Subjective Probability Theory Research Articles

KEYNES, RAMSEY, AND PRAGMATISM

In his recent paper in this journal, Bradley Bateman (2021) breaks with the “standard view” of Frank Ramsey’s influence on Jahn Maynard Keynes and argues that Ramsey’s pragmatist philosophical thought underpinned both Keynes’s acceptance of Ramsey’s subjective theory of probability and Keynes’s adoption of a narrative theory of the role of confidence in economic fluctuations in the General Theory. In this paper it is argued that Bateman is right both in emphasizing the influence of Ramsey’s pragmatist philosophy on Keynes’s thought during the development of the General Theory and afterwards and in arguing that the influence of Ramsey’s pragmatist philosophy partly explains Keynes’s emphasis on the importance of the state of confidence in Chapter 12 of the General Theory. However, it is argued that Ramsey’s pragmatist philosophy had a much greater influence on Keynes than acknowledged by Bateman. Furthermore, contra Bateman, Keynes’s move to a more pragmatist philosophical position does not imply that Keynes accepted Ramsey’s subjective theory of (measurable) probability.

Theoretical-probablic approach to the modeling of uncertainty in economic activity from the perspective of the historical path of its development

The article is devoted to the problem of modeling uncertainty in the field of economics and business based on probability theory. Specifically, the purpose of the study was to review the features, potential and limitations of probability theory as a means of quantitative analysis and modeling of uncertainty in economic activity from the point of view of the historical path of its formation and development. As part of this, the key events of the origin and development of probability theory, key aspects of substantiating its logical foundations and building it as a purely mathematical discipline were considered. Particular attention was paid to the issue of distinguishing between stochastic and non-stochastic uncertainty in the plane of practical situations of economic decision-making. As one of the important methodological emphases of the work, the thesis that when the situation of making an economic decision is burdened by non-stochastic uncertainty of one or another origin, it is justified and useful to turn to an expert approach. At the same time, the theory of subjective probabilities, the theory of fuzzy sets, and interval analysis stand out as the system-forming components of the theoretical basis of the latter.

The notion of event in probability and causality: Situating myself relative to Bruno de Finetti

As Bruno de Finetti taught us, the notion of event in a theory of probability is fundamental, perhaps determinative. In this paper, I compare the notion of event in de Finetti's subjective theory of probability with the more situated notion of event that underlies the theory of probability and causality that I developed in the 1990s.This text was prepared for talks in Pisa, March 14, 2001, and Bologna, March 15, 2001.

PRAGMATISM AND PROBABILITY: RE-EXAMINING KEYNES’S THINKING ON PROBABILITY

As we celebrate the centenary of John Maynard Keynes’s Treatise on Probability (1921), we are still faced with unresolved, fundamental questions about his foray into the philosophy of probability. One of these unresolved questions concerns whether Keynes (1931) later changed his mind in response to intense criticism from Frank Ramsey (1922, 1931) and abandoned the logical theory of probability. This essay draws from Cheryl Misak’s recent biography of Frank Ramsey (2020) to argue that Ramsey had an even wider influence on Keynes’s work than has been recognized, and that this influence was not just on his philosophy of probability but also on his economics. Understood in this fuller context, it seems even more clear that Keynes embraced and built upon Ramsey’s subjective theory of probability in The General Theory of Employment, Interest, and Money (1936).

Sequentially Forecasting Economic Indices Using Mixture Linear Combinations of EP Distributions

This article displays an application of the statistical method motivated by Bruno de Finetti’s operational subjective theory of probability. We use exchangeable forecasting distributions based on mixtures of linear combinations of exponential power (EP) distributions to forecast the sequence of daily rates of return from the Dow-Jones index of stock prices over a 20 year period. The operational subjective statistical method for comparing distributions is quite different from that commonly used in data analysis, because it rejects the basic tenets underlying the practice of hypothesis testing. In its place, proper scoring rules for forecast distributions are used to assess the values of various forecasting strategies. Using a logarithmic scoring rule, we find that a mixture linear combination of EP distributions scores markedly better than does a simple mixture over the EP family, which scores much better than does a simple Normal mixture. Surprisingly, a mixture over a linear combination of three Normal distributions also makes a substantial improvement over a simple Normal mixture, although it does not quite match the performance of even the simple EP mixture. All substantive forecasting improvements become most marked after extreme tail phenomena were actually observed in the sequence, in particular after the abrupt drop in market prices in October, 1987. However, the improvements continue to be apparent over the long haul of 1985-2006 which has seen a number of extreme price changes. This result is supported by an analysis of the Negentropies embedded in the forecasting distributions, and a proper scoring analysis of these Negentropies as well.

Why Did F. P. Ramsey Never Repeat the Claims He Had Made on the First Page of His Jan., 1922 Cambridge Magazine Three Page Note Concerning Keynes’s Logical Theory of Probability?: It Is Easy for a Reader To See That Ramsey’s Review Is Dead Wrong if That Reader Has Actually Read the 'A Treatise on Probability'

The first page of the 18 year old, F. P. Ramsey’s very short three page review, in the Cambridge Magazine issue of Jan., 1922, of Keynes’s A Treatise on Probability is comprised of claims about Keynes’s logical theory of probability that, to use L. J. Savage’s characterization of academics who tried to apply his Subjective Expected Utility model to Large Worlds (macro, intertemporal, long run decision making), as opposed to Small Worlds (micro ,short run decision making), was “utterly preposterous” and complete ”nonsense”. Ramsey’s very small review was obviously never refereed J. M. Keynes and/or Bertrand Russell could have made short work of the 18 year old Ramsey’s note in a few minutes, thereby permanently ending his academic career at Cambridge before it ever had a chance to get started. However, they decided not to do so, as they recognized that Ramsey had special intellectual gifts, although they were clearly undeveloped at the time. Keynes decided to take Ramsey under his wing and train him. The very, very severe problems with the first page consist of two claims made by Ramsey. The first claim made by F. P. Ramsey is that: “We have, then, numerous probability relations; these it is commonly supposed are all numerical, that is, correlated with the real numbers from 0 to 1 in such a way that the ordinary rules of the probability calculus hold, e.g., that the product of the numbers correlated with two probabilities is equal to the number correlated with the product (in Mr. Keynes' sense) of the two probabilities. Mr. Keynes denies this; he supposes not only that not all probabilities are numerical, but also that it is possible to have two probabilities which are unequal and such that neither is greater than the other. This view is based on the difficulty in so many cases of saying with any confidence which of two probabilities is the greater, or of assigning any numerical measures to them. But it would appear that the force of this objection to the ordinary view is exaggerated to Mr. Keynes for two reasons.” The second claim made by F.P. Ramsey is that: “First, he thinks that between any two non-self-contradictory propositions there holds a probability relation (Axiom I), for example between 'My carpet is blue' and 'Napoleon was a great general'; it is easily seen that it leads to contradictions to assign the probability 1/2 to such cases, and Mr. Keynes would conclude that the probability is not numerical. But it would seem that in such cases there is no probability; that, for a logical relation, other than a truth function, to hold between two propositions, there must be some connection between them. If this be so, there is no such probability as the probability that 'my carpet is blue' given only that 'Napoleon was a great general', and there is therefore no question of assigning a numerical value.” Ramsey’s first claim is the result of his gross ignorance of Keynes’s imprecise, interval valued ,non additive approach to probability, as was illustrated by Keynes in the discussions of the beauty contest problem on pp.25-28, as well as by six other illustrations contained in Chapter III of the A Treatise on Probability. The mathematical analysis was presented in Part II of the book, a part that Ramsey never got around to ever reading in his lifetime. The second claim made by Ramsey has nothing to do with Keynes’s use of propositions, which must be stated in the form of an argument- one proposition must contain relevant evidence while the second proposition must be a conclusion with respect to the proposition containing the relevant evidence. Only then is a relation of logical probability present. Nowhere at any place in his A Treatise on Probability or any other work written in Keynes’s lifetime did Keynes state: “…that between any two non-self-contradictory propositions there holds a probability relation (Axiom I)…” There is no such Axiom I in Keynes’s A Treatise on Probability. Therefore, Ramsey’s”… 'My carpet is blue' and 'Napoleon was a great general…” example is an oxymoron because his two propositions do not form an argument. The current belief among academics, that has been a belief for 100 years, that Ramsey not only destroyed and demolished Keynes’s logical theory of probability, but that Keynes himself felt compelled by the overwhelming logical power of Ramsey’s critique to accept Ramsey’s critique and adopted a subjective theory of probability himself, calls into question the claims made by academics writing on Keynes that they are publishing scientific works that contribute to the growth of knowledge. All I see is utter and complete nonsense.

It Is Impossible to Understand Keynes’s Logical Theory of Probability without An Understanding of Part Ii of Keynes’s a Treatise on Probability: The Mccann-Bateman Exchanges Over Ramsey’s Critique of Keynes of 1992

The crucial differences between Keynes’s and Ramsey’s theories of logical and subjective probability are insurmountable Keynes’s theory is based on propositions, imprecise, Inexact, interval valued probability (or decision weights that are non-additive), and deals with degrees of rational belief while Ramsey’s theory is based on actual events or outcomes, is precise and exact, additive, and deals with degrees of belief. The only overlap between the two theories occurs if, and only if, Keynes’s w, 0≤w≤1, which measures the completeness of the evidential weight of the Argument, V(a/h), equals 1 and probability preferences are linear. L J Savage’s important restriction, ignored by most all economists ,that his subjective theory of probability can only be applied to Small worlds (micro and short run) and never to Large worlds (macro and long run), would be a compromise that Keynes would most likely have accepted, since the question of Keynesian weight measured by w, usually does not show up in short run, micro applications, but only in long run, macro and intertemporal applications. However, Ramsey never inserted any such restriction to his theory. The McCann-Bateman exchanges demonstrate that neither McCann nor Bateman understand the great, yawning abyss that separates the precise theory of Ramsey from the imprecise theory of Keynes. There are no extant philosophers or economists, as of 2021, who understand this point, as well as why it was simply impossible for Keynes to have accepted Ramsey’s theory in any way, shape or form or to have ever been the slightest bit worried about the so called “points” Ramsey thought he was making against Keynes’s alleged “non numerical “ probabilities, which Part II of the A Treatise on Probability demonstrate are interval valued.

A Parsimonious Theory of Subjective Probability

We axiomatize subjective probabilities on finite domains without requiring richness in the outcome space or restrictions on risk preference using Event Exchangeability (Chew and Sagi, 2006), which has been implicit in the prior literature (Savage, 1954; Machina and Schmeidler, 1992; Grant, 1995). In three successively stronger theorems, we characterize a probability representation of the exchangeability relation, followed by characterizing a unique subjective probability, and finally endowing this subjective probability with the property of reduction consistency—acts inducing the same lottery are indifferent. This subjective probability can serve as foundation to derive expected utility and rank linear utility by imposing the sure-thing principle and its comonotonic variant. Moreover, our finite-domain setting reveals a novel possibility of state dependence arising from our subjective probability not being reduction consistent. Our axiomatic treatment can be further adapted to smaller collections of events and deliver small worlds probabilistic sophistication.

J M Keynes Was Never Concerned About Ramsey’s ‘Critique’ of His Logical Theory of Probability Because He Realized That Ramsey Had No Idea About What His Theory of Imprecise Probability Entailed: Ramsey Was an Advocate of Precise Probability

Keynes had successfully applied his theory of logical, imprecise probability in his Indian Currency and Finance(1913), during his time in the British Treasury from 1914 till 1919, and in his The Economic Consequences of the Peace(1919). What Keynes applied was the concept of inexact measurement and approximation, which in Part II of the A Treatise on Probability is clearly shown by Keynes to be an interval valued theory of probability of upper and lower bounds. In January, 1922,an 18 year old Frank Ramey published an extremely poor review of Keynes’s A Treatise on Probability in the Cambridge Magazine. Keynes realized immediately that Ramsey’s conceptualization of probability was an exact and precise version of additive mathematical probability with better epistemological foundations, while his theory was about inexact, imprecise, non additive interval valued probability. Keynes also realized that Ramsey’s theory always assumed that w, the evidential weight of the evidence, was complete, so that Ramsey’s foundation could only accommodate additivity, whereas for Keynes the foundation was always based on non-additivity, with additivity restricted to fields like physics and engineering. Keynes recognized, however, that Ramsey’s great intellectual capabilities would lead him to have a tremendous academic career, although Keynes himself was not an academic, given his vast understanding of actual, ambiguous, real world decision making. Keynes thus used his great influence and reputation to assist Ramsey’s academic career, while also clearly understanding that Ramsey’s theory of subjective probability was basically one that would be generally limited and restricted to academic and board room exposition in journals and business reports. It is amazing that after 100 years there still are no academics who have the slightest understanding of the interval valued theory of non additive, imprecise probability erected in Part II of the A Treatise on Probability by Keynes or the decision weight approach of the conventional coefficient C. There is not a single mention of Ramsey and/or subjective probability in: • Keynes’s pre-General Theory drafts and writings from 1932-35 • Keynes’s 1936 General Theory • Keynes’s 1937 Quarterly Journal of Economics article • Keynes’s correspondence with H. Townshend in 1937-1938 • Keynes’s exchanges with Tinbergen in 1938-1940

Comparing Edgeworth’s and Ramsey’s Understanding of the Meaning of 'Logical, Objective, Probability Relations.' Ramsey’s View Is 'Utterly Preposterous' and 'Nonsense', Where We Have Borrowed Savage’s Verbal Condemnation of Economists Who Attempted to Apply the Subjective Theory of Probability Beyond Small Worlds (Short Run and Micro Applications only Are Allowed) on P.16 of His Foundations (1954)

Ramsey’s complete and total ignorance of Keynes’s definition of “objective, logical, probability relations”, contained on pages 35-36 of the A Treatise on Probability, which was explicitly referenced and discussed by Edgeworth in his two reviews, can only be explained by the conclusion that Ramsey never read more than a few pages of Part I of Keynes’s A Treatise on Probability plus briefly looking at a maximum of an additional 2-3 pages from Parts II,III,and V. The very idea that an 18 year old teenager could show up at Cambridge in 1921 and ,based on a small, 4 page, unrefereed note, that contains nothing correct in it about Keynes‘s A Treatise on Probability, allegedly convince J M Keynes that his logical theory of probability had to be abandoned, is ludicrous, silly, stupid, and foolish. Ramsey’s crucial error was his failure to identify Keynes’s very clear definition of logical probability on pp.35-36,which was then developed in far, far, far greater detail in Part III of the A Treatise on Probability. Of far greater concern is that every single one of the six topics below that were covered by Edgeworth in his two reviews of the A Treatise on Probability is omitted from both of Ramsey’s reviews: • Keynes’s clearly defined connection between his objective, logical, probability relations and objective, logical, similarity relations, which form the foundation for cognitive science and psychology, on pp.35-36 of Part I(chapter III) • Keynes’s initial specification of the evidential weight of the argument relation,V(a/h), in Part I (chapter 6) which Keynes finished in Part IV (chapter 26-V(a/h)=w,0≤w≤1) • Keynes’s interval valued and non additive approach to probability (Part II,chapters 10-17) based on Boole’s upper-lower probabilities approach specified in his The Laws of Thought (1954,pp.265-269), as well as Keynes’s critique of the assumption of additivity • Keynes’s finite probabilities of Part III using a modified version of Boole’s Problem X to support his application of analogies • Keynes’s use of decision weights to explicitly modify additive probability ,thereby transforming additive probability into non(sub) additive ,conventional coefficients of weight and risk, c, in Part IV. • Keynes’s use of Chebyshev’s Inequality to establish lower bounds for a safety first approach in Part V and use of the Lexis-Q test to establish the constancy(stability) of applications of the limiting frequency approach to probability Given Edwin B .Wilson’s correct 1923 conclusion, made in correspondence with Edgeworth, that only Edgeworth was fully qualified to review the A Treatise on Probability, we reach the conclusion that Ramsey and Braithwaite never actually read more than a very few pages of a book that they claimed to have read. The only conclusion that can be drawn that is consistent with this evidence is that Ramsey and Braithwaite were involved in an intellectual fraud in 1921 and 1922 that continues in the 21st century. See, for example, Misak (2020) and Janeway (2020).

One Hundred Years After Keynes’s a Treatise on Probability Appeared, There Is Still Pervasive Confusion Among Academics About the Logical Theory of Probability: Keynes’s Theory of Logical Probability Is an Interval Valued Theory of Probability Based On Boole That the 18 Year Old Ramsey Never Understood in His Life

The very recent publication of C. Misak’s autobiography of F P Ramsey in 2020, as well as a number of book reviews made by different reviewers of that book, have resulted in the resurrection of highly misleading claims made by F. Ramsey, when he was 18 years old, that can only be characterized as being silly -to someone who has actually read the entire book. Therefore, individuals, who have only read Part I of Keynes’s book, are highly susceptible to claims made when reading book reviews of academics who never read the book they claimed to be reviewing. Such is the case with Frank Ramsey. The Keynes -Townshend correspondence in 1937 – 1938 over the connections between the A Treatise on Probability and the General Theory, as well as the Keynes-Tinbergen exchanges of 1938-1940 concerning Keynes’s critique or Tinbergen’s use of precise probability and the Normal distribution to model the business cycle, make it crystal clear that Keynes never accepted Ramsey’s critique in his lifetime and continued to use his own logical theory of imprecise probability .Ramsey’s subjective theory of probability is a theory of precise probability that can’t deal with overlapping evidence or conflicting evidence. Of course, Keynes did believe that Ramsey had strengthened the logical foundations for PRECISE probability with his betting quotient approach combined with his Dutch book argument regarding degrees of belief. However, Keynes’s logical theory is one that is based on rational degrees of belief and imprecise probability. Only in a very special case, where Keynes’s degree of the completeness of the relevant evidence, w, equaled 1 on the unit interval would Keynes have considered using Ramsey’s theory. A similar fate has occurred regarding Keynes’s separate theory of the Evidential Weight of the Argument. Here we will find a plethora of mathematical and logical errors littering the academic journals in economics and philosophy.

The strength of de Finetti’s coherence theorem

I show that de Finetti’s coherence theorem is equivalent to the Hahn-Banach theorem and discuss some consequences of this result. First, the result unites two aspects of de Finetti’s thought in a nice way: a corollary of the result is that the coherence theorem implies the existence of a fair countable lottery, which de Finetti appealed to in his arguments against countable additivity. Another corollary of the result is the existence of sets that are not Lebesgue measurable. I offer a subjectivist interpretation of this corollary that is concordant with de Finetti’s views. I conclude by pointing out that my result shows that there is a sense in which de Finetti’s theory of subjective probability is necessarily nonconstructive. This raises questions about whether the coherence theorem can underwrite a legitimate theory of rational belief.

The Early Mathematics of Welfare

Bruno de Finetti (1906–1985) is well known as the founder of the subjective theory of probability. Less known is his contribution to economic theory. The article presents the contributions of de Finetti in the field of welfare economics. He advanced a new mathematical tool: the theory of simultaneous maxima. On this base, he criticized the laissez-faire interpretation of the Paretian theory and advanced the idea of a social welfare function, reflecting the debate on economic planning among Italian corporatist economists.

Post Keynesian Economics Is Based on Joan Robinson’s Many Canards About Supposed Gaping Holes in Keynes’s Theory: The Real Problem Is Gaping Holes and Gross Ignorance in the Post Keynesian Understanding of Keynes’s a Treatise on Probability

There is no Post Keynesian economist or allied philosopher who can comprehend the following, basic 100 year old fact-Keynes, building on Boole ‘s The Laws of Thought (1854), created an interval valued approach to probability, as well as a decision weight approach, the c coefficient, that re-expresses interval valued probability as non additive and non linear probability, that has nothing to do with radical uncertainty or ordinal probability as asserted continuously for 50 years. Consider the example of R. Skidelsky. R. Skidelsky was very much like Joan Robinson in his academic skills, upon whom he has built his view of Keynes’s contributions. R. Skidelsky, like Joan Robinson, has admitted many times that he is mathematically illiterate, inept, and innumerant. This self admitted fact made Skidelsky very susceptible and receptive to the Frank P. Ramsey myth, recently resurrected by C. MIsak (2020). This myth purports that Ramsey, an 18 year old teenager who came to Cambridge University in 1921, was able to convince Keynes in 1922 that his logical theory of probability, as presented in his 1921 A Treatise on Probability, was full of logical, epistemological and philosophical errors that demolished the entire logical foundation and edifice of Keynes’s theory. Of course, given the fact that Keynes’s theory is built directly on a foundation and edifice of George Boole’s mathematical propositional logic and algebra,which Ramsey (nor any other supporter of Ramsey, such as R.B. Braithwaite) dared not challenge at any time in his lifetime, the belief that Keynes, who had used his approach to approximation and inexact measurement in his Indian Currency and Finance and Economic Consequences of the Peace successfully, would accept Ramsey’s purely academic theory based on additivity and linearity, which Keynes knew did not hold at all in the real world of decision making involving missing evidence and vague, conflicting knowledge, is simply silly. Keynes,of course, realized that Ramsey’s great formal, intellectual skills would make him a great academic thinker. The acceptance by all Post Keynesians and heterodox economists, that Keynes capitulated, either in part or wholly, to Ramsey, has led to a complete failure to properly connect the Keynes of the A Treatise on Probability to the Keynes of the General Theory. This is very similar to the failure of Adam Smith academics to properly connect the Smith of The Theory of Moral Sentiments to the Smith of The Wealth of Nations. Both Keynes’s and Smith’s are, of course, identical in both books. The Ramsey myth has been continually promulgated since 1921. Misak’s 2020 book on Ramsey continues to make assertions about Keynes which are directly contradicted by Keynes himself. The best exposition that explodes the Ramsey myth is the Keynes-Townshend correspondence over the TP of 1937-38, where non numerical probability, weight of the evidence, and the logical theory of probability, and the relation to the GT are covered. There is no mention made of Frank Ramsey or the subjective theory of probability by Keynes or Townshend. The elimination of the Frank Ramsey myth is a necessary step that must be taken before any progress can be made on understanding the linkages between the TP and GT. From Hahn and Skidelsky in 1986 to Walsh in 2001 to Togati in 2020, we can see that the real problem is not any gaps in Keynes’s theory, but the blindness of Post Keynesian and heterodox economists regarding the TP and GT, who are either unable or unwilling to read the TP and/or chapters 20, 21 and appendix to chapter 19 of the GT.

How Did Clive Bell, One of Keynes’s Bloomsberry Artist Friends, Become a Recognized Expert on Keynes's a Treatise on Probability, given that He Had No Knowledge of Mathematical Logic, Statistics, Probability or Boolean Algebra?

Clive Bell was an artist.There is no possible way that Clive Bell could have understood/advised Keynes about material appearing in his 1921 A Treatise on Probability or have had any understanding of the roles that intuition and perception played in Keynes’s logical theory of probability unless he had been a rated tournament chess player who understood the important role of intuition and perception, a role that could only be grasped by someone who has actually played Over-The-Board (OTB) tournament chess under time constraint (a clock). The belief that Clive Bell’s recollections/memories about his friendship with Keynes encompass a knowledge of Keynes’s logical theory of probability or Keynes’s concept of the role of intuition in decision making under time constraint are simply nonsense. Bell has been cited in work done by C. MIsak in 2020, that is related to her biography on Frank Ramsey, whose subjective theory of probability was regarded by Keynes as a academic exercise that had very limited applicability in the real world of messy, unclear, ambiguous decision making and in tournament chess, although there is a role for Ramsey’s blunt force approach in Correspondence (Postal) Chess. The failure to understand the relevance of the role of the time constraint in decision making is at pandemic levels in the academic fields of history, philosophy, psychology, economics, political science and decision theory. Consider the following claim made by R. Skidelsky, a historian: “Keynes’s people are thinkers, and he equips them with the tools of thought: logic. Ramsey’s people are actors and he equips them with the tools of action: calculating power.” Skidelsky,1992,pp.71-72). Keynes correctly realized that such calculating power is very rarely used in an OTB tournament chess game. It primarily occurs in opening play and/or in a situation where one player has prepared in advance an innovation (new move) that requires his opponent to be able to avoid a forcing line or lose. Keynes’s decision makers are thinkers who analyze the position on the board using their intuition to perceive the fundamental dynamic elements of the position. It is impossible to make any specific calculation. Ramsey’s decision makers are memorizers who are looking to calculate forced lines OTB that usually do not exist. A rare exception is the following game where memorization and calculating power come into play: White:Towne (USCF -1750) Black: Brady (USCF-1850) - August, 2007 (La Palma Chess Club, Calif., USA) 1)e4 g6 2)d4 c5 3)Nf3 cxd4 4)Nxd4 Bg7 5)Nc3 Qa5 6) Bc4? Qc5! 7)Bxf7 + KxBf7 -/+ and White resigned in forty moves, although he could have resigned at move 6.

On Misak’s 2020 Story about Ramsey, Keynes,and Logical Probability: Keynes Never Took Ramsey’s Claims Seriously at Anytime in His Lifetime

A myth has been in existence since 1922 about Keynes, Ramsey and the logical theory of probability that Keynes constructed in Parts I-V of the A Treatise on Probability, 1921. This myth claims that Ramsey found major errors in logic and epistemology in Keynes’s work, which supposedly was about mysterious,unfathomable non measurable,non numerical Platonic probabilities that could only be intuited. Keynes supposedly, according to this myth, instantly realized that his theory had been decimated, annihilated and demolished by the 18 year old boy genius, Frank Ramsey. Keynes then supposedly retracted his theory in 1931 and supported the subjective theory of probability presented in 1926 by Ramsey in “Truth and Probability” thereafter. This myth is the foundation for Robert Skidelsky’s Post Keynesian assessment of Keynes’s Theory of Probability and appears to be what S. Bradley presents as Keynes’s theory in the latest 2019 assessment of Keynes’s contributions in the Stanford Encyclopedia of Philosophy. In C. Misak’s recent 2020 biography of Ramsey ,as well as in other reviews and media, this myth is simply being restated. In reality, Ramsey’s critique of Keynes, in either 1922 or 1926, was so poor that it is quite amazing that the vast majority of economists, philosophers, psychologist, and historians in the 20th and 21st centuries continue to believe something for which there is not a shred of historical evidence. Keynes was not going to waste his very valuable time restating the points he had already made in the A Treatise on Probability for an 18 year old boy. Everything is there in Parts II-V of the A Treatise on Probability that demonstrate that Ramsey’s views on Keynes’s theory of probability are nothing short of silly, preposterous and absolute nonsense masquerading as serious scholarship. What explains the longevity, nearly 100 years of this myth is the complete and total failure of academics to read the technical parts of the A Treatise on Probability, Parts II, III and V. Emile Borel made it very clear in his 1924 review of Keynes’s book, a review that never mentions Ramsey ‘s 1922 review, that his review will be about Part I of Keynes’s book only. Borel, alone among academics over the last 100 years, honestly admitted that he could not follow Keynes in Part II, although he also realized that this was the most important part of the book.For this oversight, he apologized to both Keynes and Russell in print. The Ramsey myth exists only due to the failure of historians, psychologists, philosophers and economists to read Part II of the A Treatise on Probability.

George Box’s Realization, That All Models, Especially Statistical Models, Are Wrong Means That It Is Impossible for There to Be Any True Probabilities, True Models, True Theories, True Expectations or True (Accepted) Hypotheses: The Claims, Made By Rational Expectations Proponents About True Objective Probabilities, True Models, True Expectations, True Expected Values, etc., Have No Scientific Foundation

R. Muth’s 1961 paper in Econometrica is an example of an academic economist suffering from extreme and extraordinary ignorance about very basic scientific, statistical, methodological, epistemological, philosophical, and logical tenets. These tenets were all discussed rigorously by Haavelmo in his 1944 paper in Econometrica on methodological and epistemological issues related to the question about exactly what conclusions a statistical model using economic data could support as far as sound(never valid, right ,correct, true). Haavelmo’s entire 115 page article can be summarized briefly by George Box’s brief statement noted above .Muth’s belief ,that economists had derived true theories and true models is simple nonsense. What Muth should have argued in his 1961 article, but did not, is that rational expectations, when compared to its rivals,was a better model compared to the rival models in terms of minimizing its forecasting error.Of course, Muth would have had to have supported this claim of forecast superiority with explicit proper scoring rule studies showing that the rational expectations statistical model did in fact yield superior forecast results. No such study exists at the present time because no proponent of the rational expectations hypothesis has ever demonstrated such forecasting superiority. Two additional, very severe problems result from Muth’s confused understanding of what scientific modeling is capable of regarding the specification of objective and subjective probabilities or probability distributions. First,It is simply impossible to assume the truth of the objective theory of a limiting frequency interpretation of probability and then claim that decision makers can learn from experience what the convergence properties of such a distribution are in the short run when such properties will only manifest themselves in the far ,distant(infinite)long run. It is impossible for any human ,unless rational expectations proponents are claiming that there are actual decision makers who live to infinity,to learn of such properties .Kolmogorov made it quite clear that the strengthened limiting frequency interpretation he had provided for R.Von Mises law of large numbers,which resulted from the substitution of the assumption of countable additivity for finite additivity “ …does not contribute anything to substantiate the application of the results of probability theory to real practical problems where we always have to deal with a finite number of trials”(Kolmogorov). Second, given L. J. Savage’s clearly expressed and emphasized restrictions concerning the applicability of the theory of subjective probability and expected subjective utility to the short run at the micro level ,any attempt to apply Savage’s theory at the macro level or to the intermediate to long run or intertemporally over infinite time is “utterly preposterous” and complete”nonsense according to Savage.This means that Muth’s claim about subjective probability transforming itself into objective probability might only be considered a subject for possible study and scrutiny in the short run at the microeconomic level. Economists and econometricians are good number crunchers only. Their subjective claims and beliefs about infinitely lived decision makers, who are able to learn about so called true ,objective probability distributions ,are “utterly preposterous “ and anti scientific. William McChesney Martin ,FRS chair of the BOD in Washington,D.C.from 1950 and 1970 ,correctly kept the econometricians ,economists, and Paul Volcker in the basement of the NY Federal Reserve Bank, where they had no input or say in actual or proposed monetary policy decisions. Martin realized that the extremely narrow understanding of what was required in the real world of monetary policy on the part of economists necessitated this setup. Alan Greenspan, in his 2004 (May) paper in the AER ,also rejected the applicability of the theory of rational expectations in monetary policy from 1987 to 2005,given his emphasis on the importance of taking into consideration all models, including those dealing with uncertainty where the knowledge base ranged from complete ignorance to complete knowledge. On the other hand ,A. Burns, P.Volcker,B. Bernanke, and T .Geithner did believe that their mathematical and econometric models were true. One can compare the great success of Martin and Greenspan with the failures of Volcker and Bernanke(Geithner) and reach the conclusion that it is time to return the economists and econometricians back to the basement of the FRBNY where they belong as effective and useful number crunchers only.

On the Impossibility That Any Academic Will Ever Understand Keynes’s 1931 Assessment of Ramsey’s Work in Probability, When Compared to His Own, Until Part II of the A Treatise on Probabilit y(1921) Has Been Read: Ramsey’s Subjective Theory of Probability (Precise, Exact, Numerical, Linear, Additive, Degree of Belief) Is a Special Case of Keynes’s Logical Theory of Probability (Imprecise, Inexact,

On the Impossibility That Any Academic Will Ever Understand Keynes’s 1931 Assessment of Ramsey’s Work in Probability, When Compared to His Own, Until Part II of the A Treatise on Probabilit y(1921) Has Been Read: Ramsey’s Subjective Theory of Probability (Precise, Exact, Numerical, Linear, Additive, Degree of Belief) Is a Special Case of Keynes’s Logical Theory of Probability (Imprecise, Inexact,

Rational Action and Systemic Response: Using Time to Integrate Subjective and Objective Probabilities

Macro theories explore the properties of an economic system in its entirety, in contrast to the focus of micro theories on parts of that system. Where most macro theories reduce an economy to a representative agent, we follow Wagner (2012, 2020) in treating a macro economy as an ecology of plans. An ecology of plans contains two distinct analytical objects: the ecology as an entirety and the individual entities that constitute that ecology. To reduce the ecology to a representative or average agent is to create a category mistake by giving the ecology the property of rationality that it cannot possibly have. To avoid this mistake, we work with both subjective and objective probability concepts. Individual action is set within the purview of a theory of subjective probability. The ecological system is treated as a mechanism that can be described in terms of objective probability. There is, moreover, a significant interval of time that separates the initiation of individual plans from the subsequent market evaluation of those plans.

De-biasing role induced bias using Bayesian networks

AbstractThe merits of using subjective probability theory as a normative standard for evidence evaluation by legal fact-finders have been hotly debated for decades. Critics argue that formal mathematical models only lead to an apparent precision that obfuscates the ad-hoc nature of the many assumptions that underlie the model. Proponents of using subjective probability theory as normative standard for legal decision makers, specifically proponents of using Bayesian networks as decision aids in complex evaluations of evidence, must show that formal models have tangible benefits over the more natural, holistic assessment of evidence by explanatory coherence. This article demonstrates that the assessment of evidence using a Bayesian network parametrized with values obtained from the decision makers reduces role-induced bias, a bias that has been largely resistant to de-biasing attempts so far.