The story I'm trying to tell is that utilities are something that kind of falls from heaven

in this picture.

And the question is how do we get utilities?

And there is a nice utility theory that tells us instead of utilities, which is not something

you can actually ask from people, what you can ask is rational preferences.

And if you want to have a utility function, you not only have to assess preferences of

two prizes or outcomes or results, whether you prefer A to B, but you also need to, well

no, if you only assess those things here for real prizes, then what you're going to get

is an ordinal value function or utility function, which is basically you have long strings of

inequalities and equality.

You can always, given a bunch of those assessed values, if they're consistent, we've looked

at that with these axioms, if you have preferences that obey these axioms, then you can always

kind of order that into a total order, total non-straight partial order.

I think that's the right one.

If you want to have a utility function, which is something from states to real numbers,

you need a little bit more.

You also need to assess basically something that is more continuous, and you have to throw

in these lotteries into the mix.