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6: Integrating Beliefs and Preferences for Decision Analysis

J.B. Hardaker CAB International PDF


Integrating Beliefs and

Preferences for Decision Analysis

Decision Trees Revisited

In Chapter 2 we introduced the notion of a decision tree to represent a risky decision. Recall that decision problems are shown with two different kinds of forks, one kind representing decisions and the other representing sources of uncertainty. We represented decision forks, where a choice must be made, by a small square at the node, and we represented event forks, the branches of which represent alternative events or states, by a small circle at the node. We showed how a decision tree can be resolved working from right to left, replacing event forks by their certainty equivalents (CEs) and selecting the optimal branch at each decision fork.

We now return to the simple example relating to insurance against losses from foot-and-mouth disease (FMD) to show how probabilities and utilities are integrated into the analysis. For convenience, the original decision tree developed in Chapter 2 (Fig. 2.2) is repeated here as Fig. 6.1. Note that the uncertainty about the future incidence of the disease is represented in the tree by the event fork with branches for ‘No outbreak’ and ‘Outbreak’. To measure the uncertainty here we need to ask the farmer for subjective probabilities for these two events. Suppose that, as explained in Chapter 3, the farmer assigns a probability of 0.94 to there being no outbreak and a complementary probability of 0.06 to an outbreak occurring. Similarly, the farmer is uncertain about what policy for control of the disease might be implemented if an outbreak occurs, as shown by the event forks further to the right in Fig. 6.1. Again, the farmer is able to assign some subjective values to these conditional probabilities of 0.5 and 0.5

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9: Risk and Mathematical Programming Models

J.B. Hardaker CAB International PDF


Risk and Mathematical

Programming Models

A Brief Introduction to Mathematical Programming

Mathematical programming (MP) is the term used to describe a family of optimization methods that may be familiar to many readers. Therefore, only a brief introduction to these useful methods is provided here and readers needing to learn more by way of background are referred to one of the many introductory texts on the topic, such as Williams (2013).

Almost all optimization problems, including planning problems accounting for risk and uncertainty, can be expressed as the optimization of some objective function subject to a set of constraints. MP has been developed just for such problems. Unfortunately, however, many real-world planning problems are complex, especially when accounting for risk and uncertainty. The result is that, while most risk-planning problems can be formulated as MP models, at least conceptually, not all can be reliably solved using available algorithms. Sometimes it may not be possible to be sure that a generated solution is the true optimum. The models for some problems may grow so large that the computing task may be beyond the capacity of the computer or software being used.

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1: Introduction to Risk in Agriculture

J.B. Hardaker CAB International PDF


Introduction to Risk in


Examples of Risky Decisions in Agriculture, and their Implications

The development of agriculture in early times was partly a response to the riskiness of relying on hunting and gathering for food. Since then, farmers and others have tried to find ways to make farming itself less risky by achieving better control over the production processes. As in other areas of human concern, risk remains a seemingly inevitable feature of agriculture, as the examples below illustrate.

Example of institutional risk

A dairy farmer finds that the profitability of his herd is constrained by his milk quota. He now has the opportunity to buy additional quota, using a bank loan to finance the purchase. The farmer, however, has serious doubts about the profitability of this investment because he believes that milk quotas will be removed at some time in the future. Cancellation of quota would make the purchased quota valueless from that point in time. He also thinks it is likely that milk prices will drop significantly when the quotas go.

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2: Decision Analysis: Outline and Basic Assumptions

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Decision Analysis: Outline and Basic Assumptions


Basic Concepts

As explained in Chapter 1, decision analysis is the name given to the family of methods used to r­ ationalize and assist choice in an uncertain world. In this chapter we focus on the concepts and methods of decision analysis. Figure 2.1 provides an outline of the typical steps in decision analysis of a risky choice. These stages are discussed in turn below.

Establish the context

This first step is concerned with setting the scene and identifying the parameters within which risky choice is to be analysed. Particularly in a large organization, it may be important to take note of the level in the organizational structure at which the choice will be made. For example, different sorts of decisions may be made at different levels, perhaps with important strategic issues decided upon at board level, with key tactical decisions made by senior management and with a range of more routine choices made at the operational level. Identifying the level may lead to identifying the decision maker (DM) or makers – a critical need for proper conduct of the steps to follow. Similarly, it will be important to identify the stakeholders – those who will be affected by the outcomes of the decision. For a family farm, the principal stakeholders are farm family members who typically will be concerned with their standard of living and the continued survival of the family business.

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5: Attitudes to Risky Consequences

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Attitudes to Risky



In Chapter 2 we have shown how a simple risky decision problem, such as that faced by the dairy farmer thinking about insuring against foot-and-mouth disease (FMD), can be solved. The key step was to transform the risky consequences of an event fork into the DM’s certainty equivalents (CEs). However, the assessment of CEs can become very tedious if there are many such risky event forks. Moreover, the introspective capacity needed to decide on CEs rises with the number of branches emerging from the fork.

As explained in Chapter 2, the central notion in decision analysis is to break this assessment of consequences into separate assessments of beliefs about the uncertainty to be faced, and of relative preferences for consequences. In Chapters 3 and 4 we dealt with the former of these assessments. Now it is time to look in more detail at how preferences for consequences can be assessed and how those preferences can be encoded.

In Chapter 2 we laid the theoretical foundation for this chapter on utility theory via the presentation of the axioms of the subjective expected utility hypothesis. Readers might find it useful to review the

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