Choice Theory: A Very Short Introduction
Format: PDF / Kindle (mobi) / ePub
We make choices all the time--about how to spend our money, about how to spend our time, about what to do with our lives. And we are also constantly judging the decisions other people make as rational or irrational. But what kind of criteria are we applying when we say that a choice is rational? What guides our own choices, especially in cases where we don't have complete information about the outcomes? What strategies should be applied in making decisions which affect a lot of people, as in the case of government policy?
This book explores what it means to be rational in all these contexts. It introduces ideas from economics, philosophy, and other areas, showing how the theory applies to decisions in everyday life, and to particular situations such as gambling and the allocation of resources.
chose A today’ and ‘A today and A tomorrow if I chose B today’; that is, you choose A today and A tomorrow regardless of what I have chosen. Thus nothing essential changes. Now suppose that we each have to choose on a hundred successive days. You may then feel that it might be worth your while choosing B on some of the early days in the expectation that this would build up some trust between us and that consequently I would start choosing B, which would be to our mutual advantage. However,
group chooses X alone from X and U because of unanimity; it chooses U alone from U and V because the set is effective over this pair; and it chooses V alone from V and Y because of unanimity. Then it chooses X alone from X and Y because choice is rational. Since everyone in the set prefers X to Y and everyone else prefers Y to X this means that the set is effective over X and Y. As X and Y are arbitrary the set is effective over all pairs. Second, I shall define a set of people contained in
indifferent between the two. These preferences are your empathetic preferences. They are not the same as your personal preferences, which simply compare Air travel with Boat travel, and so forth. Although you do not know which role you will occupy you do know what the possibilities are. Then, being rational in the sense discussed in Chapter 3, you assign probabilities to roles and cardinal utilities, representing your empathetic preferences, to item–role pairs. For example, you might assign
or more: ties are allowed. Recall that to say that two items tie, that is, that you choose both jointly, is just to say that you are equally content with either. Reasonable choices Consider the following example of apparently odd choices. Hors d’œuvres example Your menu consists of Asparagus, Beetroot, and Chicory: you choose Asparagus. On your waiter, perhaps having misheard you, telling you that Chicory is off you choose Beetroot. Your choices can be represented schematically,
which is what is known as transitive. An ‘at least as good as’ relation is transitive if, when X is at least as good as Y, and Y is at least as good as Z, then X is at least as good as Z. For example, the ‘at least as tall as’ relation among people is transitive: if I am at least as tall as you, and you are at least as tall as Montmorency, then I am at least as tall as Montmorency. The preference relation underlying the Meat example is transitive, and thus a preference ordering. Even though