Description

Decision theory presents a rigorous approach for making real world decisions.

The development of this approach raises many important theoretical and practical questions. The aim of this project is to choose interesting areas to explore in further developing the theory.

Here is a (very much non-exhaustive) list of example topics that might be explored.

(i) How should we represent and solve decision problems? Decision trees are a simple and powerful tool for this purpose. However, when the problem is even moderately complex (in terms of numbers of decisions and states of information) then they quickly become very unwieldy to draw and to solve. There are various alternative graphical representatiosn of decisions which have been developed, such as influence diagrams, which are much simpler to draw, and show much more clearly the underlying structure of the decision problem. How these representations work and how they may be used to solve decision problems is an important area of study.

(ii) Sequential decision making. Decision theory shows that we should solve decisions by backwards induction (i.e. starting at the end of the tree and working backwards). When there are many alternatives (for example, our sampling procedures are sequential with many possible outcomes) then this backward induction quickly becomes very complicated to evaluate. This leads us to consider alternative approximate solutions. These might be as simple as one step look ahead rules or they might be more elaborate approximations based on simulating the full solution of the decision problem. These approximations can be investigated at a practical and theoretical level.

(iii) Real world decisions rely on many attributes, which, for example, may be combined in multi-attribute utility functions. These may be further elaborated in utility hierarchies. For example, our decision might have two attributes, namely costs and benefits. Each of these attributes itself might itself have attributes, for example benefits might combine social benefits and individual benefits, each of which might have its own collection of attributes, and so forth. How we build such structures and use them to provide practical decision support is an important practical problem, including, for example, such questions as how we might deal with disagreements between stakeholders about the relative weightings of the various attributes in the hierarchy.

(iv) There is a whole area of study related to the important question as to how people really do make decisions and how much this is actually related to the methods of formal decision theory.

Prerequisites

Resources

Google will lead you to much discussion of these topics and also suggest further interesting avenues to explore. Please contact me if you have particular enquiries about the project.