44. “Has David Howden Vindicated Richard von Mises’s Definition of Probability?”
by Mark R. Crovelli
Abstract: In my recent article on these pages (Crovelli 2009) I argued that members of the Austrian School of economics have adopted and defended a faulty definition of probability. I argued that the definition of probability necessarily depends upon the nature of the world in which we live. I claimed that if the nature of the world is such that every event and phenomenon which occurs has a cause of some sort, then probability must be defined subjectively; that is, “as a measure of our uncertainty about the likelihood of occurrence of some event or phenomenon, based upon evidence that need not derive solely from past frequencies of ‘collectives’ or ‘classes.’” I further claimed that the nature of the world is indeed such that all events and phenomena have prior causes, and that this fact compels us to adopt a subjective definition of probability.
David Howden has recently published what he claims is a refutation of my argument in his article “Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations” (Howden 2009). Unfortunately, Mr. Howden appears to not have understood my argument, and his purported refutation of my subjective definition consequently amounts to nothing more than a concatenation of confused and fallacious ideas that are completely irrelevant to my argument. David Howden has thus failed in his attempt to vindicate Richard von Mises’s definition of probability.
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I do not see David Howden as failing to vindicate Richard von Mises. So I give my nod to Howden and Mises.
One point I want to make: There are those who bet and those who manage a sportsbook. The individual placing the bet cares about the final result. The bookie does not care about the result, he only cares about the dollars bet on both sides of the line.
So the bookie is looking to find the line that leads to equal bets, for and against. If the bookie ever hits this sweet spot, he can relax knowing that, regardless the outcome, he takes his cut.
Assume event E (a football game), where the line is 7 points. The payoff is $100 for every $110 bet. So the bookie wants $1.1 million bet on team A and another $1.1 million bet on team B. Then, regardless the outcome, one side wins $1 million and the bookie makes $200K, free and clear.
If the bookie sets the line so that (say) $1.65 million is bet on A and $550K is bet on B, the bookie is now a bettor himself — a way to guarantee sleepless nights.
So, from the bookies perspective, he is an entrepreneur trying to find the sweet spot based on his knowledge of bettors.
Mr. Fedako,
I am extremely interested to know why you think David Howden has vindicated Richard von Mises’s definition of probability. You must have a reason for thinking this is the case beyond a mere restatement of how a sportsbook manager runs his operation.
Is it not clear that the odds generated by sportsbook managers are numerical probabilities for singular events. That is, they are precisely the type of numerical probabilities that the brothers von Mises condemned as “absurd?” If so, and Richard von Mises had a correct definition of probability, then we, too, must condemn these odds as “meaningless” and “absurd.” Are you willing to follow Richard von Mises and David Howden in doing that?
Cheers,
Mark Crovelli
I might not have made myself clear. The bookie is not defining odds that team A will win event E, per se. The odds — the line — is about equal betting only (an entrepreneurial activity — a guess of human action).
A line of +7 does not mean that there is a 50% chance that the final spread will be greater than 7 points. It simply means that the bookie believes that at +7, half of the money will be on A and half on B.
Regarding probability, here’s an real life example:
Today I bet a coworker on tonight’s Steelers/Brown’s game. We made two bets. Bet one was at the Vegas spread — +10. As a Steelers fan, I believed the Steelers would prevail, but I didn’t think they could cover the spread.
So I enticed him into a second bet (a hedge for me). This was a bet that neither team would score more than 20 points (I figured that the weather would guarantee a low scoring game).
I’m cheap — a real pennypincher. So the bets were for $1 each (but, for me, a dollar is 100 pennies).
In the end, my hedge protected me (the Browns won 13-6).
Neither of those bets were based on probability, as defined by Mises. Though they were based on some past knowledge of football and my ability to predict lines that would entice my coworker to wage a couple of bucks.
I made entrepreneurial decisions, and won one and lost one. But I never defined probabilities by any stretch of the term.
Mr. Fedako,
My question for you was not specifically dealing with the methods utilized by the sportsbook manager. I agree with your explanation about how the line for sporting events is calculated. The question, however, is why these amazingly accurate odds are not probabilities. You rightly note that if we adopt the definition of probability advanced by the brothers von Mises, we have to say that these are not probabilities.
So what are they, then? It is clearly question begging to say that they are not probabilities, simply because the von Mises brothers said so. And it is clearly question begging to simply restate how the sportsbook manager generates them as some sort of evidence that they are not probabilities. (Recall that odds can be transformed into probabilities and vice versa, so odds of, say 3 to 1 can be directly translated into a numerical probability– a number between 0 and 1).
So, I’m curious what these amazingly accurate numbers are? When you read the line for today’s sporting events in your local newspaper, what is that you are looking at? Is it just a miracle that these odds and lines are remarkably accurate?
Cheers,
Mark Crovelli
Mr. Crovelli:
I will argue once again that a bookie’s odds do not equate to probabilities.
The probability of event A and the probability of event not-A have to sum to 1. When applying the RvM addition rule, the attributes that make up event A (a’, a”, a’”, etc.) sum to A. On this we should agree.
However, one bookie’s odds of A (that one of the names on his list will be elected president in 2012), when converted to probabilities, sum to 1.235. And that doesn’t include not-A (the election of someone not on the list, a catastrophic event that leads to no election, etc.).
You might ask: How can that be? I would reply that the bookie does not believe that (as one example) Ron Paul has any chance of winning (should he even run), let alone the 1% chance the bookie quotes. The bookie is only putting up odds that include Paul in order to generate bets on his book for Paul (free and clear income for the bookie).
This bookie’s odds are certainly not probabilities.
Mr. Fedako,
I’m afraid that you are falling into the same errors in reasoning that David Howden did which I identified in my most recent paper. Specifically, what you are doing here is begging the question, over and over again. Recall that the question at hand is to define probability. I claim that probability is subjective, and you, Richard von Mises and David Howden all claim that probability is a relative frequency. In order to answer this question you must give us a reason why probability must be defined as a relative frequency. In the context of discussing my paper, moreover, you really ought to offer an argument as to why my argument was mistaken.
If all you can do to counter my argument is to cite Richard von Mises’s methods and rules for generating numerical probabilities as the only evidence that Richard von Mises’s definition is correct, you are making a circular argument. You are saying Richard von Mises’s argument was right because his rules and methods for generating probabilities are such and such. Is it not obvious that this begs the question?
Setting that problem aside, if you are absolutely convinced that odds and lines are not probabilities, can you tell me what on Earth they are, then? They are extremely accurate numbers that tell us the likelihood of some event occurring. How is that not a probability? If not, then please tell me what they are?
Cheers,
Mark Crovelli
Mr. Crovelli:
We are going around in circles.
Let me cut to the chase, so to speak: Can probabilies sum to more than 1? If so, then you refute both your comment above and every theory of probability. If not so, then bookies use something other than probability.[1]
And you are begging the question when you continually claim that bookie odds and lines are extremely accurate.[2] You have neither defined this accuracy (as noted by Howden) nor proven that your (as yet undefined) accuracy exists.
Notes:
1. Bookies are using, as I have noted above, knowledge of bettors to make entrepreneurial decisions — they are using their understanding of human action.
2. In my example about (Steelers v. Browns), the line was off by 20 points. Would that qualify as accurate?
PS. I have enjoyed this exchange, just as I enjoyed RvM’s book and the articles by both you and Howden. The Libertarian Papers is a hidden gem of Mises.org.
Mr. Fedako,
I am enjoying this exchange as well.
As to the question of whether probabilities must sum to one, it should be clear that the answer depends upon what definition of probability we adopt. If we adopt Richard von Mises’s definition, then, yes, probabilities must sum to one, by definition. But, if we adopt a subjective definition of probability, then this does not necessarily follow. So, to assume that they must sum to one begs the question: Who has the correct definition of probability, Richard von Mises or me?
In saying this, however, I must note that probabilities must sum to one, (and satisfy certain other requirements), in order for someone to utilize the vast mathematical apparatus that has been developed for numbers that satisfy those requirements.
In addition, the idea that bookie odds do not necessarily sum to one is something of a red herring, because there is no reason why betting odds for singular events cannot be expressed as odds that can directly be transformed into probabilities that satisfy Richard von Mises’s criteria. Bookies are not always concerned to express their odds in a manner that would please mathematical probabilists, just as practicing engineers sometimes make use of theories (e.g., Newton’s), that might make physicists cringe. The reason why they do this is simply because 1) it is important, for their purposes, to express their odds in a manner that is understandable to the betting public, 2) it is completely unnecessary, for their purposes, to produce odds that would make mathematical probabilists happy. They obviously could produce such odds (just look in any probability textbook for an explanation of odds that can be directly transformed into probabilities of the sort Richard von Mises wrote about), but it is completely unnecessary to do so.
So, to complain that bookies are rather loose in their use of odds from the perspective of mathematical purists, is rather like complaining that engineers don’t always use trigonometry the way they “should.” Perhaps this is a valid point, if we are trying to instruct bookies in the rigorous use of mathematical probability, but as far as the definition of probability is concerned, this is completely irrelevant.
Cheers,
Mark Crovelli
Mr. Crovelli:
Then do we agree in the LvM sense? There are two types of probability: class and case. Class is RvM probability and case is your subjective probability.
LvM calls them both probabilities.
You seem to agree that there is a dualism with regard to probabilities (mathematical and subjective — I believe these would be the two types you recognize).
I only term class probability as probalistic. But that flows directly into the Mises/Hoppe view of insurance.
Note: This sentence is poorly written, When applying the RvM addition rule, the attributes that make up event A (a’, a”, a’”, etc.) sum to A.
It should read, When applying the RvM addition rule, the probabilities of the attributes that make up event A (a’, a”, a’”, etc.) sum to probability of A.
Mr. Fedako,
No, I don’t think we are finding any agreement here. When I talk about probability being subjective I do not mean that only some probabilities are subjective, while other probabilities are not. I mean that ALL probability is subjective; that is, all probabilities are a measure of man’s subjective ignorance of the causal factors involved in the world. Ludwig von Mises’s distinction between “case” and “class” probability, on the other hand, is a conceptual distinction between those instances where an event (virtually) repeats itself over and over again, and those instances where only one singular iteration is involved. This distinction only addresses the question of when the relative frequency method can legitimately be applied.
There are two very important but distinct problems involved here. On the one hand, we have the problem of what methods can legitimately be used to generate a probabilities expressed as a number between 0 and 1. The von Mises brothers claim that there is only one legitimate method for doing this: the relative frequency method , which deals with (virtual) repetitions of the same event over and over again. I claim that there are other methods that can yield a number between 0 and 1, (like the methods employed by bookies, forensic scientists estimating DNA matches, etc.), which deal with singular events, but which nonetheless generate numbers between 0 and 1.
On the other hand, we have the question of the conditions under which we may legitimately utilize the mathematical methods of probability. On this, there is no question, because everyone agrees that the axioms of probability must be met in order to apply the mathematical methods. But, this question is completely separate from the question of how we come up with the number in the first place, before we apply the mathematical methods to it. As long as the number is between 0 and 1 we can utilize the mathematical methods, regardless of whether the number was generated by a relative frequency method or a non-frequentist method.
Cheers,
Mark Crovelli
Mr. Crovelli:
I have a contractor doing work on my house. He said that there was one unknown that might cause an increase in his estimate. I asked him what the probability was for the unknown to occur (I had this discussion in mind). He replied, “5%.”
Well, the unknown did not occur. So was he right?
Did his “5%” answer have more meaning than a reply of “slight?”
Since he replied with a subjective number between 0 and 1, was his answer a probability in your view? Does it have the same meaning as your esteemed bookie saying “5%?”
And, back to that bookie.
You still have not shown that bookies are accurate at predicting results — not betting patterns, but results. And you have not defined accurate.
Additionally, you have not shown how probabilities can sum to more than 1 and still have meaning.
They can, and do, sum to more than 1 — they sum to more than one since that is how bookies take a cut. But is a bookie’s cut a component of the probability of an event?
And, while you are at it, explain what odds a bookie would set if he — and only he — knew the outcome of an event before it occurred (the fix was in). Would his lines be infinity and 0 (100 pays 0 if A wins — a is certain to win, and 100 pays infinity if B wins)? And what of his cut?
Or would he align with his fellow bookies (who do not know that the fix is in)?
Mr. Fedako,
You are grossly misunderstanding what I mean when I say that probability is subjective. Again, when I say that probability is subjective, I mean that ALL probabilities are subjective; that is, ALL probabilities are measures of man’s subjective ignorance about the causal factors at work in the world. Hence, my argument means that the numbers generated by Richard von Mises’s relative frequency method are also subjective. So, for you to continue to refer to only some probabilities as subjective is to radically misunderstand my argument.
As for the question of whether the odds generated by bookies are accurate, I encourage you to follow the line in your local paper for any sport for a length of time. Or, better yet, check out the odds generated by Fed Funds Futures for the likelihood that the Fed will increase rates. These numbers are astonishingly accurate predictors of outcomes, and it is hard to imagine that anyone (beyond Richard von Mises, that is) could consider them to be “absurd” or “meaningless.” On the contrary, they are extremely useful and accurate predictions about future events.
I am curious to know what you think these numbers are. Are you really suggesting that they are not accurate predictions about future events? Are you claiming that they are absurd or useless? What on Earth are they, then? Please give me some hint about what I’m looking at when I open my newspaper, since you are absolutely certain that I am not looking at probabilities.
To reiterate what I’ve already written about odds that do not sum to one, I agree that not all odds are expressed in a manner that pleases traditional probabilists. But, as I have already indicated, the reason why their odds are expressed in that manner is due to the fact that 1) they need to express their probabilities in a manner that is easily understandable by the betting public, and 2) it is completely unnecessary for their purposes to make odds that would make traditional probabilists happy. Quite obviously, their goal is only to make odds for betting– they have no intention whatsoever of applying mathematical methods to their odds, so they don’t care one whit if the numbers sum to one. However, and this is absolutely vital, THERE IS NO REASON WHY BOOKIES COULD NOT EXPRESS THEIR ODDS IN A MANNER THAT WOULD PLEASE TRADITIONAL PROBABILISTS (AS A RATIO THAT COULD BE DIRECTLY TRANSLATED INTO A NUMBER BETWEEN 0 AND 1) IF THEY WANTED TO. Since this is the case, it is another red herring to point to their supposedly lax use of odds as proof that they are not producing probabilities, because it is obvious that they COULD express their odds in a manner that would comport with the purists’ desire.
To conclude, I think it is important to keep this discussion from getting too far away from the original question, which is about the definition of probability. I have argued that probability as a measure of man’s subjective ignorance about the causal factors at work in the world. Like David Howden, you have not provided any argument against my argument. So, I think it would be useful for us to start from the beginning, and you can give me your argument as to why my argument in my original paper was mistaken.
Cheers,
Mark Crovelli
More to follow, but I wanted to capture this nugget from Doug French’s Fortune Sellers:
“Besides the free predictions that float around, some people and companies pay big money for predictions. But is it money well spent? After all, no one can really foretell the future. ‘This necessity of guessing the course of the relevant conditions and their possible change during the forthcoming action is called the act of entrepreneurship,’ Murray Rothbard wrote in Man, Economy and State.”
Mr. Fedako,
I eagerly await your comments, but I can’t help making a few of my own about Doug French’s quote here. First, I want to make it perfectly clear that just because I want to define probability subjectively, this does not mean that I think man can thereby perfectly foresee the future through probability. Indeed, if we were dealing with perfect foresight about future events, we would no longer be in the realm of probability at all, since, the word “probable” only applies to those things about which we are uncertain. So, it would be unfair for you to criticize the the subjective definition of probability as an absurd attempt to perfectly foresee future events. That is certainly not a claim that any subjectivist would make.
On the other extreme, it is important not to fall into the error of thinking that we know absolutely nothing about future events and phenomena, just because we cannot perfectly predict them. I doubt that this is the point that Doug French is making in this quote, but it is very important nonetheless to avoid saying things like “man cannot perfectly foresee future events, therefore man knows absolutely nothing about what will happen.” This would be an obvious non sequitur.
Cheers,
Mark Crovelli
Mr. Crovelli:
I want to keep this string alive, but it has been busy around here.
A brief comment on subjectivity: I agree that subjectivity exists even with frequency theorists. If RvM had flipped a coin 100 times and heads appeared in 70 of those flips, he most likely would have considered the coin to be biased toward heads. I sincerely doubt that he would have assumed that he was witnessing a once-in-a-lifetime occurrence.
This is due to a coin not being fair when its frequency of heads is above some subjective threshold. So if RvM was searching for a fair coin, he likely would have discarded the one at hand. But, if he was looking to find the probability of heads for the coin at hand, he would have continued flipping until a limit became apparent.
note: Of course my discussion assumes some case probability of RvM’s actions since we will never know how he would have responded.)
More to follow as time allows.
Mr. Fedako,
I’m sorry it’s taken me a while to comment on this.
I think that you are absolutely right that there is inexorably a degree of subjectivity in the use of the relative frequency method. As I said in my paper, there is even subjectivity involved in deciding what cases are sufficiently similar to one another to count as part of a “collective.”
I think that this is a critical point, because if what we are dealing with is subjective even in the case of Richard von Mises’s supposedly “objective” method, then it seems obvious to me that the entire project is an attempt to measure something that resides in man’s head, and not “out there” in the world.
Cheers,
Mark Crovelli
Mr. Crovelli,
In my world, there are three categories of probability.
First, a definition of probability — Probability is the term used to describe the lack of knowledge of whether a given event will occur.
1. Analytical Apriori Probability — Thought exercises that are found only in the mind, textbooks, etc. Here, mathematics apply by definition. Black swans do not exist by definition — all possible outcomes are known. There is no way to find the factors that lead to the probability — by definition, the probability exists.
2. Class Probability (Frequency Probability) — Based on Misesian collectives (i.e. fixed limits and no place selection). Here, mathematics apply by the fact that the collectives exist. Black swans do not exist since the collective precludes them. This is gambling.
3. Case Probability (Subjective Probability) — All other applications of probability (where collectives cannot be defined). Here, mathematics does not apply. Black swans are everywhere. This is betting.
The analytical apriori probabilities have no real world application — other than providing a basis for the mathematics that apply with class probability.
Class probabilities can be used to (inter alia) insure against risk, but not uncertainty (black swans, etc.).
When speaking of a singular occurrence of class probability, case probability applies. This is due to the fact that probability is based on a lack of knowledge of the processes that drive the future occurrence.
As an example: When drug A has a class probability of 50/50, as far as efficacy, that really means that drug A has a 0% chance and a 100% effectiveness, based on unknown factors F1 … Fn. Here, with a large enough population, the limit of effectiveness would be 50%. But that must not be used to claim that the drug has a 50% chance of being effective on person P.
If factors F1 … Fn where known, then we would know the outcome 100% of the time.
When we learn of factor (say) Fm, we lose the collective and have to redefine the problem to include the additional knowledge.
There is nothing subjective about the unknown factors. They exist due to there being a probability. You may have more knowledge of the processes causing probability than me, but that is in an objective sense, not a subjective sense.
We enter the subjective world when we move to case probability. Here we deal with uncertainty. Probabilities are based on subjective intuition. Sure, there are likely class constituents of any case problem, but the problem does not have a true collective (in the class sense) so is different from class. Black swans are everywhere. And we can only bet on outcomes.
——-
As far as sports betting, you have never defended your claim that sports lines predict results. Bookies remain in business because they are good entrepreneurs — they themselves are betting on the actions of those placing the bets, not the event itself.
So bookies employ case probability just as an entrepreneur does when he “predicts” that consumers desire good A.
note: That is why the lines are nearly always the same. Not because the bookies hold the same subjective probabilities, but because the market established an equilibrium, of sorts.
Mr. Fedako,
I think we are getting somewhere, because, unless I am misreading your definition, you essentially agree with my definition of probability, (and not Richard von Mises’s definition), as a measure of man’s subjective uncertainty about the likelihood of occurrence of some event. You explicitly take my position later on when you say that there would be NO uncertainty at all involved in a situation where man knew “Fn.” This is precisely the point I try to make in my paper: probability is an attempt to measure man’s uncertainty about the world.
As for chopping up probability into classes (i.e., “analytic,” “class,” and “case”), I think that this is rather beside the point of my paper, which only dealt with trying to establish that the definition of probability is subjective. However, I would have to say that I do not agree with this awkward and artificial division of probability into these classes. In the first place, it is simply not true that the mathematical methods of probability can only be utilized in cases where one has a “collective.” As I’ve stated before, all that is required to be able to utilize the mathematical methods is that one has a number between 0 and 1. How that number was generated is completely irrelevant– it could have been generated by the classical method, relative frequency method, or whatever method, and one can still utilize the mathematical methods. If, for example, one generates the number 1/6 (as the likelihood of throwing a 3 with a die) utilizing the classical method, one can utilize the mathematical apparatus of probability on this number. So, too, can one apply the mathematical apparatus on a number generated by other methods, like the methods of the bookie. To claim that the mathematical methods only can be applied to problems involving a collective is simply not true.
As for your claim (and David Howden’s claim) that the numbers generated by bookies are not probabilities simply because the bookie is an entrepreneur, I have a difficult time even understanding how this could be an objection to my definition of probability. What difference does it make that a bookie is an entrepreneur? Insurance companies are also entrepreneurial firms and they generate numbers about the likelihood of occurrence of certain events, yet you and he do not condemn their numbers as “not probabilities” simply because they are involved in entrepreneurial activity. Indeed, to attack the numbers generated by the bookie as “not probabilities” simply because he is an entrepreneur seems like a rather bizzarre form of the ad hominem!
What matters is not whether the person generating a probability is an “entrepreneur” or a “mathematician,” but how accurate the numbers are at predicting uncertain future outcomes. And, I would be shocked if you or David Howden would really claim that the numbers generated by bookies are not good predictors of the outcomes of future (and singular!) sporting events. Take a look at the odds for the Super Bowl that will come out this week, and tell me with a straight face that they are “meaningless” or “absurd.”
Cheers,
Mark Crovelli
Mr. Crovelli:
You seem to be missing my point.
I did not state that probability is “a measure of a man’s subjective uncertainty about the likelihood of occurrence of some event.” Under case probability, I agree with you. But not under class probability.
In my previous post I stated that uncertainty in class probability is the result of a lack of objective knowledge. Factors F1 … Fn are objective. You may know some factor (Fm) that I do not know. But that is not subjective uncertainty. Once I learn about Fm, my probabilities will change to match yours — under class probability, that is.
“However, I would have to say that I do not agree with this awkward and artificial division of probability into these classes.” Of course you do not agree. That is the reason for this comment string.
If I were to make the statement that one cannot play a violin with a sledgehammer, I do not mean that it is impossible to take a sledgehammer to a violin and call it music. I simply mean that the sledgehammer is not the appropriate tool to use. So, yes, mathematical methods can be applied to case probability — nothing can stop someone from doing so. However, that does not mean that the end product is the mathematical equivalent of chamber music.
Your claim that I employed an ad hominem fallacy has certainly expanded that fallacy’s definition. I’d delve into this deeper, but I suspect that you threw that out as a red herring.
I ask one more time (in vain?) for your proof that sports lines are predictive of the winner.
Are sports lines meaningless? Of course not. Are they probabilities? No. Once again: Sports lines are an attempt to establish an equilibrium position between dollars bet on both sides of the event. They are not probabilities of who will win the event.
Mr. Fedako,
I’m afraid that this string is going to go nowhere if you insist upon using the terminology of Ludwig von Mises and Richard von Mises without first establishing that their categories are legitimate. I have said that all probability is subjective, in the sense that all probability measures man’s subjective uncertainty about the world. You disagree with me, and side with Ludwig von Mises and Richard von Mises.
It’s fine to disagree with me, but it is not acceptable for you to keep referring to “case” probability and “class” probability without first establishing that these classes are defensible. As I have stated with regard to David Howden’s arguments, it is baldly question begging to refer to these classes as “proof” that I am mistaken, without first giving me a legitimate reason why I must accept them. The question at hand is whether my definition of probability or the brothers von Mises’s definition is correct. To refer to the brothers’ definition in the way you have been doing is to assume the very thing you are attempting to prove. So, I implore you to either cease referring to these categories, or else give me a reason why I must accept them.
As to your use of the words “objective” and “subjective” in this post, I have to say that you are misunderstanding my argument if you think that I am claiming that the factors involved in any given event are not “objective.” Indeed, my entire paper revolves around the claim that NOTHING in the world occurs randomly. The claim that probability is subjective means merely that man is not in a position to know all of the various factors involved in causing an event. If he were in a position to know all of them, however, he would have perfect foreknowledge of the event’s outcome. Man uses probability as a means of measuring his subjective uncertainty about the outcome.
As to my comment about the ad hominem, it was meant as a joke, but I really do not understand why it is relevant at all that a bookie is an entrepreneur. Who cares that a bookie is an entrepreneur? Insurance companies are entrepreneurial firms, too. So what? All that matters for our purposes is whether the numbers the generate are accurate predictors of future outcomes.
Having said this, I have to push you on your claim that the numbers generated by bookies indicate nothing more than an “equilibrium” between sides of a bet. Are you honestly saying that that is ALL they are? When you read that the line in the next game is, say, San Antonio by 3 points, all you think to yourself is: “that’s the equilibrium position”? Does it surprise you that the line is remarkably accurate, then?
Moreover, even if you do not consider the line to be anything more than the “equilibrium position,” is it not obvious that you need to provide an argument as to why they are not probabilities? For, if you do not provide any argument, you will be begging the question, yet again.
Cheers,
Mark Crovelli
P.S. let me reiterate that I am enjoying our exchange quite a bit, even though I can be rather direct in my replies.
Mr. Fedako,
Allow me to add one final and direct question:
Why are the odds established by bookies not probabilities?
Please answer this question without referring to how bookies calculate their odds, and for what purpose they calculate them. Those aspects are completely irrelevant for this question.
Cheers,
Mark Crovelli
Mr. Crovelli:
Let’s rewind a bit.
Please define objective and subjective. Then we can move forward.
Thanks.
Note: re ” … even though I can be rather direct in my replies.” As someone from Pittsburgh, I appreciate directness. That said, if you were truly direct, we might have settled this by now
Mr. Fedako,
I use the term “subjective” in my papers to refers to nothing more than the idea that uncertainty lies in man’s own head and not “out there” in the world. In other words, since everything in the world happens for a reason (i.e., has a cause), the reason man is uncertain about the events that occur in the world lies in his own mental limitations. Probability is thus a numerical measure of man’s subjective uncertainty about the world.
I do not use the term “objective” in my papers, but it should be obvious that my argument implies that if every event has a cause, then those causes are “objective,” in the sense that they are not objective facts about the world in which man lives. The cause(s) of any event or phenomenon are objectively determined by the nature of the world in which man lives.
Does this clarify anything?
Cheers,
Mark Crovelli
The second to the last sentence should read “..then those causes are ‘objective,’ in the sense that they are objective facts about the world in which man lives.”
Cheers,
Mark Crovelli
Mr. Crovelli:
Let’s assume that event E1 is caused by A with 100% certainty. When we make that claim, it is with the understanding that A is made up of factors F1 … Fn. We know all the factors of A either explicitly or through a proxy. Note that we can never be certain of any given factor since our knowledge is limited. It may be that what we refer to as factor Fm is really a proxy for some other factor (say Fq ) that correlates 100% with Fm (note that there are variations of proxies and true factors, so it is not always a one-to-one correlation between proxy and true factor). This we call objective — objective since the concatenation of factors leads to E1 in a time, place and individual invariant manner.
Now let’s assume that, for whatever reason, we do not know factor Fn. Because of this lack of specific knowledge, we correctly predict E1 only (say) 50% of the time (based on a high frequency of trials that leads to a probability limit of 50%). We will define A’ as factors F1 … Fm. Now A’ is objective since it predicts E1 with a 50% effectiveness in a time, place and individual invariant manner. The probability of E1 is not simply a product derived in my head alone, nor is it based on anything that is subjective on my part. Other analysts will arrive at the exact same probability given F1 … Fm.
Your subjectivity arises when you look at case probability. Here you do not have a probability limit. So you begin to make subjective predictions (prediction in your head that may indeed appear valid given your small sample size). You have now entered the subjective realm.
Mr. Fedako,
I’m afraid you are clouding the issue badly here. In the first place, there is no need whatsoever to couch this debate in quasi-mathematical jargon. Everything that we have been discussing can be described, (and described more clearly and usefully, in fact), using ordinary English.
If I translate this jargon into ordinary English, here’s what I come up with. In the first paragraph, it appears that you are claiming that in situations in which we know everything about the causes of some event, we know with perfect certainty what the outcome will be. This is precisely the point that I make in my paper, and I claim that in these situations we are not dealing with probability at all.
In the second paragraph, it appears that you are claiming that in situations where we do not know everything about the causes of some event, then probability enters the scene. Again, this is exactly the point I make in my paper.
You then appear to be arguing that there is only one method for generating a numerical probability in these situations; namely, the relative frequency method. It should be clear that this is not necessarily true, because there are other methods for generating numerical probabilities– like the classical method. And the other methods may or may not generate probabilities that are the same as the relative frequency method.
In other words, you are assuming all along that there is only one method (i.e., the relative frequency method) for generating numerical probabilities. But, this is precisely the question we have been debating! You are begging the question, yet again.
So, too, are you begging the question when you drag Ludwig von Mises’s “case probability” into the mix without first demonstrating that this category is defensible or even relevant to the definition of probability.
Let’s get back on topic. Recall that we are discussing the definition of probability. I have defined probability as a measure of man’s subjective uncertainty about the causal factors at work in the world. You disagree. So, let’s hear your ARGUMENT (in English) as to why probability MUST be defined as a frequency.
In your next post, it would help our debate if you can just state your argument in one or two sentences for the need to define probability as a frequency.
Cheers,
Mark Crovelli
Mr. Crovelli,
Perhaps I should play the devil’s advocate regarding some axioms stated in one of your previous comments.
“Indeed, my entire paper revolves around the claim that NOTHING in the world occurs randomly. The claim that probability is subjective means merely that man is not in a position to know all of the various factors involved in causing an event.”
How do we know that everything in the universe is NOT random? Even if it is true that nothing IS random, there is no means of testing the axiom in the first sentence, especially if the second axiom is true.
If the leg you are standing your theory upon is an axiom that is currently unprovable with our current knowledge, then how is what you are theorizing logically superior to anyone else’s argument?
Also, is this whole argument just splitting hairs? It appears to me that whether or not what you or Mr. Fedako say is true, the resulting data that might be gleaned from this subset(?) of probability would still be mathematically inconsistent, thus limiting it’s uses (which has previously been illustrated with mention of “black swans”). This is not to say the data is useless, but merely currently beyond our ability to model or fully comprehend (which, alas, may be an irresolvable condition).
Hopefully I’ve confused the issue just a bit more.
Or am I just a red herring too? Hohoho…
-Andy
Mr. Baugh,
Could you clarify what you mean by “random?” Can you even imagine a situation in which something would occur in the world without having any prior cause whatsoever? For the axiomatic status of the principle of causality, see, for example, Mises, Human Action, and Hans Hoppe Economic Science and the Austrian Method.
Cheers,
Mark Crovelli
Mr. Crovelli:
Oh, no. You’ve devolved into using capitalization as a form of argumentation. Is font size next?
You appeal to directness and succinctness while you repeatedly skirt questions around what appear to be false claims on your part – claims central to your argument.
You have never satisfied my request for proof of your assertion that sports lines predict outcomes accurately (and you would also have to define accurate while you are at it). Why has this simple request gone wanting?
Please note that using the hippie response of a question for a question is not a valid argument. So your “What do you call it?” response is not a valid defense of your claim.
And you have never framed what exactly bookies do. A cursory review of the bookie process contradicts your claim. Have you performed such a review?
To your implicit claim that I have not stated my argument in English (strange claim, indeed – though I am from Pittsburgh), please review this complete discussion thread. I have repeatedly stated my definition of probability. That you do not agree is the reason for our continued discussion.
Switching the focus from my specific question to back to the more-general discussion is a logical technique that makes me believe you recognize your arguments are deficient. I assume that you are not able to adaquately define subjective v. objective. And that is the reason for your redirection – a logical sleight of hand.
So let’s get some clarity here:
1. Prove that sports lines accurately (and define accurately) predict outcomes.
2. Define exactly what a sports line is (by first reviewing what bookies do).
3. Define subjective and objective. Falling back on your own (dare I say subjective) definition of subjective is not proper English, so to speak. It is merely question begging on your part.
My focus on sports lines should not be shaken off as pointless. It is central to both your understanding on probabilities and your argument.
Regarding: “You then appear to be arguing that there is only one method for generating a numerical probability in these situations; namely, the relative frequency method.”
I have never made such a claim. Nor would I ever argue that such a claim is true. You are free to assign a numerical value to anything – I clearly stated that above. But that does not mean that I must assign the same significance to your subjective probability of (say) a football games as I assign to mortality tables.
If I use your loose definition of subjectivity (where you conflate subjectivity and probability), then you are correct at a very high level. I make a further claim that this general understanding of probability can be made more granular and more exact – here you and I disagree.
You are wrong, but that does not make you a bad guy
Mr. Fedako,
I’m afraid that at some point you are going to have to give me an argument of some sort that probability must be defined as a frequency. As I have already given my argument in my paper, you must give me some sort of argument in response, or else we are completely wasting our time.
Will you please give me some argument– any argument– as to why probability must be defined as a frequency?
Cheers,
Mark Crovelli
I make this request, to remind you, as you have defended the definition of probability advanced by the brothers von Mises
Mr. Crovelli:
You made your argument and Howden refuted it. Seem we have come full circle.
But we have not wasted our time since it’s now obvious that your claims relative to bookies and sports lines are empty. Kinda shoots a big hole in your original argument.
We’ll just leave this thread at that.
note: When you keep asking for an argument as to why probability must be frequency based, you are asking me to frame an argument that I never made.
Mr. Fedako,
It’s clear that you have not read my papers at this point, if you honestly think that sports lines are the nucleus of my argument. Sports lines are completely irrelevant to my argument. Again, to state my argument yet again in the hope that you will read it this time: since everything that happens in the world has a cause, the reason man is uncertain about those causes lies in his own subjective ignorance. Probability is thus a numerical measure of man’s subjective beliefs about the causal factors at work in the world.
So, your obsessive focus on sports lines is completely missing the point. Not only that, but you keep asking me to do something that’s virtually impossible: to “prove” that sports lines are accurate. How exactly would one go about doing that? Which line? The point, for my argument, is simply that it is possible to create probabilities for singular events. If you are convinced, for whatever reason, that the line on the Super Bowl is just some random number that has no predictive value whatsoever, then perhaps we can talk about Fed Fund Futures. Would you also say that Fed Fund Futures have no predictive value for knowing when the Fed will hike rates?
My argument says that probability is a measure of man’s subjective beliefs about the causal factors at work in the world. There is thus no problem under this definition for people to disagree about certain methods for generating probabilities. They are subjective, after all. So, don’t start strutting about as though you have struck a blow against my argument just because you think sports lines are useless predictors, when my definition of probability allows for such disagreement!
It is also clear that you have not read David Howden’s paper either. How else could you make the mistake of claiming that David Howden’s argument was right, and also claim that you don’t believe probability must be defined as a frequency. Let me clue you in: David Howden defends Richard von Mises’s relative frequency definition. So, since you keep saying David Howden was right, you are ipso facto defending the relative frequency definition.
If you are not defending David Howden & Richard von Mises’s definition of probability, then what definition are you defending? This is what I keep asking you, and you refuse to give me any argument at all. IF YOU DISAGREE WITH ME AND DAVID HOWDEN AND RICHARD VON MISES, THEN PLEASE TELL ME WHAT YOUR ARGUMENT IS.
Another obvious clue that you have not read David Howden’s paper is you claim that he “refuted” my argument. If you had read his paper, or especially my reply to his paper, you would know that his paper contains no arguments–zero, nada. Not only did he provide no arguments against my own argument, but he offered no arguments against anything. His paper offers only a trivial restatement of Richard and Ludwig von Mises’s claims.
I encourage you to read both of my papers and David Howden’s paper, and then get back to me.
Cheers,
Mark Crovelli
Mr. Crovelli:
Oh, no. Not more capitalization.
What is central to your argument is that you make assertions that you do not prove (and now you say you cannot prove). So why would I accept anything you argue and defend with equal veracity?
And your claim that I have not read the papers is hollow. How would you know what I have read or not read? Despite your lack of knowledge, are you able to predict my actions with objective certainty. Hmmm.
We all agree that the general definition of probable is the lack of knowledge of future events. Are you claiming that RvM and LvM have some other definition of that word?
Your error occurs when you conflate probable in the general sense with probability in the technical sense. And you abuse the definition of probability by equating that which is objective and with that which is subjective.
By doing so, you argue that your subjective statement about a sporting event carries the same quality of information as mortality tables. I disagree – which is something that you will have to live with.
In addition, you state nonsense such as it is valid to claim that the sum of probabilities of an event can exceed 1. To you this also carries information of high quality — it’s predictive. You can make such a claim since, for you, words themselves are themselves subjective (I’m sensing a little too much Derrida here).
I’ll restate what I said at the top: I do not see David Howden as failing to vindicate Richard von Mises. So I give my nod to Howden and Mises.
Note: I love this tidbit: “Another obvious clue that you have not read David Howden’s paper is you (sic) claim that he ‘refuted’ my argument.”
From that I gather Howden also never read his own paper – he obviously claims to have refuted your argument too.
Until you give me your definition of probability, and an argument to back it up, we have nothing more to discuss.
Cheers,
Mark Crovelli
Mr Crovelli:
Interesting defense. Your argument is true because … well, because want me to supply (again) my definition of probability.
Hmmm. What logical fallacy are you now guilty of?
Mr. Fedako,
Actually, my argument was defended and explained in…my papers! Where have you stated and defended your definition of probability? Up to this point, you have yet to even state it!
I think at this point that it is useless to discuss this any further, because you are completely misunderstanding the argument in my papers. This would not be a serious problem for our discussion, except for your arrogant refusal to even consider my argument on its own terms.
Here’s an example of what I mean. I have stated to you that my argument is about the definition of probability. My argument is that probability is a measure of man’s subjective beliefs about the causal factors at work in the world. As such, this definition allows for putting numerical probabilities on singular events. This was denied to be possible by the brothers von Mises.
Apparently, you side with the brothers von Mises in claiming that putting a numerical probability on a singular event is absurd. Your defense of this claim, to this point, consists of nothing more than repeating over and over again that sports lines are not probabilities. (You are free to believe this, of course, but the rest of the world, when they hear that Denver is favored by 3 points over Dallas, would surely laugh at this suggestion).
But, only those who were grossly ignorant of the methods of probability could possibly assume that the methods of the sports bookie are the ONLY methods available for assigning a numerical probability to a singular event. For example, as I have stated over and over again, but you apparently do not understand, a probability could be assigned to a singular event using the classical method; i.e., by assuming that all outcomes have an equal likelihood of occurrence. Or, we could survey a group of experts, or we could build a model to bring in more variables that we thought were relevant to the event’s outcome, etc.
This is not to say that all methods are equally useful for all applications. Some are probably better for calculating probabilities when we lack repetitions of the event, and others are probably better when we have multiple repetitions. None of this is relevant in the slightest to the question my paper addresses, however. All I was concerned with was the DEFINITION of probability, and that is all you, too, should be concerned with.
Your focus on the sports bookie is thus completely misguided for the task of defining probability. And yet, I see no more criticism of my argument than simply berating the poor sports bookie.
If you truly wanted to disprove my argument, you would have to show that the definition of probability does not depend upon the nature of the world in the manner that I have argued. You would have to demonstrate that ONLY the relative frequency method can produce probabilities that would be useful for predicting the outcome of uncertain events. This means that you would have to claim that ALL other methods for generating probabilities (e.g., the classical method) are absurd and meaningless.
In conclusion, I think this discussion is and will continue to be completely pointless as long as you are unwilling to approach and discuss my argument on its own terms. And, so long as you are unwilling to do this, I am overjoyed to see you place yourself in the intellectual company of David Howden. The spirit and nature of his “arguments” are perfectly suited to your own.
Cheers,
Mark Crovelli
Mr. Crovelli:
I was serious when I stated that you are wrong, but that does not (necessarily) make you a bad guy.
It seems you truly expect everyone to agree with all of your arguments. And those who dare to disagree are idiots (I suggest that you get over both beliefs).
Do you really believe that your arguments so intelligent and cogent that you easily refute all others?
You have twisted this whole discussion from the focus on you (it’s your argument we are discussing) to the focus on me. This isn’t about me, it’s about you and your argument — you wrote the paper, remember?
The best I can gather from this last comment is I need to agree with you so I may earn your respect. Either I accept your argument or I am in the heap pile with RvM, LvM, Hoppe, Howden, and all the other broken toys.
“Your defense of this claim, to this point, consists of nothing more than repeating over and over again that sports lines are not probabilities.”
You are the one who needs to defend the claims you made in your papers. Had you performed a simple Google search, you would know that you are incorrect. Of course, not performing that search allows you the out of plausible deniability.
“(You are free to believe this, of course, but the rest of the world, when they hear that Denver is favored by 3 points over Dallas, would surely laugh at this suggestion).”
In the pursuit of truth, do we ever make such unfounded, absolute statements? And since when does the opinion of “the rest of the world” really matter?
If you reread (read?) Human Action, you might note this: This man believed that he risked very little when laying such a wager. The relation 3:1 is the outcome of the interplay of two factors: the opinion that Roosevelt will be elected and the man’s propensity for betting. (emphasis mine).
So it is not just me against the world.
The list of village idiots includes (besides me, the least of the idiots) RvM, LvM, Hoppe, Howden, etc. So keep up the good work. And never, never rest — please. We are all lost without your sledgehammer-edged guidance.
Mr. Fedako,
Once again, you have proven the points I made in my previous post. You are absolutely incapable or unwilling to consider my argument on its own terms. You do not even make an attempt to understand what I keep saying about bookies; namely, that the way they calculate their odds is completely IRRELEVANT to my argument.
Let me repeat that, in the hope that you will finally read and understand it: BOOKIES’ ODDS ARE IRRELEVANT TO MY ARGUMENT!
Perhaps I should explain to you what I mean when I say that you beg the question, as well. What I mean by this is that you assume the very thing you are trying to prove, such as when you reference Ludwig von Mises’s undefended statement about betting odds as the only proof that they are not probabilities. This is what we mean when we say that a statement is question begging, especially in the light of my long explanation (see above) for the reasons why bookies’ odds do not sum to one.
As for your claim that you are part of a larger group that defends the relative frequency definition, two points should be made. The first thing that should be said at this point is: “we’ll see who sides with whom in this debate!” Since I published these papers less than a year ago, we do not yet know what position Professors Hoppe and Hulsmann will take on this. All we have so far is David Howden’s feeble attempt at refuting my argument. You seem to think that all Austrians will reflexively side with Richard von Mises. But, what makes you so confident that they will do this?
I recall that virtually all Austro-libertarians sided with Murray Rothbard in saying that patents and copyrights were morally defensible institutions until Stephan Kinsella changed everyone’s way of thinking about them. So, we’ll have to wait and see who sides with whom with regard to the definition of probability.
Secondly, there is a huge question mark that you refuse to clear up about whether you actually side with Richard von Mises et al about the definition of probability. You refuse to explicitly state the definition you are defending, and you have made the following claim as well:
“When you keep asking for an argument as to why probability must be frequency based, you are asking me to frame an argument that I never made.”
So, at this point you cannot don the mantle of the frequentists and claim that I am an outsider and heretic, for you, too, are apparently a non-frequentist like me!
If you should decide that you are willing to consider my argument for what I say it is, rather than what you assume it is, then I remain at your service to explain and defend it. But, I have no inclination to further “debate” with a man who still refuses to even state the definition of probability that he is supposedly defending. What kind of “debate” would that be?
Cheers,
Mark Crovelli
Mark (let’s drop the pretence):
Once again …
You made claims that you cannot prove true. Yet that is OK with you. And now you switch to stating that your original claim regarding sports lines was “irrelevant.”
I harp on this because it is a window into how you present your arguments. And I’m not liking what I see.
“You seem to think that all Austrians will reflexively side with Richard von Mises.”
Have I made that claim?
It’s like you have some persecution complex — Mark against the world. I do not understand your unwillingness to let this all go. Is my agreement with you some sort of tipping point? Really?
But how can that be? I took your comments to mean that I am the fool (and remember that it is me against the world).
So why the need to pound away with your repetitive and unconvincing arguments, all in an attempt to convince the fool?
Your argument is wrong. Howden won in my eyes. So get over it.
All that said, I am petty enough to continue to reply to comments since, in my opinion, internets debates are won by the last comment — something you also seem to agree with
Mr. Fedako,
Have you actually read David Howden’s paper? Are you aware of the weakness of his “argument” that you are claiming “won” the debate? I only ask you this, because anyone reading this who has also read Howden’s paper is going to find it pretty silly that you keep claiming he “won.” It makes me laugh out loud every time you say it.
As for you denial that you have claimed that the big-named Austrians are on your side, let me remind you that you wrote this:
“The list of village idiots includes (besides me, the least of the idiots) RvM, LvM, Hoppe, Howden, etc.”
If you are going to continue to reply to these posts, then why don’t you go ahead and explicitly state the definition of probability that you are defending. The debate can continue as soon as you do this, and I am willing to continue the debate in good-faith as soon as you state it. If you are unwilling to do this, then, really, why do you continue to post here? For my part, I am defending my arguments against those, like yourself, who do not understand it. I will respond to all posts here. But, you, on the other hand, have nothing at stake. So, if you will not even state the definition of probability you are supposedly defending, then why don’t you get out of here and do something useful with yourself?
I eagerly await hearing what your definition of probability is.
Cheers,
Mark Crovelli
h, yes, the Crovellian logical fallacy: An invalid argument is considered to be true until a valid argument is substituted in its place. Example: Someone argues that probability is subjective to the individual. Someone else finds flaws in the argument. The arguer then states that since the refuter has not proposed a counter argument, the original argument is apodictically true, regardless of its flawed logic. This is similar to the demanding negative proof fallacy.
When you make a proposition, you need to defend it. So when I question your claim as to how bookies establish sports lines, you must defend it. And that defense cannot be built on the fallacy of appeal to ridicule.
“As for you denial that you have claimed that the big-named Austrians are on your side, let me remind you that you wrote this:”
This is your argument. Remember, it’s you against them?
“In my recent article on these pages (Crovelli 2009) I argued that members of the Austrian School of economics have adopted and defended a faulty definition of probability.”
Your words, not mine.
I understand your argument, I just don’t agree with it. I’m not stating that it’s foolish or weak, but it is flawed and invalid. Sorry.
Mr. Fedako,
You will notice that I never claimed that you were “wrong” for not stating the definition you are supposedly defending. On the contrary, I only observed that this is a parody of a “debate” if you won’t even offer a definition of your own.
As for my defense of the methods of the sports bookie, perhaps you have already forgotten that I defended him above. For example, I wrote:
“To reiterate what I’ve already written about odds that do not sum to one, I agree that not all odds are expressed in a manner that pleases traditional probabilists. But, as I have already indicated, the reason why their odds are expressed in that manner is due to the fact that 1) they need to express their probabilities in a manner that is easily understandable by the betting public, and 2) it is completely unnecessary for their purposes to make odds that would make traditional probabilists happy. Quite obviously, their goal is only to make odds for betting– they have no intention whatsoever of applying mathematical methods to their odds, so they don’t care one whit if the numbers sum to one. However, and this is absolutely vital, THERE IS NO REASON WHY BOOKIES COULD NOT EXPRESS THEIR ODDS IN A MANNER THAT WOULD PLEASE TRADITIONAL PROBABILISTS (AS A RATIO THAT COULD BE DIRECTLY TRANSLATED INTO A NUMBER BETWEEN 0 AND 1) IF THEY WANTED TO. Since this is the case, it is another red herring to point to their supposedly lax use of odds as proof that they are not producing probabilities, because it is obvious that they COULD express their odds in a manner that would comport with the purists’ desire.”
You chose not to respond to this defense of bookies’ odds, however, which is rather curious.
Why is it that you are unwilling to state your definition of probability? Anyone reading this thread must be thinking the same thing that I am: Why is Fedako afraid to state his own definition, or come out and explicitly defend Richard von Mises’s definition? If Fedako is so sure Crovelli is wrong, then why does he not come out and defend an alternative definition? Something is fishy about a man who claims to know another man is wrong, but who has nothing to offer in its place.
I still eagerly you stating your own definition, should you manage to muster up the courage to defend one. Or, should you choose to respond to my defense of bookies’ odds, I would respond to that as well.
Cheers,
Mark Crovelli
Mark,
Such nonsense.
When I ask: What is a probability that sums to something greater than one? Your answer is always so very Derrida-esque.
As far as your supposed defense of your bookie statements … you are suffering from the fallacy of moving the goal posts (also known as the Not a true Scotsman fallacy. You subtly switch from is to could. As I have said repeatedly, bookies can do anything. The question is what do they do.
Your supposed refutation of Howden included statements around how bookies create sports lines. Those statement were not true. Either you admit that you did not perform research, but instead relied on your subjective view, or you defend those statements with facts. That you skirt this continually is telling.
Once again (and I am getting very repetitive), this is about your argument — something you cannot defend without resorting to the Crovellian fallacy.
Mr. Fedako,
Ha! you are quite clever, this is indeed a superb bon mot!
Your confusion in this “debate” apparently knows no bounds. You are apparently unaware that the debate at hand is partially about whether it is POSSIBLE to assign numerical probabilities to singular events (hence the title of my original paper). Thus, I am not switching the focus of the debate by pointing out that it is indeed possible to assign odds that probability textbooks would condone to singular sporting events. That is part of what the debate involves, after all! Nice try, though.
You admit something interesting here, though. you state that “I have said repeatedly, bookies can do anything.” Does this “anything” mean that you admit that they COULD INDEED frame their odds in the manner that probability textbooks prescribe (i.e., as a ration that is directly translatable into a numerical probability)? If so, then you have admitted what the brothers von Mises denied; namely, that it is possible to assign numerical probabilities to singular events.
My refutation of Howden’s “argument,” (again, we have to use the term loosely when we talk of his paper), had nothing to do with how bookies calculate their odds. I claimed that he was begging the question, as you would know if you had read my paper. Here’s what I wrote:
“Setting aside the fact that this is not how bookies manage a sportsbook, (and
setting aside the fact that Mr. Howden is here admitting that odds-makers can
indeed accurately predict who will win a fight!), it should be obvious that it is
question begging to use claims such as this as evidence that probability must
be defined as a frequency. Again, the question thus begged would be: well,
what is the definition of probability in the first place? To assume from the
outset that the methods of odds-makers utilizing non-frequentist methods are
not “exercise(s) in probability,” is to assume the very thing one is attempting
to prove!”
What do the methods of the bookie have to do with my argument here? Please enlighten me.
In case you were wondering, I am still waiting for you to state the definition you are defending. Are you a frequentist? Are you an a priorist? What on Earth are you?
Cheers,
Mark Crovelli
Mr. Fedako,
Allow me to add some more extremely important observations about your confusion here. In the first place, let me remind you that the question of whether probabilities must sum to one is dependent upon which definition of probability we adopt. You continue to claim that probabilities must sum to one. Is it not obvious that this claim depends upon one’s definition of probability? If the subjective definition is correct, as I contend, then this means that probabilities do not need to sum to one.
You asked me to state what a probability is if it does not sum to one. Well, the short answer is that it is a measure of man’s subjective beliefs about the likelihood of occurrence of some event. This is how I have defined probability.
For you to argue against this claim, you must demonstrate that probability ought not to be defined as I have defined it. If you refer to the fact that some odds do not sum to one as “proof” that my definition is mistaken, you will be begging the question. You will be assuming that they must sum to one without first establishing that the definition of probability requires this. You have not, I will remind you, established that the definition of probability requires that they sum to one.
In fact, you have not even stated what you believe to be the correct definition of probability! This is one important reason why you must state your definition of probability for this “debate” to have any meaning.
Cheers,
Mark Crovelli
Mark,
Can you at least be honest … just once?
In your original article, you wrote:
:As is well known, however, casinos and bookies do nevertheless assign numerical odds to these singular sporting events based upon indirect evidence (e.g., common opponents, injury reports, physical conditioning of the fighters, the fighters’ ages and weights, perceived psychological advantages and disadvantages of each fighter, venue, etc.), and their odds are astoundingly accurate most of the time.
If it is so well known, cite a reference. The one you used would suffice. Oh, and a circular reference back to your original paper would be cute … invalid, but cute, nonetheless.
Isn’t it ironic that you constantly … and I mean constantly … pound away at your “begging the question” claims when I must suffer your use of a myriad of logical fallacies — begging the question included.
Any guess as to the fallacy you use when you make the claim of “as is well known?”.
How about this claim: “…and their odds are astoundingly accurate most of the time.
And what fallacy is used there?
You might want to run your fallacy sniffer on you own papers.
And I never said that you cannot assign whatever and call it a probability. That would be a false claim since you continue to do just that.
So if you want to go around stating that the sum of the probabilities of A or not A is 2.0, have at it. If you consider that bit of nonsense Kirznerian action-knowledge, best of luck. I only hope that your guardians hold back a few bucks for your later years.
You’ll need it.
Mark,
“So if you want to go around stating that the sum of the probabilities of A or not A is 2.0, have at it.”
You can claim the probabilities sum to “dog” and I’ll take no issue. You are free to skip down your yellow brick road. Enjoy!
Mr. Fedako,
What are you asking me to show you, exactly? Are you looking for a sports line that was an unbelievably accurate prediction of a future singular event? Is that what you want?
Well, here’s one for you, then. On Monday morning, the line on the Cleveland/Miami game was Cleveland by 1 1/2 points. The outcome of the game Monday night? Cleveland by one point. What would you call that? I suppose that was…well, you don’t know, except that it was definitely not a probability.
How many times do I have to state this before you listen: my argument is that, because every event has a cause in the world, the reason why man is uncertain about the outcomes of those events lies in his own subjective ignorance. Probability is thus a measure of man’s subjective ignorance about the causes at work in the world. What argument have you put forward to counter this definition? Sports lines are not relevant to this argument in the least, although it is clear that if the definition of probability is subjective, as I claim, then these are indeed probabilities.
I’m not sure what you think you are demonstrating by showing that some odds in the betting world sum to one. So what? Those odds that sum to more than one (as in cases where odds on pairs of teams in, say, the NBA playoffs do not sum to one when combined), any mathematician can instruct you on the method for “normalizing” those odds so that they sum to one. Where’s the problem?
Moreover, I don’t know how many times I can say this without you listening, but whether probabilities must sum to one depends upon the definition of probability we adopt. Is it really not obvious that if the definition of probability is subjective, then this is not required? How many more times do I have to say this?
If you disagree, THEN PLEASE TELL ME WHY THE DEFINITION OF PROBABILITY REQUIRES THAT PROBABILITIES SUM TO ONE.
As for your allegation that I am lying, I will only remark on this once. Gentlemen do not use such language in arguments, and if you call me a liar again, I swear to God that you will wish you had not when you meet me in person, which you certainly will at some point in your life. Do not stoop to such vulgarity.
Cheers,
Mark Crovelli
Mr. Fedako,
I forgot to mention in my previous post that you are completely mistaken about the quote of mine that you cite. You cited this quote:
“As is well known, however, casinos and bookies do nevertheless assign numerical odds to these singular sporting events based upon indirect evidence (e.g., common opponents, injury reports, physical conditioning of the fighters, the fighters’ ages and weights, perceived psychological advantages and disadvantages of each fighter, venue, etc.), and their odds are astoundingly accurate most of the time.”
Are you disputing that bookies assign numerical odds to sporting events? This quote of mine does not say it is common knowledge that bookies assign PROBABILITIES to sporting events; rather, it states that bookies assign NUMERICAL ODDS. This is a matter of common knowledge, as any glance in the local newspaper will show you. Are you disputing that bookies do indeed put numerical odds on sporting events?
Cheers,
Mark Crovelli
Mark,
This is the claim awaiting proof: “and their odds are astoundingly accurate most of the time.”
“Well, here’s one for you, then. On Monday morning, the line on the Cleveland/Miami game was Cleveland by 1 1/2 points. The outcome of the game Monday night? Cleveland by one point. What would you call that? I suppose that was…well, you don’t know, except that it was definitely not a probability.
Are you kidding me? This is your proof? Please.
“Those odds that sum to more than one (as in cases where odds on pairs of teams in, say, the NBA playoffs do not sum to one when combined), any mathematician can instruct you on the method for “normalizing” those odds so that they sum to one.”
Sports lines NEVER sum to one (oops, the capitalization fallacy).
“As for your allegation that I am lying, I will only remark on this once. Gentlemen do not use such language in arguments, and if you call me a liar again, I swear to God that you will wish you had not when you meet me in person, which you certainly will at some point in your life. Do not stoop to such vulgarity.”
A very non-Rothbardian statement. Shame on you.
As I stated above, you made the claim that bookies “odds are astoundingly accurate most of the time.” It is central to this string of comments. In fact it is what lead me to post my initial comment. And it is central to your argument, in my opinion. Yet you refuse to provide proof. Why?
As I wrote before, one citation would suffice.
And don’t throw out the red herring of “it’s not central to my argument.” Just provide the citation. You do have one?
Oh, and threats are not the mark of a gentleman (but you knew that already). Nor do they prove your claim.
Let me see … what fallacy would that be?
Mr. Fedako,
I was not threatening you. You called me a liar just because you disagree with me. In any place in the world, when a man who calls another man a liar just because he disagrees with him, he is looking to start a fight. I was just letting you know that I would be absolutely delighted to oblige you, if that is indeed what you are looking for.
There is now no doubt in my mind that you still have not read my paper. How many times will I have to state my argument before you actually read it? My argument is this: Because everything that occurs in the world has a cause, the reason man is uncertain about those causes lies in man’s own head, not “out there” in the world. Probability is thus a measure of man’s subjective uncertainty about the likelihood of occurrence of some event.
That is my argument. I am the one who made the argument, so I should know.
What the hell do sports lines have to do with this argument?
You are trying desperately to give the impression that you know what you are talking about. You are making an absolute fool of yourself, however, because you are flailing away at what you claim was my argument, but in actuality is just a giant straw man you have constructed. Maybe if I state my argument one more time, you might deign to read it: Because everything that occurs in the world has a cause, the reason man is uncertain about those causes lies in man’s own head, not “out there” in the world. Probability is thus a measure of man’s subjective uncertainty about the likelihood of occurrence of some event.
Having finally read the argument, would you care to retract your absurd claim that sports lines are “central” to the argument, before you completely embarrass yourself?
Cheers,
Mark Crovelli
Mark,
“What the hell do sports lines have to do with this argument?”
You are the one who introduced sports lines as a defense of your argument (my issue all along — read from the top of this string).
You clearly stated it as fact even when you had no proof. Did you just make it up? That is reason enough to disregard your paper.
In the end, I’ll let this tread speak for itself. Your childish, playground behavior appears to be the only defense you have.
The main issue (my reason for the dialogue) is the fact that you made a claim in your paper for which you have no proof. You have not backed away from it nor made correction. You call that honesty. I’ll let the readers judge your intent.
You may be pugnacious (the result of a chip on your shoulder, I assume), but that does not cover your inability to stand by what you claim. Readers of this string will note that as well.
Mr. Fedako,
Let me restate my argument for the hundredth time, and see if it depends upon sports lines.
Everything that happens in the world has a cause. The reason why man is uncertain about those causes lies in man’s own mind, not “out there” in the world. Hence, probability must be defined as a measure of man’s subjective ignorance about the causal factors at work in the world.
You continue to state that sports lines are central to this argument. It boggles my mind to understand why you think this. This argument has absolutely nothing to do with sports lines, and indeed the argument does not even mention sports lines.
You are getting yourself confused because my argument has the obvious implication that, if probability is indeed defined as I have defined it, sports lines are probabilities. And, I do indeed hold that they are probabilities because this follows from my argument.
But, this is an IMPLICATION of my argument, not the argument itself.
The reason why sports lines were introduced in my papers and in this string is that most people I have ever encountered intuitively sense that sports odds are probabilities. My argument merely provides a reason why their intuition is correct.
The question of whether sports lines are probabilities forces us to ask a more fundamental question; namely, what is probability in the first place? My paper attempts to answer that question, and my answer has absolutely nothing to do with sports lines. (I would also insert here that you still have yet to provide your definition of probability, which is a rather obvious indication that you are missing the point of the debate at hand).
So, for you to claim that I “made a claim in your paper for which you have no proof” exposes your gross misunderstanding of the debate. My “proof” is in my argument, and my argument has nothing whatsoever to do with sports lines. They are probabilities, because probability, as I have defined it, is a measure of man’s subjective ignorance about the causal factors that will affect the outcome of the event.
I earnestly hope that you will read this post and finally come to recognize that sports lines being probabilities is not part of the argument itself, but rather an IMPLICATION of the argument.
Cheers,
Mark Crovelli
Mark,
“In this paper, I argue that Richard and Ludwig von Mises were mistaken to claim that numerical probabilities cannot be assigned to singular, non-replicable cases like boxing matches.” (emphasis mine)
Did I miss understand your use of the term argue?
Of course, your use of “cannot” is also incorrect. I sincerely doubt that either RvM or LvM would not agree that you have the ability to do such. They would only argue over the quality of (action) knowledge contained in those statements.
In fact, in Human Action, LvM himself allows for such probabilities, writing, “A statement is probable if our knowledge concerning its content is deficient.”
He simply does not assign value to results of the “calculus of probability” derived from those statements. To him they are metaphors, becoming datum used in entrepreneurial decisions.
And I don’t think a comment like, “It looks like a 50% chance of rain,” would have resulted in a punch in the nose from RvM.
“Are the numerical odds assigned by casinos and bookies to singular boxing matches (and other singular events and phenomena, like the 2008 presidential election) absurd or meaningless, simply because they are not derived from long-run frequencies of ‘collectives’ or ‘classes,’ as the von Mises brothers contend?
This becomes irrelevant since casinos and bookies do not act in your proposed manner — the statement is similar to a vacuous truth.
“Conclusion
We are now in a position to return to the question posed in the introduction; namely, is it meaningless or absurd to calculate numerical probabilities for singular events and phenomena like boxing matches, as the brothers von Mises contend?
In our discussion, we have never encountered this man of yours — the one who calculates probabilities for boxing matches. That alone does not mean that such calculated probabilities would be meaningless. But neither does his absence bolster your argument.
Mr. Fedako,
You are really grasping at straws here.
As I said in my previous post, I do indeed hold that the numbers put on sporting events by bookies, and any other number assigned to any event to signify its likelihood of occurrence is indeed a probability.
What you are missing, though, is WHY I hold these to be probabilities. I hold this position because it is logically implied by my argument. And what is my argument? You should already know, because you cherry-picked a quote from my paper where I outline my argument. Here’s the quote in its entirety:
“In this paper, I argue that Richard and Ludwig von Mises were mistaken to claim that numerical probabilities cannot be assigned to singular,
non-replicable cases like boxing matches. I argue that Richard von Mises developed a demonstrably mistaken definition of probability, and that his
mistaken definition inexorably led both von Mises brothers (and all Austrians who have followed their lead) to unduly proscribe the application of
numerical probability to singular, non-replicable cases. Instead of defining probability in terms of purportedly “objective” long-run relative frequencies
of “collectives” (as did Richard von Mises), I argue that consistent Austrians must define probability subjectively; that is, as a measure of our uncertainty
about the likelihood of occurrence of some event or phenomenon, based upon evidence which need not derive solely from observations of past frequencies of “collectives” or “classes.””
Hence, my argument is that whether or not the numbers bookies assign to sporting events are probabilities depends upon the definition of probability we adopt. I argue that Austrians must define probability subjectively, and this definition implies that the numbers generated by bookies are indeed probabilities.
Is it really not obvious to you that my claim that sports lines are probabilities is a necessary IMPLICATION of my argument, and not the argument itself?
As for your claim that the brothers von Mises and other Austrians do not view the numbers assigned to singular events as absurd and meaningless, I encourage you to read their quotes in my paper, where they explicitly state as much. Richard von Mises made the following claim, for example: “The phrase “probability of death,” when it refers to a single person, has no meaning for us at all.”
Finally, allow me to observe that your last claim here, that “in our discussion, we have never encountered this man of yours — the one who calculates probabilities for boxing matches,” you are begging the question to an absurd degree.
Whether or not the numbers bookies assign to sporting events are indeed probabilities depends upon the definition of probability we adopt. If I am right that probability must be defined subjectively, then the numbers we have been discussing are indeed probabilities, regardless of whether they sum to one, or are stated as odds, etc. Is this really not obvious that you are begging the following question when you deny that we have been discussing probabilities all along: what is the definition of probability in the first place?!
Cheers,
Mark Crovelli
Mark,
Don’t ya think this is getting old?
Bookies do not assign probabilities to sports events. They assign lines in the hope of drawing equal money to both sides of the line (and taking their cut to the bank). Bookies are entrepreneurs looking to set a (for them) market clearing price, so to speak. They are, in essence, betting on the bettors.
Your sports line argument is similar to one stating that prices in the market are probabilities — a product of knowledge whose content is deficient. That you cannot understand this is beyond me. But try anyway. Please.
I agree that your view of sports lines is a necessary implication of your argument. But your argument is false, your premise is an empty set — a vacuous truth. So your conclusions are not necessarily true (logically following from a false proposition) as you so claim.
Please reread (read?) Human Action. LvM discusses case probability as uncertainty (chapter 6). He then simply refers to case probability as uncertainty going forward.
As I said repeatedly, I understand your argument. It really is not that sophisticated. But neither is it correct.
Note: I am still waiting on proof of your statement around the amazing accuracy of sports lines. And once again, your inability to provide proof (or to withdraw it) is quite telling. Don’t you want your readers to see that what you claim as truth is truth?
Mr. Fedako,
Do you really not see that your claim that bookies do not assign probabilities to sporting events is question begging unless you define probability first? In order to say that something is or is not a probability, we have to have a definition first! I am surprised how long it is taking for you to notice this obvious point.
In addition, as I have repeatedly noted, the question of HOW bookies generate lines is completely irrelevant for the task of defining probability. Who cares HOW they generate their odds? All that matters is whether they are indeed probabilities, and in order to be able to say whether or not they are probabilities, you must have a definition first! You still have not even defended a definition of probability, which shows how baldly question begging your claims are that betting lines are not probabilities.
Moreover, you are simply mistaken if you think that bookies just magically generate their lines to equalize betting out of thin air. The initial (or, “opening”) line is generated by handicappers who weigh all of the various factors they think are relevant to come out with the line before any bets are placed– and there are different lines generated by different handicappers. Without an opening line, no bets could be taken, of course. But, again, this is all irrelevant for the task of DEFINING probability in the first place.
You have admitted that my argument does not depend upon sports lines (finally!). But, I doubt that you recognize the importance of this concession, because, if my argument does not depend upon sports lines, you have not provided ANY argument whatsoever to support your claim that my definition is mistaken. All you have done is simply claim, begging the question over and over again, that sports lines are not probabilities. What argument do you have to counter my subjective definition of probability?
Finally, I still don’t know what you mean by “proof” that sports odds are amazingly accurate. I provided a line above that was a shockingly accurate prediction of the outcome of a basketball game. You can open a newspaper and find these amazing predictions every morning, if you like. Or, have a look at the line on this afternoon’s Super Bowl. The line today is Indianapolis by 5 points. Let’s see how accurate this is.
But, again, what difference does this make for our task at hand: DEFINING PROBABILITY?
Cheers,
Mark Crovelli
Mr. Fedako,
Maybe we can get this discussion back on track if you bluntly state your objection to my definition of probability in the following form:
“Probability ought not to be defined subjectively, because…”
Cheers,
Mark Crovelli
Mr. Fedako,
One final note on the topic of sports lines is in order. For the sake of argument, let’s assume that you are right, that sports lines are not particularly accurate predictions about the likelihood of occurrence of sports events, even though I do not share this opinion of their accuracy. What would this prove?
The answer is, of course, that this would prove nothing about the definition of probability. If probability is defined subjectively, then the accuracy of the prediction is completely irrelevant. They would still be defined as probabilities, because they are a measure of certain men’s ignorance about the likelihood of occurrence of some event.
So, even in the case that you are right that sports lines are not particularly accurate predictors, (again, I disagree with this, however), this is completely irrelevant, and would be absolutely no argument against my definition of probability.
So, even in the best case scenario for you, you have provided no argument whatsoever against my definition of probability.
Cheers,
Mark Crovelli
Mark,
You are the quite the sophist (of course, it could be that I am exaggerating your abilities by calling a sophist).
” For the sake of argument, let’s assume that you are right, that sports lines are not particularly accurate predictions about the likelihood of occurrence of sports events, even though I do not share this opinion of their accuracy.”
Beautiful non sequitur. However, I never made any such a claim. So I couldn’t be correct in that statement — no matter what you assume. The statement is inherently false.
Note: I did catch that you now use “opinion” where your paper claims fact. But that still does not get you out of proving your statement or withdrawing it. Or even rewriting your paper from the get-go.