The Enduring Allure of Objective Probability

0:00I'm going to argue that the probability measures we conventionally use should be interpreted as being subjective rather than objective phenomena, if only as a result of the knowledge limitations of human experience. Even if objectively objective probability can be demonstrated as an unambiguously verifiable property of the physical world, our necessarily imperfect access to such aspects of reality would necessitate the construction of subjective probability measures for examinations of human behavior. The view that there are ontologically privileged, objectively verifiable probabilities and expectations will be examined and criticized.

0:45It appears to be one source of the discredited, though nonetheless widespread and persistent belief in the efficacy and feasibility of central economic planning. One of the most important economic proponents of the subjective interpretation was Ludwig von Mises, who asserts that deterministic causality is assumed to underlie apparently random events. We cannot definitively prove causal determinism, but because it is a necessary presupposition of human action, it is not a hypothesis but a Kantian category of the understanding. The next most important proponent of subject probability among economists was Keynes. In Mises and Keynes' subjective formulation of probability, randomness is not actually present in the causally deterministic physical world, but is introduced in our understanding of the world by limitations on our knowledge, which can never be completely removed. We can only have finite knowledge of an infinite universe. Hayek's views on how the brain In the social sciences, if consumer behavior were uncaused, there would be no basis for entrepreneurial planners to respond to or anticipate that behavior with human action.

2:08In the absence of this deterministic causality, acting man would be helplessly reduced to a passive observer. We would not plant crops or engage in production because our output would be no more likely to grow under cultivation or planned assembly than it would appear spontaneously as if by magic. And under the assumption that deterministic causality governs every aspect of reality, this is something for which we can never possess, imagine or desire perfect or complete knowledge at either subatomic or macroscopic scales. The mathematician Augustus de Morgan wrote in 1838, quote, probability is the feeling of the mind, not the inherent property of a set of circumstances.

2:55This view would largely be adopted by Keynes in the Treatise on Probability. This paper suggests an explanation for the historical curiosity of probabilities being mistakenly considered objective properties of the real world. The objective interpretation of probability views uncertainty as a property which inheres in the universe, rather than a consequence of our knowledge limitations. The mathematics of the relative frequency approach, which dictates one sixth as the probability for the role of a fair die, one half with a toss of a fair coin, etc. is invariant across individuals. In this sense, relative frequency is objective, verifiable, and ontologically privileged. This view was advanced most forcefully by Ludwig von Mises' younger brother, the mathematician, engineer and aerodynamicist, Richard von Mises.

3:49So it's all in the family. If probability is in fact subjective, there can be no basis to reject the purportedly objective relative frequency approach as long as it is understood as only one among many possible metrics. In this sense, the subjective interpretation of probability is more general and the objective Interpretation is a special case. Subjective probability merely requires that relative frequencies be viewed as only one among several valid approaches to defining probabilities. Relative frequency differs from alternative probability measures in that it is widely accepted as a privileged and objectively verifiable assessment. Subjectivity has two inroads to overcoming the ontologic primacy of relative frequency mathematics. First, information varies across individuals, making probability assessments subjective. Second, the class definitions of the relative frequency approach may also vary across individuals, making the applicability of the relative frequency approach idiosyncratic and thus subjective. I will emphasize that I'm not attacking the validity of the mathematics of relative frequency, which is beyond question, but the fair die and fair coin hypothesized by the relative

5:07frequency definition have no more existence in reality than the straight line of Euclidean geometry. They are all conceptual constructs rather than physical objects. The smallest objects known in the physical world are the smallest measuring sticks we can use against subatomic phenomena. These are short wavelength photons also known as has high energy quanta, which have correspondingly high frequencies and energies. The more precise we attempt to make a subatomic measurement, the higher the energy, because the shorter the wavelength of the photons we have to use as measuring sticks, and the more this perturbs the target particles we'd be trying to measure. In honor of Werner Heisenberg, I will share this physics joke, a neutron walks into a The Neo-Indeterminist School of Physics arrived at the conclusion that the measurement uncertainty is a property of the external reality, not of the limitations of human understanding.

6:26If we cannot simultaneously determine the location and momentum of an electron, we cannot rigorously assert that the particle has both definite location and momentum. Einstein, for one, rejected this interpretation. God does not play dice with the universe. One way around this difficulty is the appeal to Kant's categories of the understanding. We cannot conceive of the particle apart from its occupying some location and having some I wanted a picture of Glenn Ford cheating at craps in Gilda, but this was as close as I could come and I think it's, you know, contemplating this kind of image makes us better rounded people.

7:12Gilda is a 1946 film starring Rita Hayworth and Glenn Ford. I want to argue that it's one of the most culturally significant and most entertaining films ever made by Columbia Studios. In the treatise on probability, Keynes attempted to generalize beyond the strict relative frequency definition, defining probability as the, quote, objectively rational degree of belief in a and Proposition Given the Available Evidence. Now this weirdly sort of combines both objective and subjective characteristics. Keynes really wanted to say everything I'm trying to argue for is objectively correct. However, he was led into almost inevitably to acknowledge the subjective aspects of probability.

8:04Keynes unfortunately failed to recognize that evidentiary information varies across individuals and necessarily always must, as subsequently emphasized by Hayek. Keynes' baseline assumption was that there should always be an objective, rational assessment all individuals should arrive at, given that they apply the rules of probability correctly, given the same evidence. To Keynes, a probability is a rationally justified degree of belief, quote unquote, objectively derived by logic, rather than a matter of individual subjective evaluation. Keynes should be applauded as a precursor of Ludwig von Mises in advancing the subjective interpretation, but he was somewhat inconsistent.

8:49His view that subjective probabilities could conform or converge to an objective limit would have supported arguments for central economic planning, though Keynes never pursued This is Trigby Havelmo. Havelmo suggested economic models rely on a subjective process of identifying variables of interest, and then hypothesizing relationships among them. The choice of variables, which relationships to include, and the form of relationships posited among them, is subjective and relies on aesthetic intuition as much as on scientific analysis. And he might, he didn't actually say this, but he might have said that building an econometric model is as much an art as a science.

9:38Avelmo suggested that frequency of occurrence can be substituted for theoretical probability as a practical matter, but it is not clear that this is always necessary or even possible. In individual cases, the ex ante probability is superseded once the individual case has has occurred, and when repetitive trials are not invoked, the a priori confidence is always a subjective assessment. The rigorous notion of the relative frequency approach exists only subjectively in our rational mind, or in some cases irrational minds, rather than objectively in the external world. Nevertheless, Havelmo argues that the relative frequency approach can serve, quote unquote, as a tool for deriving practical statements.

10:25The subjective interpretation of proposed probability measures is always and everywhere more general and powerful than the alternative objective interpretation typified by the relative frequency approach. In fact, any proposed objective measure must always be nested within the class of subjective measures as a special case. Any proponent of objective probability might retort that this amounts to the assertion that their correct answer, the relative frequency or objectively correct probability, is always a subset of the set of all possible probabilities, including wrong answers. In their view, subjective probabilities which conflict with the relative frequency definition are always and everywhere wrong answers, never mind that they underlie much of human behavior and can offer outlets for inarticulable intuition, insight and entrepreneurial awareness.

11:22Several arguments for viewing probability as subjective were presented. Uncertainty need not be viewed as a property of the external world, but of the limitations on our knowledge which can never be fully overcome. Mises' view that the world is governed by deterministic causality is not one which can be proven, nor can it be disproven since the issue If the view is ontologically indeterminate, the case for objective probability is necessarily much weaker than for an encompassing subjective view of probability. Thank you very much.