WEBVTT NOTE The Enduring Allure of Objective Probability 1 00:00:00.000 --> 00:00:04.920 I'm going to argue that the probability measures we conventionally use should be interpreted 2 00:00:04.920 --> 00:00:10.480 as being subjective rather than objective phenomena, if only as a result of the knowledge 3 00:00:10.480 --> 00:00:14.000 limitations of human experience. 4 00:00:14.000 --> 00:00:22.080 Even if objectively objective probability can be demonstrated as an unambiguously verifiable 5 00:00:22.080 --> 00:00:28.640 property of the physical world, our necessarily imperfect access to such aspects of reality 6 00:00:28.640 --> 00:00:34.600 would necessitate the construction of subjective probability measures for examinations of human 7 00:00:34.600 --> 00:00:35.600 behavior. 8 00:00:35.600 --> 00:00:42.600 The view that there are ontologically privileged, objectively verifiable probabilities and expectations 9 00:00:42.600 --> 00:00:45.240 will be examined and criticized. 10 00:00:45.240 --> 00:00:49.840 It appears to be one source of the discredited, though nonetheless widespread and persistent 11 00:00:49.840 --> 00:00:55.320 belief in the efficacy and feasibility of central economic planning. 12 00:00:55.320 --> 00:01:00.160 One of the most important economic proponents of the subjective interpretation was Ludwig 13 00:01:00.160 --> 00:01:06.480 von Mises, who asserts that deterministic causality is assumed to underlie apparently 14 00:01:06.480 --> 00:01:08.380 random events. 15 00:01:08.380 --> 00:01:14.300 We cannot definitively prove causal determinism, but because it is a necessary presupposition 16 00:01:14.300 --> 00:01:20.900 of human action, it is not a hypothesis but a Kantian category of the understanding. 17 00:01:20.900 --> 00:01:26.880 The next most important proponent of subject probability among economists was Keynes. In 18 00:01:26.880 --> 00:01:32.360 Mises and Keynes' subjective formulation of probability, randomness is not actually 19 00:01:32.360 --> 00:01:38.240 present in the causally deterministic physical world, but is introduced in our understanding 20 00:01:38.240 --> 00:01:43.680 of the world by limitations on our knowledge, which can never be completely removed. We 21 00:01:43.680 --> 00:01:49.280 can only have finite knowledge of an infinite universe. Hayek's views on how the brain 22 00:01:49.280 --> 00:02:02.340 In the social sciences, if consumer behavior were uncaused, there would be no basis for 23 00:02:02.340 --> 00:02:08.640 entrepreneurial planners to respond to or anticipate that behavior with human action. 24 00:02:08.640 --> 00:02:13.420 In the absence of this deterministic causality, acting man would be helplessly reduced to 25 00:02:13.420 --> 00:02:15.680 a passive observer. 26 00:02:15.680 --> 00:02:20.240 We would not plant crops or engage in production because our output would be no more likely 27 00:02:20.240 --> 00:02:25.960 to grow under cultivation or planned assembly than it would appear spontaneously as if by 28 00:02:25.960 --> 00:02:26.960 magic. 29 00:02:26.960 --> 00:02:33.960 And under the assumption that deterministic causality governs every aspect of reality, 30 00:02:33.960 --> 00:02:39.940 this is something for which we can never possess, imagine or desire perfect or complete knowledge 31 00:02:39.940 --> 00:02:44.140 at either subatomic or macroscopic scales. 32 00:02:44.140 --> 00:02:50.460 The mathematician Augustus de Morgan wrote in 1838, quote, probability is the feeling 33 00:02:50.460 --> 00:02:55.260 of the mind, not the inherent property of a set of circumstances. 34 00:02:55.260 --> 00:03:00.780 This view would largely be adopted by Keynes in the Treatise on Probability. 35 00:03:00.780 --> 00:03:06.280 This paper suggests an explanation for the historical curiosity of probabilities being 36 00:03:06.280 --> 00:03:10.760 mistakenly considered objective properties of the real world. 37 00:03:10.760 --> 00:03:15.400 The objective interpretation of probability views uncertainty as a property which inheres 38 00:03:15.400 --> 00:03:20.120 in the universe, rather than a consequence of our knowledge limitations. 39 00:03:20.120 --> 00:03:24.640 The mathematics of the relative frequency approach, which dictates one sixth as the 40 00:03:24.640 --> 00:03:31.640 probability for the role of a fair die, one half with a toss of a fair coin, etc. is invariant 41 00:03:31.640 --> 00:03:33.520 across individuals. 42 00:03:33.520 --> 00:03:40.160 In this sense, relative frequency is objective, verifiable, and ontologically privileged. 43 00:03:40.160 --> 00:03:45.020 This view was advanced most forcefully by Ludwig von Mises' younger brother, the mathematician, 44 00:03:45.020 --> 00:03:49.100 engineer and aerodynamicist, Richard von Mises. 45 00:03:49.100 --> 00:03:51.180 So it's all in the family. 46 00:03:51.180 --> 00:03:55.860 If probability is in fact subjective, there can be no basis to reject the purportedly 47 00:03:55.860 --> 00:04:01.980 objective relative frequency approach as long as it is understood as only one among many 48 00:04:01.980 --> 00:04:03.900 possible metrics. 49 00:04:03.900 --> 00:04:08.640 In this sense, the subjective interpretation of probability is more general and the objective 50 00:04:08.640 --> 00:04:14.760 Interpretation is a special case. Subjective probability merely requires that relative 51 00:04:14.760 --> 00:04:21.540 frequencies be viewed as only one among several valid approaches to defining probabilities. 52 00:04:21.540 --> 00:04:26.040 Relative frequency differs from alternative probability measures in that it is widely 53 00:04:26.040 --> 00:04:32.560 accepted as a privileged and objectively verifiable assessment. Subjectivity has two inroads to 54 00:04:32.560 --> 00:04:38.680 overcoming the ontologic primacy of relative frequency mathematics. First, information 55 00:04:38.680 --> 00:04:44.720 varies across individuals, making probability assessments subjective. Second, the class 56 00:04:44.720 --> 00:04:50.760 definitions of the relative frequency approach may also vary across individuals, making the 57 00:04:50.760 --> 00:04:56.360 applicability of the relative frequency approach idiosyncratic and thus subjective. I will 58 00:04:56.360 --> 00:05:02.080 emphasize that I'm not attacking the validity of the mathematics of relative frequency, 59 00:05:02.080 --> 00:05:07.360 which is beyond question, but the fair die and fair coin hypothesized by the relative 60 00:05:07.360 --> 00:05:12.920 frequency definition have no more existence in reality than the straight line of Euclidean 61 00:05:12.920 --> 00:05:19.420 geometry. They are all conceptual constructs rather than physical objects. 62 00:05:19.420 --> 00:05:23.380 The smallest objects known in the physical world are the smallest measuring sticks we 63 00:05:23.380 --> 00:05:29.060 can use against subatomic phenomena. These are short wavelength photons also known as 64 00:05:29.060 --> 00:05:34.420 has high energy quanta, which have correspondingly high frequencies and energies. 65 00:05:34.420 --> 00:05:39.860 The more precise we attempt to make a subatomic measurement, the higher the energy, because 66 00:05:39.860 --> 00:05:44.700 the shorter the wavelength of the photons we have to use as measuring sticks, and the 67 00:05:44.700 --> 00:05:49.940 more this perturbs the target particles we'd be trying to measure. 68 00:05:49.940 --> 00:05:57.060 In honor of Werner Heisenberg, I will share this physics joke, a neutron walks into a 69 00:05:57.060 --> 00:06:19.980 The Neo-Indeterminist School of Physics arrived at the conclusion that the measurement uncertainty 70 00:06:19.980 --> 00:06:26.180 is a property of the external reality, not of the limitations of human understanding. 71 00:06:26.180 --> 00:06:31.680 If we cannot simultaneously determine the location and momentum of an electron, we cannot rigorously 72 00:06:31.680 --> 00:06:36.420 assert that the particle has both definite location and momentum. 73 00:06:36.420 --> 00:06:40.580 Einstein, for one, rejected this interpretation. 74 00:06:40.580 --> 00:06:43.860 God does not play dice with the universe. 75 00:06:43.860 --> 00:06:48.260 One way around this difficulty is the appeal to Kant's categories of the understanding. 76 00:06:48.260 --> 00:06:53.380 We cannot conceive of the particle apart from its occupying some location and having some 77 00:06:53.380 --> 00:07:12.380 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. 78 00:07:12.380 --> 00:07:18.140 Gilda is a 1946 film starring Rita Hayworth and Glenn Ford. 79 00:07:18.140 --> 00:07:23.940 I want to argue that it's one of the most culturally significant and most entertaining 80 00:07:23.940 --> 00:07:27.620 films ever made by Columbia Studios. 81 00:07:27.620 --> 00:07:33.180 In the treatise on probability, Keynes attempted to generalize beyond the strict relative frequency 82 00:07:33.180 --> 00:07:39.500 definition, defining probability as the, quote, objectively rational degree of belief in a 83 00:07:39.500 --> 00:07:42.660 and Proposition Given the Available Evidence. 84 00:07:42.660 --> 00:07:49.620 Now this weirdly sort of combines both objective and subjective characteristics. 85 00:07:49.620 --> 00:07:55.700 Keynes really wanted to say everything I'm trying to argue for is objectively correct. 86 00:07:55.700 --> 00:08:04.300 However, he was led into almost inevitably to acknowledge the subjective aspects of probability. 87 00:08:04.300 --> 00:08:09.420 Keynes unfortunately failed to recognize that evidentiary information varies across individuals 88 00:08:09.420 --> 00:08:15.580 and necessarily always must, as subsequently emphasized by Hayek. 89 00:08:15.580 --> 00:08:20.500 Keynes' baseline assumption was that there should always be an objective, rational assessment 90 00:08:20.500 --> 00:08:27.980 all individuals should arrive at, given that they apply the rules of probability correctly, 91 00:08:27.980 --> 00:08:29.620 given the same evidence. 92 00:08:29.620 --> 00:08:34.860 To Keynes, a probability is a rationally justified degree of belief, quote unquote, objectively 93 00:08:34.860 --> 00:08:41.220 derived by logic, rather than a matter of individual subjective evaluation. 94 00:08:41.220 --> 00:08:45.660 Keynes should be applauded as a precursor of Ludwig von Mises in advancing the subjective 95 00:08:45.660 --> 00:08:49.560 interpretation, but he was somewhat inconsistent. 96 00:08:49.560 --> 00:08:54.060 His view that subjective probabilities could conform or converge to an objective limit 97 00:08:54.060 --> 00:08:58.820 would have supported arguments for central economic planning, though Keynes never pursued 98 00:08:58.820 --> 00:09:28.820 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. 99 00:09:28.820 --> 00:09:33.980 And he might, he didn't actually say this, but he might have said that building an econometric 100 00:09:33.980 --> 00:09:38.020 model is as much an art as a science. 101 00:09:38.020 --> 00:09:44.220 Avelmo suggested that frequency of occurrence can be substituted for theoretical probability 102 00:09:44.220 --> 00:09:50.260 as a practical matter, but it is not clear that this is always necessary or even possible. 103 00:09:50.260 --> 00:09:55.620 In individual cases, the ex ante probability is superseded once the individual case has 104 00:09:55.620 --> 00:10:01.880 has occurred, and when repetitive trials are not invoked, the a priori confidence is always 105 00:10:01.880 --> 00:10:04.560 a subjective assessment. 106 00:10:04.560 --> 00:10:09.500 The rigorous notion of the relative frequency approach exists only subjectively in our rational 107 00:10:09.500 --> 00:10:15.820 mind, or in some cases irrational minds, rather than objectively in the external world. 108 00:10:15.820 --> 00:10:21.040 Nevertheless, Havelmo argues that the relative frequency approach can serve, quote unquote, 109 00:10:21.040 --> 00:10:25.840 as a tool for deriving practical statements. 110 00:10:25.840 --> 00:10:30.140 The subjective interpretation of proposed probability measures is always and everywhere 111 00:10:30.140 --> 00:10:35.940 more general and powerful than the alternative objective interpretation typified by the relative 112 00:10:35.940 --> 00:10:37.860 frequency approach. 113 00:10:37.860 --> 00:10:43.940 In fact, any proposed objective measure must always be nested within the class of subjective 114 00:10:43.940 --> 00:10:46.660 measures as a special case. 115 00:10:46.660 --> 00:10:52.020 Any proponent of objective probability might retort that this amounts to the assertion 116 00:10:52.020 --> 00:10:58.000 that their correct answer, the relative frequency or objectively correct probability, is always 117 00:10:58.000 --> 00:11:03.320 a subset of the set of all possible probabilities, including wrong answers. 118 00:11:03.320 --> 00:11:09.520 In their view, subjective probabilities which conflict with the relative frequency definition 119 00:11:09.520 --> 00:11:15.460 are always and everywhere wrong answers, never mind that they underlie much of human behavior 120 00:11:15.460 --> 00:11:18.660 and can offer outlets for inarticulable intuition, 121 00:11:18.660 --> 00:11:22.020 insight and entrepreneurial awareness. 122 00:11:22.020 --> 00:11:24.220 Several arguments for viewing probability 123 00:11:24.220 --> 00:11:26.320 as subjective were presented. 124 00:11:26.320 --> 00:11:28.580 Uncertainty need not be viewed as a property 125 00:11:28.580 --> 00:11:31.340 of the external world, but of the limitations 126 00:11:31.340 --> 00:11:34.740 on our knowledge which can never be fully overcome. 127 00:11:34.740 --> 00:11:36.900 Mises' view that the world is governed 128 00:11:36.900 --> 00:11:41.060 by deterministic causality is not one which can be proven, 129 00:11:41.060 --> 00:11:43.460 nor can it be disproven since the issue 130 00:11:43.460 --> 00:11:53.460 If the view is ontologically indeterminate, the case for objective probability is necessarily much weaker than for an encompassing subjective view of probability. 131 00:11:53.460 --> 00:11:55.460 Thank you very much.