Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T11:18:46.984Z Has data issue: false hasContentIssue false

8 - Choice Under Uncertainty

Published online by Cambridge University Press:  05 January 2016

Christopher P. Chambers
Affiliation:
University of California, San Diego
Federico Echenique
Affiliation:
California Institute of Technology
Get access

Summary

In this chapter we turn to models of choice under uncertainty. We consider an agent who makes choices without fully knowing the consequences of those choices, and focus on models in which uncertainty can be quantified and formulated probabilistically. The most important such model is, of course, expected utility.

OBJECTIVE PROBABILITY

There are times when probabilities can be thought to be objective and known, or observable. This is the case, for example, when outcomes are randomized according to some known physical device—such as a game in a casino, or a randomization device used by an experimenter in the laboratory.

We consider two basic environments. In one the primitive objects of choice are lotteries. In the other, the objects of choice are state-contingent consumption.

Notation

Let X be a finite set. We denote by Δ(X) = ﹛pRX : p ≥ 0; ∑x∈X p(x) =1﹜ the set of all probability distributions over X.

Choice over lotteries

Given is a finite set X of possible prizes. Δ(X) is the set of all lotteries over X. We imagine an agent who chooses a lottery. The agent understands that there is uncertainty over the realization of the lottery: over which prize the lottery will result in. But the probabilities specified in the lottery are accurate (or at least useful) representations of that uncertainty.

We investigate a very basic result on revealed preference in this environment.

An expected utility preference is a binary relation for which there exists u : XR such that for all p,q ∈ Δ(X),

The classical axiomatization of expected utility preferences relies on the independence axiom of decision theory; namely, that for all p,q, r ∈ Δ(X) and all.

Most experimental studies refuting the expected utility model are direct refutations of the independence axiom. The best-known such refutation is through a thought experiment, known as the Allais paradox. Instead of setting up a thought experiment, we are going to assume that we are given data on choices among pairs of lotteries.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2016

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×