Economics Questions

Re: Is there anything wrong with Hoppe's views on probability theory?

Jeremiah Dyke — Mon, 10 May 2010 01:46:19 GMT

http://libertarianpapers.org/articles/2009/lp-1-44.pdf

I never got around to the paper but the 81 comments http://libertarianpapers.org/2009/44-crovelli-david-howden-probability/ are valuable.

Re: Is there anything wrong with Hoppe's views on probability theory?

abskebabs — Mon, 10 May 2010 01:23:04 GMT

But there is a crude circularity in the frequency definition of probability, as well. In fact, it is the frequency interpretation of probability that cannot escape Hume's induction problem.

Indeed that is the usual criticism of the frequentist position. The way I see it though, is that if we take on board such a critique to its logical conclusion then we must toss aside virtually almost all scientific knowledge, since our tests have only shown them to match the tendencies we expect so far. The main argument of frequentism is that there must at least be a tendency towards a convergent limit towards a well defined distribution as one expands one's set.

For example, if we know that there are only two possible outcomes of something, we can assign a numerical interpretation to the degree of belief we have of those events occurring... namely, if we're completely ignorant of any reason why it should turn out one way or another, we can say that our degree of belief in each outcome is 50%, or, for N events our degree of belief in any particular one is 1/N.

This could be done and is done, for instance when assuming a priori equally likely outcomes for microstates in statistical mechanics in the absence of degeneracy. These assumptions must be shown to be valid independently however, in the case of statistical mechanics this is found with the theory producing correct macroscopic predictions as a result of incorporating these assumptions.

Aside of this a degree of belief is just that; a degree of belief.

Re: Is there anything wrong with Hoppe's views on probability theory?

Clayton — Sun, 09 May 2010 20:06:13 GMT

I just glanced over Mises's section on probability in Human Action again. I agree with his general criticism of the whiz-bang nature of much of probability theory and the mysticism surrounding it. However, there are a couple assertions he makes that I think are not correct. For example, if we know that there are only two possible outcomes of something, we can assign a numerical interpretation to the degree of belief we have of those events occurring... namely, if we're completely ignorant of any reason why it should turn out one way or another, we can say that our degree of belief in each outcome is 50%, or, for N events our degree of belief in any particular one is 1/N.

Mises says,

The definition of the essence of class probability as given above is the only logically satisfactory one. It avoids the crude circularity implied in all definitions referring to the equiprobability of possible events.

But there is a crude circularity in the frequency definition of probability, as well. In fact, it is the frequency interpretation of probability that cannot escape Hume's induction problem. If the frequency interpretation is the only correct definition of "class probability", as Mises calls it, then induction and prediction is not possible.

In stating that we know nothing about actual singular events except that they are elements of a class the behavior of which is fully known, this vicious circle is disposed of. Moreover, it is superfluous to add a further condition called the absence of any regularity in the sequence of the singular events.

But - and this is something Mises could not have known at the time he wrote - we can define what we mean by an absence of regularity in a sequence of singular events. That is, we can give an abstract definition of the absence of regularity.

Clayton -

Re: Is there anything wrong with Hoppe's views on probability theory?

Kenneth — Sun, 09 May 2010 18:27:40 GMT

I actually have a vague idea on both positions on probability. Can you give me a brief summary of the two?

Re: Is there anything wrong with Hoppe's views on probability theory?

abskebabs — Sun, 09 May 2010 15:02:43 GMT

I think I broadly sympathise with his position, which is essentially Mises'. Many Bayesians don't like it, notably Bryan Caplan, who correctly notes that if such a view of probabillity was correctly understood and adopted, it would clearly rubbish the way in which neoclassicals currently "deal" with uncertainty in the form of providing the actors in their models with complete probability distributions regarding future events. Personally, I find this pretty hilarious, though their defense is usually something along the lines that knowledge and probability is necessarily subjective anyway...

Also, Ludwig Van den Hawe thinks he is incorrect conflating Richard Von Mises' and Ludwig Von Mises' views on probabillity, an interesting point considering Mises never even cites his own brother.

Re: Is there anything wrong with Hoppe's views on probability theory?

Kenneth — Sun, 09 May 2010 14:39:21 GMT

anybody

Is there anything wrong with Hoppe's views on probability theory?

Kenneth — Sun, 09 May 2010 11:24:34 GMT

I'd be interested to know