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so I say ‘decision theory’ but sometimes people talk about ‘rational choice theory’. Same thing.

simple question: How do rational agents decide which of several available actions to perform ?

what i want to do in this section is just to introduce you to the kinds of representation which are used But it's important first of all to talk a little bit about the motivation the people who study decision theory ...

This isn’t quite right: they are writing about game theory of course (but the idea is fine)

so here we have a super lofty aim and of course one of our questions will be to what extent that is possible and what assumptions they're relying on

Maybe not everyone who uses their mathematical principles shares the founders’ ambitions. Wombles abound.

so as i said we're going to start with trying to understand how actions are represented from the point of view of somebody who wants to go on and construct decision theory. what we're doing now is just a simple background what does the representation look like. let's be sure we understand it

Expected utilities can be derived from desirabilities and probabilities. One procedure for choosing an action is to compute expected utilities (in the way illustrated) and then perform the action with the highest expected utility.

I can illustrate it using gambling

First illustration is a simple bet.

Which gamble would you prefer? If you are like me, you are interested in the expected gain ...

Second illustration is about which of two bets you should select if you can only choose one.

OK so that was an illustration with money.

I used money to simplify the idea of expected utility.

But what we are really interested in is preferences.

This is because your preferences do not necessarily vary linearly with monetary amounts. Once you have the first £100, the next £100 might not make nearly as much difference to you and so it might be rational to care a lot less about whether you have it.

Make sure you understand the terminology and can relate it to the scenario.

Be sure to use the terminology consistently, and with precision, in your writing.

It is important to understand that we haven’t done anything more than introduce a way of representing things.

We have not yet considered a theory. But understanding the representation is an essential first step towards von N \& Mo’s objective.

Why is what we have done so far not sufficient?

(Because we have not anchored preference or subjective probability to subjects.)

(We have not said anything at all about what it is for someone to have a particular preference, nor what it is for them to assign a particular subjective probability to a given condition.)