expected value rule(maximize pA,where p is a reliable probability and A is an outcome)or the expected utility rule(maximize pU(A),where U is a utility function).It is suggested that GS republish Keynes's chapter 26 from the TP in a revised edition so that the potential reader has all the evidence available on Keynes's contribution.