Talk:Von Neumann–Morgenstern utility theorem

Added experimental evidence

Linked to the Allais Paradox as an example of vNM-inconsistent behavior observed experimentally. — Preceding unsigned comment added by 209.6.36.153 (talk) 04:40, 8 October 2013 (UTC)

Rothbard stuff

There is a section about Murray Rothbard's work at the end of this otherwise fine article. A few points:

Importance

I do not think that the thoughts of this marginal figure about Von Neumann justify this section. There is a lot of discussion about the work of VNM in the literature (e.g. the book "Risky Curves: On the Empirical Failure of Expected Utility") and so this use of space is arbitrary at best. At most it justifies a comment and link onto a page with more relevance to Rothbard's book, along with comments on other relevant criticism and discussion. As a minor point it's not clear why the arguments of this section are blamed on Economists of the Austrian school and not Rothbard in particular.

Incorrect arguments

Moreover, several of the arguments presented are clearly wrong. It says Numerical probability can be assigned only to situations where there is a class of entities, such that nothing is known about the members except they are members of this class, and where successive trials reveal an asymptotic tendency toward a stable proportion, or frequency of occurrence, of a certain event in that class. Yet, in human action, there are no classes of homogeneous members. Each event is a unique event and is different from other unique events. This definition of the applicability of probability theory rules out its application to coin tossing and dice rolling and is therefore obviously absurd. The argument has nothing to do with any of the usual expressions of the dominant views of probability, as can easily be verified on wikipedia.

After that it says The neo-cardinalists admit that their theory is not even applicable to gambling if the individual has either a like or a dislike for gambling itself. Since the fact that a man gambles demonstrates that he likes to gamble, it is clear that the Neumann-Morgenstern utility doctrine fails even in this tailor-made case. But looking further up the same article we can see this is wrong. All that VNM admit is that their theory is not applicable if the gambler has a specific utility of gambling, that is, likes or dislikes to gamble for its own sake over and above the utility of what could be gained or lost. The fact that a person gambles does not demonstrate that they have a specific utility of gambling, and so it does not demonstrate any kind of contradiction in VNM's work, as is claimed here. Also the term "neo-cardinalists" is jargon.

All in all, the four arguments presented in this section seem weak and muddled and not up to standard for wikipedia, and in any case it seems arbitrary to have 10 lines about Rothbard's objections when the volume of discussion is so large and this person's views don't represent a very large school of thought. EveningTide (talk) 16:35, 16 April 2016 (UTC)

Axiom 4 (Independence)

I believe the axiom should only hold for $p\in (0,1]$ because if p=0 then we have $N\prec N$ which is absurd. BPets (talk) 12:37, 3 December 2016 (UTC)

As I write this, the preference relation is assumed to be weak: $M\preceq N$, so even p=0 works and we don't get $N\prec N$.

--editeur24 (talk) 22:59, 23 November 2020 (UTC)