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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Mark,
To help you out … and just for fun and games …
Assume that you are a bookie and you knew the final score of the Super Bowl two weeks before kickoff (the fix was in). What line would you have set given the lines being set by the market (via your competitors)?
Notes:
You are a bookie, not a bettor. So you cannot turn around and bet the money in your holding on the game through another bookie — that would be a dead give-away that you knew of some fix.
Also keep in mind that when you set a line different from your competitors, you will reactuate the equilibration process — which has nothing to do with the probabilities aroung the game itself.
Mr. Fedako,
Well, what do you have to say for your definition of probability? Are you going to try to weasel out of this discussion, now that you see that you have no argument whatsoever to counter my definition of probability, or are you going to defend a definition?
Are you going to stand up and state the reason why you disagree with my definition of probability, or are you going to just call me names?
I eagerly await hearing your argument as to why my definition of probability was mistaken.
Cheers,
Mark Crovelli
Mark,
Beautiful. This must the logical fallacy of The Crovellian Argument by Excision.
Seriously, if you are going to trim the comments, at least include the ones that show your inability to defend your argument regarding sports lines — an argument that is central to your paper.
Note: The purge of 62 comments just ended this discussion.
Gents–I’ve only been tangentially following this, but what’s this about a purge of comments? As far as I know only I can delete comments and I have not.
Mark,
Oops. I missed the little link to older posts. My error. See, it’s OK to admit to errors. It’s kind of cathartic, so to speak.
We are really not getting anywhere. You refuse to defend your assertions and argument, yet expect me to instead defend my assertions as if the paper at hand was mine.
Go over to William Brigg’s blog. He is a proponent of predictive statistics. Now, I have to say that I enjoy his articles, but …
Accepting singular probabilities allows him to do all kinds of neat statistical math. As I see it, by assigning probablistic attributes to singular cases, he is making the same error as mainstream economists when they assemble their homo economicus for use in arguments, models, etc.
It all makes for showy math and for some interesting positivistic conclusions (epistemologically false, of course, but interesting and true are different concepts) into the world.
Mr. Fedako,
Let me get this straight. After weeks and weeks of discussion, in which I restated my argument over and over again, you are still claiming that sports lines are “central” to my argument?
All I can do is laugh! You already admitted that sports lines being probabilities is an IMPLICATION of my argument, not the argument itself. So, explain to me how they are “central” to my argument?
Moreover, as I recently noted, if the definition of probability is subjective, as I claim, then the accuracy of sports lines is IRRELEVANT. They are still probabilities because they are measures of man’s subjective ignorance about the likelihood of occurrence of some event.
So far, you have provided no argument to counter my definition except for beating the dead sports lines horse into a bloody pulp. But, since the accuracy of sports lines is irrelevant if probability is defined subjectively, you have provided no argument whatsoever against my definition.
So, I have decisively won this discussion, unless you can provide some legitimate reason why my definition of probability is mistaken. If you resurrect the dead sports lines horse in order to beat it again, you will only prove that I have won this debate conclusively.
Cheers,
Mark Crovelli
Mark,
You have the argument from nonsense down pat.
I have no choice but to laugh when you cannot defend your own arguments.
And somehow that is OK with you. Your paper is a dying horse of an argument and your only counter is those darn capitals once again.
By the way, your quick yet bland response got us all out of sync, so I am appending my 9:44 response below:
Mark,
Oops. I missed the little link to older posts. My error. See, it’s OK to admit to errors. It’s kind of cathartic, so to speak.
We are really not getting anywhere. You refuse to defend your assertions and argument, yet expect me to instead defend my assertions as if the paper at hand was mine.
Go over to William Brigg’s blog. He is a proponent of predictive statistics. Now, I have to say that I enjoy his articles, but …
Accepting singular probabilities allows him to do all kinds of neat statistical math. As I see it, by assigning probablistic attributes to singular cases, he is making the same error as mainstream economists when they assemble their homo economicus for use in arguments, models, etc.
It all makes for showy math and for some interesting positivistic conclusions (epistemologically false, of course, but interesting and true are different concepts) into the world.
.
Mr. Fedako,
I appreciate your tone in most of this post. It would be good if you and I could continue to speak with one another without acrimony. Let’s continue it.
I can understand your concern about opening up the positivist floodgates if we accept a subjective definition of probability. I do not doubt for a moment that some people will view a subjective definition as a license to do whatever they want in the field of measuring uncertainty and elsewhere.
However, we cannot allow concerns such as this to force us to adopt a faulty definition of probability. We must be committed to the truth, even if some people might misuse what we say.
So, I stand with you ready to condemn the use of probability and statistics for positivist purposes, and any other scientistic purpose. But, we ought not to defend a faulty definition, simply because it might be misused.
Turning, then, to my definition of probability, I think we should stop beating around the bush and get to your argument against my definition. I am committed to discussing this with you openly and fairly, but we must first start with your criticism of my argument.
You think my definition is faulty, but I am still unclear why you think this. We have established that my argument does not depend in any way on sports lines. We have established that sports lines being probabilities is an implication of my argument, not the argument itself. We have established that the accuracy of predictions is irrelevant if we adopt a subjective definition.
So, in order to continue, we need to have your objection to my argument clearly and succinctly stated.
I look forward to hearing what your central objection to my definition is, and I really do commit to engage your argument fairly and sincerely.
Cheers,
Mark Crovelli
Mark,
Sorry, I missed this: “We have established that my argument does not depend in any way on sports lines. We have established that sports lines being probabilities is an implication of my argument, not the argument itself. We have established that the accuracy of predictions is irrelevant if we adopt a subjective definition.”
Please walk me through those points. If you are stating that we established them (that you and I agreed to them), you are mistaken.
Also note that I am not defending the frequency theory as a first defense against positivism. Frequency stands alone as truth. But it is the case that folks like Briggs need singular cases to be probalistic in order for their methods to discover truth.
Given that sports lines are not probabilities, provide another example where singular probabilities are “amazingly accurate.” Remember, this is central to your argument — that probabilities of singular events carry the same information as frequency probabilities.
Note: As an aside, you use “singular cases” to mean the same as LvM’s use of case probability. Seems that you might just be in agreement with LvM, but are stuck on terminology.
Mr. Fedako,
I say “we” established these points because you conceded that my argument does not depend upon sports lines, and that sports lines being probabilities is an implication of my argument, not the argument itself. As for the accuracy of sports lines, it should be obvious that if probability is defined subjectively, the accuracy of a probability is completely irrelevant. All that matters for them to qualify as probabilities is that they represent a person’s, or multiple people’s, estimate of how likely they think the event is. This point is obviously implied by the subjective definition of probability.
Since you have conceded that sports lines are NOT central to my argument (see above), I have no idea why you keep claiming that they are central. What makes you say this? Do I really need to state my argument again, and get you to concede this point again, before you give up this absurd claim?
My argument, once again, is that if everything that occurs in the world has a cause, then the reason man is uncertain about those causes lies in man’s own head, not “out there” in the world. This argument has absolutely nothing to do with sports lines. Please stop absurdly claiming that sports lines are even related to this argument.
As for your claim that the frequency theory “stands alone as truth,” what is your argument for this? Previously, you said that you were not necessarily defending the frequency definition, but now you say you are. So be it. But, what is your argument, then, for this definition? As I said, I am willing to look at your argument fairly and without acrimony if you just state it. Just tell me why the frequency theory “stands alone as truth” and we can have a real discussion here.
Finally, you are not understanding my argument if you think my definition of probability is related to L. von Mises’s concept of “case probability.” My argument is that ALL probability is a measure of man’s subjective uncertainty about the world. This is just as true of frequencies as it is for gambling odds.
Cheersm,
Mark Crovelli
Mark,
And here I thought we were moving in a gentlemanly direction. Oh, well …
Please show me where I conceded anything. Not by stating that I did, show me the actual statement of mine which admits concession.
“As for the accuracy of sports lines, it should be obvious that if probability is defined subjectively, the accuracy of a probability is completely irrelevant.”
You claimed that sports lines are “amazingly accurate”. This is your claim … and you argued for it in your paper. DEFEND IT. (Hey, capitalization does feel good.) Don’t dance around it — waltzing by as if it wasn’t there. You made the claim. Defend it or withdraw it.
“My argument, once again, is that if everything that occurs in the world has a cause, then the reason man is uncertain about those causes lies in man’s own head, not “out there” in the world.”
Is this really all that you are arguing? Nothing else? That’s it? So the others claims that you argued are superfluous? Hmmm.
And what makes you think that LvM would disagree with that statement?
Simply rewrite your paper around that argument alone and we are done here.
Regardless, I still love that you made this claim in your paper — a claim made without reference or proof.
“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.” (my emphasis)
Mr. Fedako,
Yes, this is all I am claiming! Probability is subjective.
Basically, your argument boils down to this: you can’t find any faults in my reasoning throughout the paper, except that you disagree that sports odds are accurate. That’s it. And you write these posts as though this, even if it were true, is devastating to my argument. That is the most ridiculous idea I can imagine, because sports lines are irrelevant to my argument. As you conceded, they are an implication of the argument, not the argument itself:
“I agree that your view of sports lines is a necessary implication of your argument.”
Now, you apparently are reneging on this.
I laughed out loud when you wrote this: “Simply rewrite your paper around that argument alone and we are done here,” because it showed you have not read my paper at all. You are a poseur, pretending to have an argument. The argument in the paper has nothing to do with sports lines– it is centered on the fact that the definition of probability depends upon the nature of the world and the nature of human knowledge.
I call on you to provide an argument to the effect that probability must be defined as a frequency. If you do not, then all your blustering about sports lines will be exposed as so much hot air.
GIVE ME YOUR ARGUMENT, or risk being exposed as a poseur.
Cheers,
Mark Crovelli
Mark,
I thought we had moved to a higher plane, a gentlemanly plane. But you now call me a poseur. By doing so, you have to know that I will mention (once again) that sticky issue where you fabricated your claim around “amazingly accurate” sports lines. What is the faux French term for that?
“A statement is probable if our knowledge concerning its content is deficient.” (LvM, Human Action)
If your paper is simply a restatement of a definition that RvM, LvM, et al, (including folks like Keynes, etc.) have accepted as truth (that probability is based on an individual’s lack of certainty ), with your implications (which your paper claims you were arguing) nothing more than meaningless fluff, what was the point of your argument and paper anyway?
Note: You might want to refresh your understanding of an argument. Your paper is structured so that what you now claim to be your sole argument is merely an inference used to prove your real arguments (what you now call implications, which you have now withdrawn as fluff).
As I stated at the top of this too long and too pointless discussion: I do not see David Howden as failing to vindicate Richard von Mises. So I give my nod to Howden and Mises.
Isn’t it ironic that you claim to be arguing against LvM, yet you agreed all along. Hmmm.
Note: By the way, it is a doltish statement that claims I did not read your paper. You might have meant that I did not understand your paper. But with you, who knows.
Mr. Fedako,
Let me get this straight. You are so confused about this topic that you actually think that my definition is merely a restatement of Richard von Mises’s definition AND Keynes definition? Where do you get this stuff? Richard von Mises thought that uncertainty was “out there” in the world. He believed probability was a “physical property” of things. Keynes thought probability was something that could be figured out a priori without even looking at the world. You are off in la-la land if you think the subjective definition is merely a restatement of either of these positions.
How could you possibly say with a straight face that the implications of my argument are trivial, when you have conceded that an implication of my argument is that sports lines and betting odds are indeed probabilities? This, alone, would make my argument non-trivial, but it should also be obvious that many other scales are also probabilities according to this definition. The “terror alert” scale (red, orange, yellow, green), is also a probability, if probability is defined subjectively. The wider implications of this definition are profound indeed.
And you are equally mistaken if you think I have withdrawn anything from my paper. I happen to follow sports lines, and I stand by my statement that they (at least the handicappers my local paper uses) are amazingly accurate. You disagree. So what?
I can’t believe you have the chutzpa to keep writing these posts without giving any argument as to why the frquency definition “is truth.” Why is my definition mistaken? Why must we define probability as a frequency? What kind of a man would continue to post here without ever providing an argument as to why probability must be defined as a frequency?
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
Tell me, in short, why you think Hodwden vindicated Richard von Mises’s position.
Cheers,
Mark Crovelli
Mark,
Once again, this is a too long and much too pointless discussion on your paper, of which we know this:
1. You fabricated your claim around sports lines. That, in itself, is enough to discount your paper as scholarly. Talk about laughable: “I happen to follow sports line …” And this is supposed to be your evidence? This is middle school level scholarship, at best.
2. The rules of scholarship (which obviously do not apply to your paper) require a reference when inserting a quote. So a true scholar would provide a reference when claiming that RvM stated probability is a “physical property” that is “out there.” If you reread (read?) Probability, Statistic and Truth, you would note (as I explained above) that RvM is excluding case probability from his theory of probability (reread [read?] “Limitation of Scope”). He is not excluding it from existence, just from his theory.
3. You claim to be arguing against the Austrian view, yet no Austrian (that you have noted) disagrees with your claim that probability is subjective. So what is your argument with them?
4. Now your implications are back to being arguments. But your sports line claim is a fabrication. So you implications are not simply trivial, they are nonsensical. By the way, do you argue for your “implications” or not? Or is your use of “argue” as slippery as your sports line claims?
5. We have agreed that your definition is not mistaken, but the non sequitur to your implications form a chasm that cannot be crossed with logic and reason. And it is the non sequitur to your implications that is your argument.
Mr. Fedako,
Now you are calling me a liar again? You are showing yourself to be a completely dishonorable person. To call a man a liar just because you disagree with him is one of the most disgusting things I can think of. Even more so because you do it openly without shame.
I have never withdrawn anything that I have written. I said that bookies do indeed put odds on singular sporting events. Is this a “fabrication”? I said that they are shockingly accurate most of the time. Is this a “fabrication,” just because you (inexplicably) disagree? Tell me what is a “fabrication,” you filthy slanderer.
What the hell are you doing mentioning “case probability” with regard to RICHARD von Mises? Are you really so clueless that you can’t even tell the brothers apart? If so, I have been way overestimating you thus far. Richard von Mises claimed, as any good indeterminist must, that probabilities were “physical properties.” Are you disputing this, too? If so, then I have been way, way, way overestimating you. “Physical properties” is his phrase, by the way, not mine.
Now you are claiming that the Austrians were subjectivists? Well, Halleluiah, you have finally squared the circle!!! First you said that the frequentist theory “is truth.” Then you said that Ludwig von Mises’s was right about probability. And now you say that the Austrians were subjectivists. This almost rises to the Marxian level of self-contradiction. I have to say that I have never seen an argument that was more incoherent and circular in my life! So which one REALLY “is truth”; my subjective definition or the frequentist definition?
I can’t believe I have to do this again, but since you have claimed that the frequency definition “is truth,” (although now you claim the Austrians are subjectivists, so I’m not sure which color your chameleon skin will be next time), but I have to keep on asking until you provide an argument:
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
GIVE ME AN ARGUMENT AS TO WHY PROBABILITY MUST BE DEFINED AS A FREQUENCY!
You said that the frequentist theory “is truth,” so let’s hear the argument. (Or, you can finally just admit that YOU HAVE NO ARGUMENT, BECAUSE YOU ARE A complete CHARLETAN).
Mark Crovelli
P.S. In calling me a liar again, does that mean that you do indeed want to fight me when we eventually meet? If so, I’m going to be presenting a paper at the ASC this year, and it would make my weekend to do so. Just say the word, my friend.
P.S. The Richard von Mises quote is this, since you are apparently a stickler for rigerous scholarship (besides you filthy slandering, that is):
“The probability of a 6 is a physical property of a given die and is a property analagous to its mass, specific heat, or electrical resistance. Similarly, for a given pair of dice (including of course the total setup) the probability of a ‘double 6′ is a characteristic property, a physical constant belonging to the experiment as a whole and comparable with all its other physical properties”
P. 6 of the 1981 Dover edition.
Ugh. Argument by capitalization has been replaced with argument by capitalization and repetition.
1. I am asking you to provide proof of your statement regarding the accuracy of bookies (the bookie/sports line issue is my reason for becoming involved in this discussion string in the first place). Repeating your claim is not a defense. Your statement is either fact (which you can back up with references) or it is a fabrication (something you pulled out of thin air). Let me know which it is. (note: If your statement around “amazingly accurate” is an accepted truth [as you imply], you would have multiple references to defend it.) Oh, and argument by threat only weakens your case.
2. You continue to conflate probability as a colloquialism (RvM) or metaphor (LvM) with the RvM theory of probability. Both brothers accept the term probable in other areas. The issue is the information contained in the claim and what fits into a theory of probability (read “Limitation of Scope”). By way of example: When I asked my contractor the likelihood of an issue arising (sending the final bill much higher than his estimate), he initially stated, “It’s not very likely.” Uncertain as to what he meant (unable to fully decode his meaning), I asked what the probability was. He said, “5%.” That I decoded to mean very highly unlikely in my terms: his 5% being nothing more than a metaphor – and he would have agreed with that. By having that discussion, I never refuted my belief in frequency-based probability. And I assume (without any proof) that RvM and LvM engaged in similar discussions (over the weather, etc.).
3. You define subjective probability to mean a lack of certainty regarding the future – a lack of knowledge that is subjective to the individual (which, by the way, is different from Rothbard’s definition of subjective probability that [ironically] is noted in today’s Daily Article – your definition is simply a general definition of the word probable). Are you claiming that RvM believed that, based on the physical properties of a die, the future (defined by the next roll of the die) became certain from his point of view, in time and place?
4. Regarding case probability: I have no reference where RvM used that term. It is simply a term whose meaning can be decoded by both of us – I think (I can’t speak for you). RvM delineates that which is in his theory from that which is not. And he even provides a few examples that sit on the border. The RvM delineation is an overlay on the LvM stratification of probability. His theory is not all-encompassing, which you mistakely believe that it is (again, read “Limitation of Scope).
All that said: I am getting nowhere. You refuse to defend your claim (because you cannot) that started this string. So this post ends my participation in this too long and much too pointless discussion.
Mr. Fedako,
You are absolutely right that you are getting nowhere, because you have never once in this incredibly long thread given any argument whatsoever as to why the frequentist definition of probability “is truth.” Au revoir.
Mark Crovelli