Decisions Involving Groups of Individuals

Two simple advantages arise from obtaining group judgments in decision analysis. First, more information about possible ranges of utilities and probabilities can be obtained, and it is then possible to perform sensitivity analysis on these ranges to see if the decision specified by the analysis is changed by these variations. Second, a group of people who are involved in such a decision process may become more committed to implementing the decision which is eventually made. As we shall see in the section on decision conferencing, this latter advantage can be a major one.Mathematical AggregationThere are a number of advantages to be gained by using mathematical aggregation to combine the judgments of the individual members of a group.Aggregating Judgments In GeneralSingle-value estimates of factors such as costs, sales or times to complete a project are often used in decision analysis models when the use of a probability distribution for every unknown quantity would lead to a model which was too complex to be useful. Two methods of combining individual estimates of unknown quantities are considered below.Taking a simple average of the individual judgmentsThe reliability of this group average will improve as the group size increases because the random error inherent in each judgment will be ‘averaged out’. However, each additional member of the group will bring progressively smaller improvements in reliability, so that a point will be reached where it will not be worth the effort or cost of extending the group because a sufficiently reliable estimate can be achieved with the existing membership.Taking a weighted average of the individual judgmentsWhen some members of the group are considered to be better judges than others then it may be worth attaching a higher weight to their estimates and using a weighted average to represent the group judgment.Aggregating probability judgmentsThere are particular problems involved when probabilities need to be aggregated, as the following example shows. Because of these types of problem a number of alternative procedures have been suggested for aggregating probabilities. One approach is to regard one group member’s probability estimate as information which may cause another member to revise his or her estimate using Bayes’ theorem. Another approach is to take a weighted average of individual probabilities, using one of the three methods of weighting which we referred to earlier.Aggregating preference judgmentsWhen a group of individuals have to choose between a number of alternative courses of action is it possible, or indeed meaningful, to mathematically aggregate their preferences to identify the option which is preferred by the group? To try to answer this we will first consider decision problems where the group members state their preferences for the alternatives in terms of simple orderings (e.g. ‘I prefer A to B and B to C’). Then we will consider situations where a value or a utility function has been elicited from each individual.Aggregating preference orderingsThese sorts of problems led Arrow to ask whether there is a satisfactory method for determining group preferences when the preferences of individual members are expressed as orderings. He identified four conditions which he considered that a satisfactory procedure should meet:

1) The method must produce a transitive group preference order for the options being considered.

2) If every member of the group prefers one option to another then so must the group. (You will recall that this condition was not fulfilled in the production manager/accountant’s problem which we considered earlier.)

3) The group choice between two options, A and B, depends only upon the preferences of members between these options and not on preferences for any other option. (If this is not the case then, as we saw above, an individual can influence the group ordering by lying about his preferences.)

4) There is no dictator. No individual is able to impose his or her preferences on the group.

Aggregating values and utilitiesIt is important to note that Arrow’s Impossibility Theorem refers only to situations where individuals have stated the order of their preferences. A statement giving an individual’s preference order does not tell you about that person’s intensity of preference for the alternatives.Unstructured Group ProcessesOne of the major conclusions of research work on descriptions of group decision making is that of well-documented shortcomings. The presence of powerful individuals can inhibit the contribution of those who are lower down the hierarchy. Talkative or extroverted members may dominate the discussions. Indeed, variations in seating arrangements can tend to direct or inhibit individuals’ contributions.Structured Group ProcessesAwareness of the factors that can degrade group decision making combined with the implicit belief that group judgment can potentially enhance decision making has led to a number of structured methods to enhance group decision making by removing or restricting interpersonal interaction and controlling information flow. One such major method has been Delphi. Essentially, Delphi consists of an iterative process for making quantitative judgments. The phases of Delphi are:

1) Panelists provide opinions about the likelihood of future events, or when those events will occur, or what the impact of such event(s) will be. These opinions are often given as responses to questionnaires which are completed individually by members of the panel.

2) The results of this polling of panelists are then tallied and statistical feedback of the whole panel’s opinions (e.g. range or medians) is provided to individual panelists before a repolling takes place. At this stage, anonymous discussion (often in written form) may occur so that dissenting opinion is aired.

3) The output of the Delphi technique is a quantified group ‘consensus’, which is usually expressed as the median response of the group of panelists

Decision ConferencingHowever, a major question which still remains to be answered is: Are decisions that are conferenced to consensus more or less valid than unaided judgment or prescriptive solutions? For example, does the situational context of decision conferencing produce conditions for groupthink? Phillips has argued that this is not so, since:

1) Participants are not on home ground. Often decision conferences take place in hotels or an especially designed room on the decision analyst’s premises.

2) The small group is carefully composed of people representing all perspectives on the issue to be resolved so that adversarial processes operate in the group to check bias and explore alternative framings of the decision problem.

3) The decision analyst who acts to facilitate the conference is a neutral outsider who is sensitive to the unhelpful effects of groupthink and reflects this back to the group.