Comments (35)

• Anonymous

  Perhaps I misunderstood the argument, but I believe the conclusions drawn in "ON THE POSSIBILITY OF ASSIGNING PROBABILITIES TO
  SINGULAR CASES" are incorrect.

  "the world is governed by time-invariant causal laws"

  Yes, the natural world may be governed by time-invariantly operating causes, but human action is not. "There are no empirical causal constants in the field of human action" (Hoppe, pg. 38).

  In fact, the author of this paper (by writing the paper) is implicitly admitting that one can learn: "We cannot predict in advance, on the basis of our previous states, the future states of our knowledge or the actions manifesting that knowledge" (Hoppe, pg. 37). Thus, the author implicitly admits that no time-invariantly operating causes exist with respect to human actions.

  Austrians are correct that calculating numerical probabilities is absurd for events that aren't repeatable, random, and homogeneous.

  Published: June 12, 2009 7:27 PM

• Dan

  As a Bayesian (those statisticians who, among other things, recognize probability as subjective degrees of belief), I'm surprised that Austrians haven't gotten together with Bayesians a long time ago. One could imagine a glorious clash of curmudgeons as Ludwig von Mises and E. T. Jaynes meet ... and feel the ground shift from the sheer awesomeness. Although the former was curmudgeonly well before the latter; even so, in NBA Live '08 I can play 80's All Stars vs. the 2007 Phoenix Suns, so sue me.

  I am a bit surprised at the author for not referring to the pantheon of subjective probability theory, Sir Harold Jeffreys, Jaynes, and so forth. Referencing Good is good but not enough. This may be the source of the author's odd assertion that subjective probabilities are appropriate because the world is governed by time-invariant causal laws. Instead, as the author points out, probabilities are subjective because (as Jeffreys recognized) they represent rational judgements based upon incomplete knowledge. This has long been known in physics as well, where we cannot know the positions and momenta of the particles in a gas, but we are nevertheless able to make useful--statistical--predictions about the behavior of the gases. These sorts of predictions are certainly influenced (and simplified) by the apparent stability of physical laws, but rather than precluding our ability to make predictions, even if physical laws changed with time, or, more mundanely, if we try to make time-dependent or nonequilibrium predictions, it just makes the calculation harder. The subjectivity of probability and the utility of that point of view allow us to make predictions given incomplete knowledge, irrespective of time dependence or causality.

  In short, time dependence and causality really have nothing to do with it. Probabilities cannot consistently be defined as frequencies in some "random" experiment; as Jaynes shows, the "probability of heads" is not a property of a coin that can be defined noncirculary in terms of randomness.

  Probabilities are instead better regarded as degrees of belief. This should be evident to anyone who isn't silly. We make probabilistic judgements all the time, automatically, when we try to predict how people will respond (knowledge we do not have before observing it) to our actions (knowledge we do have). People do behave predictably; however, people are extremely complicated, which often makes trying to predict behavior extremely difficult.

  Dan

  Published: June 12, 2009 9:18 PM

• Mark Crovelli

  In response to the comments made by Anonymous above, let me just reiterate that my argument is simply that all human actions are caused-- not that human action is governed by the same time-invariant laws as, say, oak trees. Human actions are "caused" by the intentions, beliefs, and volition of the actor. This, as I hazarded to argue, is all that is necessary to show that probability is not a property "out there" in nature. On the contrary, it is a property of our ignorance of those causes. If, for example, you knew everything about a man's beliefs, intentions, and the state of his will, you would have absolutely no uncertainty about how he would act. I am not, therefore, claiming that man's actions are governed by the same kinds of laws as trees-- only that man's actions are all caused.

  Published: June 13, 2009 12:51 AM

• Anonymous

  Mark Crovelli,

  "If, for example, you knew everything about a man's beliefs, intentions, and the state of his will, you would have absolutely no uncertainty about how he would act."

  This is not correct. It is impossible to predict what one will learn. Even if we "knew everything about a man's beliefs, intentions, and the state of his will", we would still be incapable of predicting his future states of knowledge. You are engaged in a performative contradiction because you wouldn't have written the post unless you realized humans are capable of learning. Your entire argument is ruined by the fact that people learn.
  

  "probability is not a property "out there" in nature."
  
  Probabilities are objective. To use your phrase, probability is a property "out there" in nature (they are based on experience). Using probability calculus for subjective beliefs is meaningless and is not practically useful. Any use of statements like "the probability of Boxer X winning is 48.372%" is only metaphorical.

  http://mises.org/journals/qjae/pdf/qjae10_1_1.pdf
  

  Published: June 13, 2009 12:31 PM

• Mark Crovelli

  Anonymous,

  I don't know what has given you the impression that I believe that we DO know everything about a man's beliefs, ideas and the state of his will. I have never said this. What I have said is that IF we were to possess such knowledge, then we would not be uncertain about how he would act. I have also said that IF we knew everything involved in the tossing of a coin (i.e., every single factor affecting the coin's movement), we would know in advance whether it would be a head or a tail. This is not to say that I think that we DO INDEED possess such information.

  Published: June 13, 2009 12:50 PM

• Mark Crovelli

  Anonymous,

  I'm also afraid that your argument that the probability that boxer x will win is "metaphorical" runs into the cold, hard fact that casinos do indeed generate such odds. They are, moreover, remarkably accurate and casinos make money off of them every year. How do you explain that? Do you also honestly say that this is not "useful" information?

  Published: June 13, 2009 12:57 PM

• Mike D.

  Bookmaker's in England assign odds to horses in a horse race. This is a singular event. However, the odds are calculated based on the amount of money that has been bet on each horse. These odds are adjusted as more money is bet. Odds are lowered to discourage people from betting on the favourite, and increased to encourage betting on outsiders. This typically produces a break-even if the favourite wins and a profit for the bookmaker if another horse wins.
  It is interesting to note that the relative amount of money bet on the favourite is a good indicator of the probability that the favourite will win.

  Published: June 13, 2009 3:30 PM

• Atown

  I think the boxer analogy is flawed. A sportsbook assigns a probability to a boxing fight so that people will bet equally on both sides. If a sportsbook is "balanced", the casino wins regardless of the outcome of the fight. It doesn't have to do with actual fight, just how people feel about the fight.

  Published: June 13, 2009 3:34 PM

• Stefan W. Christensen

  Dan,

  I completely agree with you that Austrians and Bayesians are natural allies (and let's not forget that the Austrians' battle with the main stream is mirrored by the Bayesians' battle with the frequentists).

  As far as E.T. Jaynes and L. v Mises meeting up; I actually once read Jaynes quote Mises in a paper (or maybe it was his book, I can't remember where). Reading the passage, you can almost literally feel the anger and sheer loathing Jaynes must have felt at the time, because of Mises being so utterly ignorant of probability theory as to accept unquestioningly the horribly limited view, which his brother was championing.

  I think Jaynes over reacted, because he thought Mises was mathematically educated, and simply couldn't believe anybody such educated could be so bone headed.

  I personally believe that Mises would have embraced mathematics, if his brother had been a gardener, or some other such thing, instead of a mathematician with a fetish for frequencies, and if Mises had been aquainted with Jeffries.

  This is not to say that Mises would have adopted the mathematical methods, that were entering main stream economics, but he might have phrased a lot of things differently.
  

  Published: June 13, 2009 3:56 PM

• Anonymous

  "What I have said is that IF we were to possess such knowledge, then we would not be uncertain about how he would act."

  I'm disagreeing with this statement. I'm saying that even if we knew "everything about a man's beliefs, ideas and the state of his will", we would still be uncertain about how he would act in the future. This is true because we cannot predict what that man will learn in the future. New knowledge affects future actions:

  "But if one can learn from experience in as yet unknown ways, then one admittedly cannot know at any given time what one will know at a later time and, accordingly, how one will act on the basis of this knowledge" (Hoppe, pg. 37).

  The existence of casinos does not prove that probability is subjective. Odds are not the probability of an event occurring, they are the amount the bookmaker will pay out if the an event occurs. Casinos are remarkably successful because they include profit margins in their odds (called the Over-Round). The alleged connection between odds and probability is only evidence that most people don't understand the meaning and limits of numerical probability.

  Published: June 13, 2009 4:56 PM

• Anonymous

  I should amend my last sentence to say: The alleged connection between BETTING odds and probability is only evidence that most people don't understand the meaning and limits of numerical probability.

  Betting is different than gambling.

  Published: June 13, 2009 5:15 PM

• Mark Crovelli

  Anonymous,

  You are missing the point here entirely. I am not denying that man can learn. All I am saying is IF we knew in advance all the various internal factors that go into a man's decision to act, then we would know how he would act. This is so obvious that it is almost tautological. We do not, obviously, possess such information, and this is precisely why we resort to generating probabilities.

  As far as odds and probabilities are concerned, they are different ways of expressing the same thing (as long as we are talking about odds from a probabilistic point of view). Odds can be transformed into probabilities, and probabilities can be transformed into odds.

  What is your position with regard to odds generated by bookies, casinos, and professional probabilists working in Vegas who generate probabilities and odds for singular sporting events (e.g., Robert DeNiro in Casino)? Are those odds "meaningless" or "absurd" simply because they are not derived from long-run relative frequencies? What would you say about the odds generated by the method discussed by Mike D. above? Are such odds really "metaphorical" and "meaningless" because they don't come from past frequencies? How is it possible that they are so accurate most of the time?

  Published: June 13, 2009 5:28 PM

• Atown

  There's no reason why gambling can't fit inside the Austrian model. There isn't anything essentially different between the market setting the price of a sandwich at $5 and the market setting the price of "boxer A wins" at you pay $5 and make $10. The price of "boxer A wins" has much to do with the probability of boxer A winning the fight as the price of the sandwich has to do with the fact that it has lettuce, tomatoes, and turkey on it, which is to say nothing at all.

  Published: June 13, 2009 6:00 PM

• Mark Crovelli

  I'm afraid I don't follow your line of reasoning here, Atown. Are you arguing for or against the frequentist theory?

  Published: June 13, 2009 6:02 PM

• Mike D.

  Just because we use a probabilistic model does not mean that the underlying phenomenon is not deterministic. Take the case of a balanced roulette wheel in a casino. A probability model that assigns a probability of 1 in 33, with no memory, to each number is a valid model - it allows the casino to make predictable profits based on the amount bet. However, some MIT students came into a casino with a hidden video cam connected to a computer that observed the initial positions and speeds of the ball and the wheel. They were able, using Newtonian Mechanics, to narrow the outcome down to a sequence of 8 numbers on the wheel.

  Published: June 13, 2009 6:11 PM

• Anonymous

  Mark Crovelli,

  Odds generated by bookies for singular sporting events are not probabilities. Such odds are the amount the bookmaker will pay out if a certain event occurs. The relationship between odds and probabilities you allude to is only appropriate when dealing with class probability. (In fact, even if we do accept your false definition of probability, odds wouldn't represent the "actual probability" because of the Over-Round.)

  To speak of "probabilities" with respect to case probability is purely metaphorical. It is an analogy. On this, Mises says:
  
  "It is a metaphorical expression ... it is an attempt to elucidate a complicated state of affairs by resorting to an analogy borrowed from a branch of higher mathematics, the calculus of probability" (Human Action, pg. 114).

  Bookies may be accurate because they "know something by understanding the people involved" (Human Action, pg. 116). But this has nothing to do with probability, and this does not prove that probability is subjective.

  Mark, have you read chapter 6 of "Human Action" and Hoppe's "The Limits of Numerical Probability"?

  Published: June 13, 2009 10:07 PM

• Mark Crovelli

  Anonlymous,

  Have you read my paper? I'm beginning to have my doubts

  Published: June 13, 2009 10:13 PM

• Mark Crovelli

  Anonymous,

  Let me make a few more observations about your arguments about me paper. First, it simply will not do to keep throwing L. von Mises quotes on probability out as though they can settle this issue. I am fully aware that my paper dissents from the standard Mises-Rothbard consensus. What I have argued is that Mises and Rothbard were incorrect to state that probability is an objective measure of something "out there" in the world. As such, any reference to Mises or Rothbard's views on the matter will be completely irrelevant to my argument. What I have claimed is that they adopted a mistaken definition of probability-- and that their definition conflicts with the Austrian view of human action and the causally-determined nature of the natural world. So, in order to refute my argument you must provide an argument yourself to the effect that either 1) the definition of probability does not depend upon the nature of the world, or 2) that the world is itself not governed by causal laws. If you cannot provide any such argument, then you are not able to argue against my paper.

  Published: June 13, 2009 10:49 PM

• Ben O'Neill

  Dan and Stefan,

  I am also a Bayesian statistician and I too have been frustrated by the poor level of statistical knowledge in the Austrian school and the silly things that Mises maintained about probability (with great respect to his other brilliant achievements). I have found the Bayesian methodology, based on an epistemic interpretation of probability a la Jaynes or de Finetti, to be the most coherent, philosophically defensible, and inferentially realistic approach to probability and statistics of all the methods known.

  Like you say, they are natural allies. It is a shame that Ludwig von Mises got sucked into the positivist view advocated by his brother (especially given that Austrians have strongly criticized positivism in other fields). There is so much convincing argument for the Bayesian method now (Jaynes, de Finetti, Savage, Bernardo and Smith, etc.) that it is high time Austrians embraced it.

  Cheers,
  Ben.

  Published: June 13, 2009 10:56 PM

• Jaishen Rajah

  This is a great debate to have. I am currently reviewing this subject from a medical perspective and trying to look at Mises contribution to medical diagnosis by contrasting case (subjective) to class (fequentist) probability. According to Mises, "A statement is probable if our knowledge concerning its content is deficient". When a doctor makes a diagnosis based on unique individual patients characteristics, it would be contradictory to state that this patients has a 25% chance of having disease X. (This unique case has not occured before, and if I assign a single number then it reflects certainty). Mises stated that such statements are metaphorical. I do not state that I owe someone 3.5 unit of gratitude, but express it as "thank you very much." Simarlarly, in medicine, we deal with events or classes that are ORDINALLY RANKED. This should be expressed as subjective terms such as likely, less likely or unlikely etc, but perhaps better expressed as intervals eg the pre-test probability of disease X (the doctors opinion after the history and physical exam)is 10-20%. This is not assigning a single number but a more humble reflection of our uncertainty in the diagnosis. (Does it not sound contradictory to hear statements such as the the patients weight was approximately 13.345 kg , the analogy being is a statement not contradictory in being 10.24% probable?).
  
  I would also refer readers to Richard von Mises book on proability. He makes reference to Bayesian methods in specific circumstances.
  I completley disagree that L Mises had no mathematical grounding. If this were the case, either he was a genius to express his mathematical concepts with such clarity in words, or we are mistaken about the mathematical grounding or lack thereof. Furthermore, Human Action has no supply and demand diagrams, not revealing his lack of mathematical knowledge but an attempt to explain in simple laguage. Einstein said that the mark of a genius was to make the complex simple.

  Published: June 14, 2009 1:47 AM

• Mike D

  Jaishen
  
  Here is a question from Deborah Bennett's book Randomness:
  
  
  “If a test to detect a disease whose prevalence is one in a thousand has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person’s symptoms or signs?”
  
  
  She follows up with the question.
  
  “what percentage of the physicians, residents, and fourth year medical students at a prominent medical school who were asked this question got it right?"
  
  (The answer is not 95%. Bayes Theorem does give the right result.)
  
  
  The answer is important. Consider a blood donor who is screened for HIV, who tests positive.
  

  Published: June 14, 2009 11:09 AM

• Anonymous

  "in order to refute my argument you must provide an argument yourself to the effect that either 1) the definition of probability does not depend upon the nature of the world, or 2) that the world is itself not governed by causal laws."

  There are two different realms of causality: the natural/physical world and mental/subjective world. This is known as Methodological Dualism. The natural world may be governed by time-invariant causal laws. The mental/subjective world is not governed by time-invariant causal laws. The ability to learn means that the mental/subjective world is not governed by time-invariant causal laws, and one can't deny that people learn without falling into a performative contradiction. Probability is objective, not subjective.

  Consider this situation: I have a stock portfolio with a Portfolio Return of 21.29% and Portfolio Volatility 18.45%. Suppose I want to use the inverse of the standard normal distribution to determine Value-at-Risk (VaR): I determine with 90% confidence that the return on my portfolio will be greater than -2.36%. Does this mean anything? No, this exercise is meaningless. Stock market returns are based on the actions of millions of people, and their actions are not infinitely repeatable, homogeneous, or random.
  
  A similar exercise could used by a doctor to determine how long a sick patient has until death. They could say with 95% confidence that the patient has at least 3 months to live. But this exercise would only give the patient and his family false hope. This exercise could be detrimental (worse than worthless).

  Do you really believe these exercises have value?

  Published: June 14, 2009 5:38 PM

• Mark Crovelli

  Anonymous,

  The issues involved here do not have anything to do with methodological dualism. All I am saying, again, is that human actions have a cause. How many times do I have to say this before you understand that I am not claiming that human beings are governed by time-invariant causal laws in the same way as, say, trees. ALL I AM SAYING IS THE HUMAN ACTIONS ALL HAVE CAUSES; NAMELY, THE IDEAS, INTENTIONS AND VOLITION OF THE ACTORS. Am I really not explaining this clearly enough?

  Published: June 14, 2009 6:31 PM

• Anonymous

  Mark Crovelli,

  This will be my last post here. I stand by my comments and I've already repeated myself far too many times. I'm sorry that your paper was unconvincing.

  One final point: probability can never be a priori. Consider the probability of rolling a die. We still don't know the probability of an outcome a priori because there's no way of knowing if it's a fair die. The die could be loaded. This means probability must be based on knowledge, not ignorance. This alone is enough to discredit your thoughts on probability.

  Published: June 14, 2009 9:41 PM

• Mark Crovelli

  Anonymous,

  I am absolutely convinced from this post that you never did read my paper. What on Earth could have given you the impression that I believe probability is a priori? I have written here, and I have written in my paper that probability is subjective.

  You can claim all you want that my paper was unconvincing, but let's not pretend that you've presented any arguments to that effect here.

  Published: June 14, 2009 10:06 PM

• newson

  any other tips for readings on probability, apart from "randomness" by deborah bennett?

  Published: June 14, 2009 10:31 PM

• Anonymous

  I did read your paper. You implicitly admit a priori probability is possible. A priori probability means that probability does not rely upon experience. You argue that probabilities can exist without reference to experience. Thus, you implicitly admit that a priori probability is possible.

  A priori probability is not possible. The die example I posted above explains why.

  You failed to comment on the finance and medicine examples I posted above? Do you believe those techniques are of any value? Or do you admit that they are completely meaningless because the events are not homogeneous, random, and repeatable?

  Published: June 14, 2009 10:40 PM

• Mark Crovelli

  Anonymous,

  How can I state these ideas any more clearly? I have argued that probability is subjective, not that it is a priori. The title of my paper states this explicitly. Economic value is similarly subjective, but this does not mean that economic value is somehow a priori, whatever that might mean. I have also certainly never argued that probability does not rely upon experience. Of course it relies upon experience if it is a subjective measure of man's beliefs about the world.

  You seem to be unclear about what I am trying to establish in my paper. I am trying to properly define probability. The von Mises brothers claim that it is some objective measure of something in the world. I claim that it is a measure of our uncertainty about the causes of events and phenomena in the world. That's it. I don't deny that relative frequency methods are useful for generating numerical probabilities-- I just dispute the claim that these are the ONLY legitimate methods for generating numerical probabilities.

  Does this make things clearer?

  Published: June 14, 2009 11:38 PM

• Jaishen Rajah

  Mike, thanks for the example. This is correct and I am betting that most doctors at all levels would get it wrong. Another reader asked about other books on probability. Anything by Gerd Gergerenzer. (Reckoning with Risk is great to start with). I am working on a paper that physicians need to become more acquainted with the Bayesian technique, even though we adopt this form of thinking uncounciously. Where I have problems with all the discussion above, is in the discussion lumping the Mises brothers together. L Mises by recognizing case probability and its subjectiveness, implicity in my opinion is adopting a Bayesian slant. Not assigning a number is a different issue. He places an emphasis of the ordinal over the cardinal measures. This is what doctors do when we use statistical terms like confidence intrervals to express our degree of uncertainty. There is more emphasis in the medical diagnostic literature in using inteval measurements as the Bayesain "prior", which is the real reflection of uncertainty rahter than a single number.

  There are a few great articles on the Austrian site (eg. Hoppe, I think Hulsman as well) discussing the difference between the Mises brothers as well as those of Keynes as far as probability theory goes.

  Published: June 15, 2009 12:09 AM

• Mike D.

  Newson
  
  http://www.amazon.com/Estimating-Choosing-Essay-Probability-Practice/dp/0387500871/ref=sid_dp_dp
  
  
  This is an excellent account of the philosophy of probability from a brilliant French mathematician who is best known for his work in Geostatistics. The book is hard to get hold of but is a good read.
  

  Published: June 15, 2009 1:57 AM

• Mike D.

  Jaishen
  
  The an answer to Deborah's question is about 1 in 51 - very different fro 1 in1000 or 95 in 100. You can arrive at a good approximation by the following reasoning. Suppose we test 1000 people.One person, who has the condition will test positive. There will be 50 false positives.Therefore only one person out of 51 people who test positive will have the disease.
  
  Deborah reports that only 19% got the right answer. However, only 50% who got the wrong answer thought that the right answer was 95%,

  Published: June 15, 2009 2:06 AM

• Anonymous

  Mark Crovelli,

  Admitting that probability can be subjective is also an implicit admission that a priori probability may exist. Consider this example of a subjective a priori probabilistic claim: I believe there is a 1.2% probability that I'll meet my soul mate tomorrow. (note, I only have one soul mate so this subjective probabilistic claim cannot be based on experience). But a priori probabilistic claims cannot exist (as explained above).

  At the very least you should have mentioned that such a subjective a prior probabilistic statement is incorrect. Of course, I would go even further and say subjective probability is nonsense. Thank you for taking the time to write the paper and respond to my posts. Your paper/posts have encouraged me to rethink the subject.

  
  

  Published: June 15, 2009 4:20 AM

• Mark Crovelli

  Anonymous,

  You're welcome for the paper. Allow me to state in conclusion, again, that I have argued for a subjective definition of probability, not an a priori definition of probability. It is thus not fair to attack my argument by arguing against the a priori idea of probability, when I say explicitly: probability is subjective, not a priori!

  Published: June 15, 2009 6:18 AM

• Anonymous

  P.S. I already met my soul mate, so the example was purely metaphorical (just like all subjective probability).

  Published: June 15, 2009 10:42 PM

• Charlie

  Hi,
  Thanks for the paper, Mark. I greatly enjoyed reading it. I agree with the analysis of subjective probability as being dependent on one's quantity and quality of information about the event in question. This follows well with the Bayes approach and information theoretic approach to objectifying probability (by objectifying, I mean making actionable. The probability is still subjective).

  Asserting that the physical world is governed by time-invariant causal laws does not seem to rule out the existence of objective (physical in this sense) probabilities. The concept of "randomness" is an a priori judgement about the character of some phenomenon. Numerically quantifying the probabilities can, of course, only be attempted a posteriori (i.e. by assuming asymptotically stable proportions ala R. v. Mises, or subjectively assigning case probabilities). This is not to say that randomness is a quality of "objects-in-themselves," but a conceptual judgement.

  An example comes from quantum physics. One may judge that a photon of a particular energy approaching an energy barrier of a higher energy has a certain chance of appearing on the other side. Whether one assumes that the nature of the phenomenon is "random" in itself, or that there are unobservable underlying causes is irrelevant to how one makes use of the phenomenon. It may be that the "randomness" theory is superceded by a deterministic one in the future, maybe not, but the information one gains by employing this theory is enough for human action.

  By the way, L. v. Mises does not necessarily assume that the world is "truly" governed by time-invariant laws, only that human reason must assume some degree of time-invariability for action to take place. From Theory and History (p. 91):

  "The very notion of a natural law whose validity is restricted to a definite period of time is self-contradictory. Experience, whether that of mundane observation as made in daily life or that of deliberately prearranged experiments, refers to individual historical cases. But the natural sciences, guided by their indispensable aprioristic determinism, assume that the law must manifest itself in every individual case, and generalize by what is called inductive inference."

  A "natural law" is a conception of the human mind -- a grasping to reckon with the variety of phenomena assaulting our senses -- and not a character of natural things-in-themselves. Without apparent regularity, though, action would be impossible. No one would be able to plan for the future if regularity on a large scale did not manifest itself.

  Thanks for accepting my commentary. I look forward to reading more of your thoughts, Mark.

  ~Charlie

  Published: June 16, 2009 11:01 AM