We understand the utility now. We can measure it. We can even compute with it in small,

for small probabilities. But actually the world isn't like that. The world isn't that you have

utility over a single variable. What you have is something where you have lots of influences.

That's something we call multi-attributed utility. Innovation network, where you can make decisions.

You typically have a whole set of random variables that characterize the state of the world.

Right now we know the utility of one of them. How good would it be if I were rich? But then

there's also how good would it be if I'm healthy? How good would it be if I'm pretty? All those

kind of things. Multiple influences on the overall desirability or utility of a state.

This is where the story gets a little bit less nice, as always. AI is kind of where you always

tell the first story and it's mathematically very beautiful. Then you start enjoying life and AI.

Then comes the real world and then things get difficult. For instance, if you want to assess

an airport site, then of course you have a couple of random variables that vary on where

you put the airport. You have air traffic itself, which is noisy. Of course there's the certain

risk that a plane misses the runway and if that happens in the city, then that's not very good.

There is basically the chance of deaths involved. We have also, when we build an airport,

there are the construction costs. Where we construct results in different costs. Of course,

the problem of litigation, which means people see that their house is near the airport,

so they'll sue you for putting the airport somewhere else and that actually adds to the

cost and the time and whatever. Say this is our world model. Say the things we really care about

in our decisions is these three variables. Those people really care about and you can find utilities

of that. This lends itself very nice to, say, micromorts. This actually lends itself to qualis

because you know how long you're going to live and on average 85 minus X or something like this.

Of course the quality goes down if it's noisy. Of course, cost is interesting in itself.

Those might vary widely. You have one location where nobody lives near. The cost would be okay,

but the airliners have to either cross directly over a city. Well, I guess that makes noise as

well. Or there's a directly high mountain so that you kind of have to dip in like that with

an airplane which drives us up the problem of deaths. How do you compare that to other

distributions of those things? You can imagine that this is difficult. You can't ask people,

would you prefer two micromorts to seven years at noise and two millions? Is that really better

than 50 micromorts and one million? We don't really know. Even with that wonderful tool of

micromorts or something like this. Here's where things get a little bit messy. We have to,

kind of, instead of knowing the exact function of three attributes, we have to kind of waffle

again and try to identify things that make life easier. We can kind of have two ideas,

which are much the same ideas we always have. We can kind of go for patterns. When our utilities

actually have certain patterns where we need fewer values. The other idea is whether we can

find some independences of preferences. Do what we did with Bayesian networks, basically,

with preferences again. Because we need to somehow get at the utility function. Otherwise,

we're not going to make good decisions here. Because, remember, a utility estimation is the

expected utility of some action given some evidence is the sum over the results given

action and evidence times the utility of what? The state. Here, in every single sum and, we

have utilities. Here, this is something where conditional independences in our Bayesian

networks are going to help. Because we can kind of drop stuff here. Now, wouldn't it be nice if

we kind of, this is a long utility, if we could drop certain things there as well. Or have a

pattern form of this. Preferably, that kind of mixes well here. So, we've been starting up on

multi-attribute utility and found that this is a difficult problem. So, now we want to do something

about it. So, basically, our situation is the following. If you just think about going to a

two-attribute utility. And remember that for utilities, we're really only interested in that

something is bigger than something else. Possibly much bigger and how much bigger, but mostly what

the qualitative thing is. And then you can see, if you want to make decisions, then say you have

these regions where you're quite safe to make decisions. In A, I have a situation here, then