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I was looking for a proof of the von Neumann Morgenstern Theorem (That the axioms lead to a unique utility function which is linear in probability). The best thing I could find was a sketch of the proof on wikipedia: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem Which I didn't like from a formal perspective (finite amount of outcomes with mixes in probability, and only an intuition why the linearity makes sense and doesn't violate the axioms, instead of actually showing that there is only one possible function apart from a linear transformation and that this function is linear in probability).

So I started to try and proof it myself and I think I managed to show this theorem for an arbitrary large set of prospects, the uniqueness and linearity in probability.

So now I don't want this work to get lost and I wonder where it makes most sense to post it. The obvious idea would be to edit the wiki entry, but I would like someone to proof read, which is probably more likely on a site like this instead of wikipedia. And I don't know what wiki policies are on full proofs - I never really engaged in wikipedia as an editor.

Would posting this here be an abuse of the site? Or generally opinions/advice on what I should do.

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    $\begingroup$ Posting it on wikipedia would be rejected, because it would be considered "original work" (which is explicitly not allowed in wikipedia). If you think you have a new proof in some aspect, you can certainly post it here and ask for doublechecking. $\endgroup$ – Alecos Papadopoulos Nov 20 '17 at 13:48
  • $\begingroup$ @Felix Out of curiosity -- which version of the continuity axiom are you assuming when the set of prizes is not finite? $\endgroup$ – Theoretical Economist Jan 22 '18 at 19:40
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The proof of the expected utility theorem is a standard component in many leading graduate micro textbooks (e.g. MWG and Jehle & Reny). What's the point of reinventing the wheel here?

Of course, if you have doubts about the correctness of your proof, you are welcome to post it here and ask for doublechecking. But I don't see the point of posting the theorem and answering it with your own proof.

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  • $\begingroup$ The only point would be, to make it available on the web. Because I really couldn't find this online. When looking for books on it there were virtually no search results on that theorem (I guess because search engines don't have access to the books you mentioned), I ended up reading the original, where it is hidden in the appendix. But vOv I had fun using the books of the library for the first time, kind of a ... "oh, that is how they had to do things back then" :-p $\endgroup$ – Felix B. Nov 19 '17 at 21:43
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    $\begingroup$ @FelixB.: A simple Google search shows at least two sources that contain the proof: (1) Section 2.4 in Levin's graduate micro notes and (2) Section A.4.1 of this set of notes on portfolio theory $\endgroup$ – Herr K. Nov 19 '17 at 21:51
  • $\begingroup$ hm okay I agree - I guess I missed those... hm I think I have seen the first one and discarded it as examples again. Well at least the proof seems to be drowned in them. So skimming it: it assumes the set of lotteries is finite, which is unnecessary as far as I know. (From reading the original proof and my own attempts) $\endgroup$ – Felix B. Nov 19 '17 at 22:11

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