Description

Decision theory tells us that there are two basic components to any decision, namely the uncertainty, quanified as probability, of the possible outcomes and the desirability, quantified as utility, of these outcomes.

In this project, we focus on features relating to utility. The topic is very broad, and there are many different aspects that you might choose to study. Here are some of the features that we have in mind.

(i) We may consider any utility as comprising a collection of attributes (for example, costs and benefits). Each attribute may itself be comprised of attributes (for example, costs may be financial and ethical, benefits may be individual and communal and so forth). Under assumptions of utility indpendence , the collection of attributes can be organised into a utility hierarchy leading to a methodology for the assessment of overall utility for any choice.

(ii) Utility hierarchies require the specification of tradeoffs between the various attributes (i.e. how do we value the relative importance of financial and ethical costs). Often we will not be able to make precise specifications of such tradeoffs (for example, the utility might represent the conflicting judgements of a group of decision makers with different priorities), leading to the specification of imprecise utility functions, and the development of the theory for appropriate decision making in such cases.

(iii) Preferences may be time dependent (for example, how do we evaluate receiving a reward now against receiving the same reward in a year's time). This leads to the theory of time discounted utility.

(iv) In some problems, we may not be sure about our utility for a reward until we receive that reward (for example, we may not know how much we like a particular type of cheese until we receive a portion of that cheese for tasting). This leads to the theory of adaptive utility, in which we learn about our utility over time.

(v) Any of these features may be combined and placed in a statistical context, in which, for example, our decision might be to choose an experiment with benefits derived from increased knowledge and costs derived from the expense and effort of the experiment.

For any of these areas, you might study and report on existing theory, develop new special cases and/or apply the theory to examples real or constructed.

Prerequisites

2H Statistical Concepts is useful if you want to develop a statistical application of these methods.

Resources

Here's a poster which gives a very compact overview of utility hierarchies with imprecise tradeoffs.

Utility hierarchies and imprecise utilities

Wikipedia gives a simple starting point for investigations into time discounted utility at this link: Time discounted utility

An introduction and overview for adaptive utility is given in "Bayesian analysis and uncertainty in economic theory" (1987) R. M. Cyert and M. H. deGroot, Chapman and Hall