• Values are numbers that represent the extent to which objectives are achieved by taking a decision. They express our likes and dislikes. There are many ways of identifying objectives and criteria that are the standards against which achievement is judged. We show how the numbers are assessed, and interpret their meaning as values.

• Evaluating options that are of different types to create portfolios of actions that meet all objectives for the available resources requires making trade-off between the types as well as criteria. The added complexity of MCDA is first described for the women’s shampoo case study, then applied to two major projects: prioritising R&D projects; and designing the UK Navy’s Type 45 destroyer.

The many tasks of the facilitator, as distinct from those of a work group’s leader, are defined and developed, including dealing with conflict. Decision analysis works for the client because the model acts as a transitional object, holding and containing the client’s uncertainty as the model is explored, new insights develop, and preferences are constructed.

As these five chapters make clear, the social and technical aspects of creating a decision-analytic model are deeply intertwined. Indeed, a decision conference is itself a socio-technical system and although it is a (fairly) closed system, its impact will permeate the larger system from which its participants were drawn as they return to the workplace aligned with a new sense of common purpose.

• A brief introduction to Bayesian statistics, showing how uncertainty expressed as probabilities should be revised as more information is received, and illustrated with an example of how data revised researchers’ degrees of belief about the effects of medical cannabis on epilepsy in children. This is followed by a major project showing how Bayesian Belief Networks can assist underwriters assess risk premiums.

A brief history of working with groups of experts in a decision conference led to the development of requisite decision models that are sufficient in form and content to resolve the decision maker’s sense of unease. The stages from an initial meeting with the client, preparation, the decision conference itself, to a follow-through are described.

Not everything we know about numbers can be interpreted as true of what they represent, so this chapter explores how far we can go in applying the numbers to real problems, and how we can be sure they are meaningful.

Weights representing trade-offs show how a little more on one criterion can be equated to a little less on another. Methods for assessing the weights are described, including properly assessing criteria weights in hierarchical models.

The six types of decision problem for which decision modelling is appropriate are previewed, each illustrated with a real case study. A key discriminator is whether the problem is mainly about multiple objectives, or uncertainty, or a mixture of both.

In decision analysis, probabilities are defined as representing the assessor’s uncertainty about the outcome of an event. We explore the rules of probability, explain how to assess good probabilities, and suggest instances when proper scoring rules can assist.

Facilitated decision modelling with groups of experts enables many heads to be better than one if experts are chosen for their diversity of views and ability to perform at the highest level. The enabling conditions for groups to be effective are summarised from laboratory research and observational studies, including the characteristics of high-performing teams.

• Three types of consultancy require different relationships with clients, and Edgar Schein’s 10 principles of process consultancy skills are reinterpreted as appropriate for the practising decision analyst. Developing trustworthiness and a helping relationship are the keys to effective decision support.

Event trees show decisions to take now that can mitigate subsequent unfavourable events defining the risk of a situation, whereas fault trees assume an unfavourable event has occurred, with decisions to be taken that reduce the undesirable consequences and their likelihood of occurring if a fault occurs in a complex system. Two case studies provide examples. Scenario analysis provides a way to understand deep uncertainty.

• MCDA can assist negotiators as they attempt to find which of the stands on the controversial issues are acceptable to both parties. A simple example is given to demonstrate how asymmetries of interests can be quantified, revealing mutually acceptable solutions. Several real-life applications by the US Government are followed by a report on how oil spillage by tankers at sea benefited from this type of model.

The people who started decision theory, how they identified the key quantifiable ingredients of good decisions: values, trade-offs and probabilities, then turned this mathematical beginning into the applied discipline of decision analysis.