Does risk aversion cause diminishing marginal utility, or vice versa?
I think I've found an answer to my question, in this excerpt from Nobel laureate John C. Harsanyi's 1994 paper "Normative validity and meaning of von neumann-morgenstern utilities", presented at the Ninth International Congress of Logic, Methodology and Philosophy of Science.  Harsanyi starts by proving the same lemma that Alecos proved in his answer, namely that if $u$ is a vNM utility function of an individual, then $u(10) - u(5) &lt; u(5) - u(0)$ if and only if they would prefer a guaranteed 5 dollars compared to a 50% of 10 dollars and a 50% chance of 0 dollars.  In the comments section I said that was insufficient to demonstrate that the vNM utility function represented intensity of preferences, because what if the individual's actual pleasure and pain was accurately described by some other utility function $v$, which is a monotonic transformation but not an affine transformation of $u$?  In that case couldn't $v$ fail to satisfy the expected value property, and couldn't $v(10) - v(5) = v(5) - v(0)$?

Harsanyi has a clever argument dealing with this issue. Let $L_1$ be the lottery where you get 5 dollars guaranteed, let $L_2$ be the lottery where you have a 50% chance of 10 dollars and a 50% chance of 0 dollars, and let $L_3$ be the lottery where you have a 50% chance of 10 dollars and a 50% chance of 5 dollars.  Then obviously the person prefers $L_3$ to both $L_1$ and $L_2$.  And Harsanyi argues that $L_3$ is preferred to $L_1$ less strongly than $L_3$ is preferred to $L_2$ if and only if $v(10) - v(5) &lt; v(5) - v(0)$.  That's because in the choice between, $L_3$ vs $L_1$, 50% of the time they get 5 dollars, and 50% of the time they have to make a choice between 10 and 5.  Similarly in the choice between $L_3$ and $L_2$, 50% of the time they get 10 dollars, and 50% of the time they have to make a choice between 5 and 0.  

Now here comes the master stroke: $L_1$ is preferred to $L_2$ if and only if $L_3$ is preferred to $L_1$ less strongly than $L_3$ is preferred to $L_2$.  Therefore, $L_1$ is preferred to $L_2$ if and only if $v(10)-v(5) &lt; v(5) -v(0)$.  And thus we reach the grand conclusion that $u(10) - u(5) &lt; u(5) - u(0)$ if and only if $v(10)-v(5) &lt; v(5) -v(0)$.

Thus Harasanyi reaches the conclusion that the vNM utility function represents preferences intensities.  So the answer to my question seems to be that diminishing marginal utility in the vNM utility function reflects genuine diminishing marginal utility when it comes to intensity of preferences, and thus (assuming the vNM axioms are true) diminishing marginal utility really is the cause of risk aversion.

By the way, on a side note I wonder whether we could identify the set of all functions $v$ that satisfy the constraint that $u(x) - u(y) &lt; u(z) - u(w)$ if and only if $v(x)-v(y) &lt; v(z) -v(w)$ (and similarly for greater than and equal to).  (EDIT: I asked about this on Mathematics.SE here.)