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alyssavance comments on Extreme risks: when not to use expected utility - Less Wrong
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If you hold lottery A once, and it has utility B, that does not imply that if you hold lottery A X times, it must have a total utility of X times B. In most cases, if you want to perform X lotteries such that every lottery has the same utility, you will have to perform X different lotteries, because each lottery changes the initial conditions for the subsequent lottery. Eg., if I randomly give some person a million dollar's worth of stuff, this probably has some utility Q. However, if I hold the lottery a second time, it no longer has utility Q; it now has utility Q - epsilon, because there's slightly more stuff in the world, so adding a fixed amount of stuff matters less. If I want another lottery with utility Q, I must give away slightly more stuff the second time, and even more stuff the third time, and so on and so forth.
This sounds like equivocation; yes, the amount of money or stuff to be equally desirable may change over time, but that's precisely why we try to talk of utils. If there are X lotteries delivering Y utils, why is the total value not X*Y?
If you define your utility function such that each lottery has identical utility, then sure. However, your utility function also includes preferences based on fairness. If you think that a one-billionth chance of doing lottery A a billion times is better than doing lottery A once on grounds of fairness, then your utility function must assign a different utility to lottery #658,168,192 than lottery #1. You cannot simultaneously say that the two are equivalent in terms of utility and that one is preferable to the other on grounds of X; that is like trying to make A = 3 and A = 4 at the same time.