The article attempts to show that you don't need the independence axiom to justify using expected utility. So I replaced the independence axiom with another axiom that basically says that very thin distribution is pretty much the same as a guaranteed return.

Then I showed that if you had a lot of "reasonable" lotteries and put them together, you should behave approximately according to expected utility.

There's a lot of maths in it because the result is novel, and therefore has to be firmly justified. I hope to explore non-independent lotteries in future posts, so the foundations need to be solid.