We've been looking at decision theory, actually very simple decision theory.

One of the key ingredients in that, let me get back to, where's my utility base now?

No agent here.

We have, we do decision theory, which is essentially taking a word model and then selecting

the best action.

And to just find out what the best actions are, we looked at utilities.

Utilities as functions that basically take a state, give you its desirability and you

want to maximize the expected utility of anything you do.

So the first question we talked about was, where do utilities come from?

The answer is, we can assess preferences of users or we can just judge behavior of intelligent

agents and derive preferences from that, just by looking at their actions.

And if you not only have access to preferences between material prizes, but actually between

prizes and lotteries and lotteries and lotteries, then you get a utility function.

And that is almost true.

The preferences have to obey the following set of rules.

One of the things I would like to, which is why I'm briefly talking about this, is my

direction of preferences, the arrows, is the opposite of Russell and Norwick.

So don't get confused.

I will at some point change the order in my slides.

Probably I'll do that after the exam so that you don't get confused and have a consistent

way.

So if you're reading Russell and Norwick, which you should do, be careful that everything

is turned around, which is fine as long as you're aware what you're reading.

The main result here is Ramsey's theorem that basically says, if I have preferences between

prizes and lotteries and lotteries and lotteries, then I can derive a utility function up to

linear transformations.

And then when I have this, I can basically look at trying to optimize expected utility.

And that's what we've been doing.

We've been talking briefly about how to measure preferences in practice.

And we've looked at things like micromorts, which is kind of the lottery between everything

staying as it is and instant death.

And you can attach a price to a micromort.

And it's surprisingly low.

So basically relatively stable.

One micromort kind of equals about 25 euros.

And we've discussed this relation between utilities and money.

And we've found that there is a nonlinear correlation, which is actually reasonable

to expect.

Because utility is more related to quality of life.

And quality of life is related to what you can do.

What you can do is not actually linearly correlated to how much money you have.

So you have a relatively good linear phase in there for small values.

And you can also, I mean, one of these nonlinearities you can see is also even if the price of a

micromort is 25 euros, most people will not actually agree to shoot themselves for 25

million.

Which would be the linear.

Which would be the, if there were a linear correlation, that would actually be what you

would expect.