Right, and finally we looked at a couple of results that make this possible. Typically,

we have, we have, we would need utility matrices for all possible combinations of values. We

would have to assign a utility, which is again going to explode in our face. So what we would

hope for is utility functions that we can either fully determine via few values or that

we can approximate by few values. And it turns out that indeed most utility functions have

a form like this, where we have single functions, one place functions that, remember we have

these diseases where we have these dampening factors. So this is the kind of sane situation

here. We have influences or weights, factors typically, that give us the influence of a

single variable. And then we have some kind of formula that is relatively simple, for

instance, that combines them. And there is a couple of theorems that essentially says

under certain conditions, which is preferential independentness, then we get indeed such functions

where F is essentially just addition. And you can strengthen those things by looking

at not preferential independence, but also by utility independence, which is what we

really want. So if you don't just have an ordinal utility function, but a full utility

function, then we can still get something where we have a simple combination. And there

we have what was called a multiplicative utility function. It's not quite as nice as for the

preferences, but of course a utility function rather than a preference function has to have

more information. And we have the same quasi-linear things where we have a sum over a variety

of products. Much better than the general case in practice, but exponential as well

eventually, unless we have lots of zero factors, which may very well be.