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Chapter 12

Decisions Involving Groups of Individuals

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We have focused on the individual decision maker, but important decisions are often made by accountable managers working within small groups of people, most, or all, of whom have information that could be utilized in the decision-making process.

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Often individuals may differ in their subjective probabilities of events, their utilities of outcomes or in their perception of the subsequent actions available as the pattern of actions, events and outcomes is unfolded into the future.

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If the opinion and values of individuals differ, how should the differences be resolved?

Obviously, several individuals who are involved in decision making bring together a larger fund of experience, knowledge and creative insights.

It is intuitively reasonable that the chances of over looking possible events and possible courses of action are diminished in group decision making.

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There are essentially two approaches to the problem: mathematical and behavioral aggregation.

Mathematical aggregation involves techniques such as the calculation of a simple average of the judgments of the individual group members.

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In behavioral aggregation, a group, judgment is reached by members of the group communicating with each other either in open discussion or via a more structured communication process.

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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.

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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.

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Mathematical aggregation

There are a number of advantages to be gained by using mathematical aggregation to combine the judgments of the individual members of a group.

The methods involved are relatively straightforward.

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The more complex and time-consuming procedures of behavioral aggregation are avoided.

Moreover, the group members do not have to meet. Their judgments can be elicited by telephone, post or computer and therefore the influence of dominant group members is avoided.

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However, there can be serious problems with the mathematical approach as the following example.

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Mathematical aggregation:The production manager’s model

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Mathematical aggregation:The accountant’s model

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Mathematical aggregation:The ‘average’ model

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Aggregating judgments in general

Two methods of combining individual estimates of unknown quantities are considered.

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Taking a simple average of the individual judgments

The individual group judgments can be regarded as being unbiased, with each person's estimate being equal to the true value plus a random error which is independent of the errors of the other estimates.

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In these circumstances it can be shown that taking the simple average of the individual estimates is the best way of aggregating the judgments.

The reliability of this group average will improve as the group size increases because the random error inherent in each judgment will be “averaged out”.

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However, the members of the group will produce estimates which are positively correlated.

This is likely to occur because group members often have similar areas of expertise or because they all work in the same environment where they are exposed to the same sources of information.

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If there is a high intercorrelation between the judgments of the group members, then little new information will be added by each additional member of the group and there may be little point in averaging the judgments of more than a small group of individuals.

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Taking a weighted average of the individual judgments

When 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.

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Clearly, the main problem of using weighted averages is that the judgmental skills of the group members need to be assessed in order to obtain the weights.

Methods which have been proposed fall into three categories: self-rating, rating of each individual by the whole group,and rating based on past performance.

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However, there can be difficulties in applying these methods.

The first two approaches compound the individual's judgmental task by requiring not only judgments about the problem in hand but also those about the skill of individual group members.

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In some circumstances these problems can be avoided by using weights based on past performance.

But The current judgmental task may not be the

same as those in the past. Past performance may be a poor guide

where judges have improved their performance through learning.

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Research has consistently indicated that simple averages produce estimates which are either as good as, or only slightly inferior to, weighted averages.

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Ferrell argues that groups tend to be made up of individuals who have very similar levels of expertise and access to the same information.

In the case of small groups, even if we are fortunate enough to identify the best individual estimate, its accuracy is unlikely to be much better than that of the simple average of the entire group's judgments.

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Situation to be Suitable for the weighted Average

a moderately large group of well-acquainted individuals that frequently works together and has a wide range of different types of expertise to bring to bear on questions that require an equally wide range of knowledge.

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Aggregating probability judgments

There are particular problems involved when probabilities need to be aggregated, as the following example shows.

In Table 12.4, it can be seen that the “group” assessment of the probability that both events will occur differs, depending on how the averaging was carried out.

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Table 12.4

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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.

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The most pragmatic approach to aggregating probabilities would appear to be the most straightforward, namely, to take a simple average of individual probabilities.

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Aggregating preference judgments

Aggregating preference orderings One obvious way of aggregating

individual preferences is to use a simple voting system. However, this can result in paradoxical results, as the following example shows.

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Aggregating preference orderings: Condorcet’s paradox

Member Preference

orderingEdwards A > B > CFletcher B > C > AGreen C > A > B

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In many practical problems alternatives are not compared simultaneously, as above, but sequentially.

For example, the committee might compare A with B first, eliminate the inferior option and then compare the preferred option with C.

Unfortunately, the order of comparison has a direct effect on the option which is chosen.

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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:

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Arrow’s impossibility theorem: Four conditions

Method must produce a transitive group preference order.

If every member prefers an option then so must the group.

Group choice between 2 options does not depend on preferences for any other option

There is no dictator.

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Arrow proved that no aggregation procedure can guarantee to satisfy all four conditions.

It suggests that it is impossible to derive a truly democratic system for resolving differences of opinion. Any method which is tried will have some shortcoming.

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Aggregating values and utilities A statement giving an individual's

preference order does not tell you about that person's intensity of preference for the alternatives.

The problem with aggregating the values or utilities of a group of individuals is that the intensities of preference of the individuals have to be compared.

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Aggregating values and utilities

Destination Person A Person B

Average

Rio de Janeiro 100 50 75San Francisco 40 100 70Toronto 0 0 0

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However, our calculation assumes that a move from 0 to 100 on one person's value scale represents the same increase in preference as a move from 0 to 100 on the other person's scale.

Could actually measure and compare the strength of preference of the two people on a common scale.

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Measuring individuals’ strengths of preference on a common scale

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Aggregating values and utilities

Destination Person A Person B

Average

Rio de Janeiro 40 50 45San Francisco 16 100 58Toronto 0 0 0

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In the absence of any obvious method for making interpersonal comparisons of intensity of preference then it seems that our search for a group value or utility function is futile.

Nevertheless, the concepts of value and utility can still be useful in group decision making.

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The derivation of individual values and utilities can help each group member to clarify his or her personal understanding of the problem and also to achieve a greater appreciation of the views of other members.

Moreover, a simple average of values and utilities may be useful in providing a rough initial model of the problem.

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Unstructured group processes: Groupthink

• The presence of powerful individuals can inhibit the contribution of those who are lower down the hierarchy.

• Groupthink is essentially the suppression of ideas that are critical of the 'direction' in which a group is moving.

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These pitfalls of groupthink are likely to result in an incomplete survey of alternative courses of action or choices.

Such an incomplete search through the decision space may result in a failure to examine the risks of preferred decisions and a failure to work out contingency plans if the preferred course of action cannot be taken.

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Conditions leading to groupthink

High group cohesiveness Insulation of group Lack of methodological procedures for searching for and appraising options Directive leadership High stress with a low degree of hope of finding a solution better than the one favoured by the leader or other influential person

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Some consequences of groupthink

Incomplete survey of alternative courses of action and objectives

Failure to examine risks of preferred choice

Poor information search

Selective bias in processing available information

Failure to work out contingency plans in case things go wrong

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Structured group processes – The Delphi method

Designed to obtain estimates from groups of people without the biasing effect of face-to-face discussion and to ensure the airing of diverse views

Does this by restricting inter-personal interaction between the group members and controlling information flow

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The phases of Delphi

1. Panelists provide estimates anonymously2. Results of this polling are tallied and statistics of group’s opinions are fed back to panelists3. A re-polling takes place 4. Process is repeated until a consensus emerges or no further changes of opinion are evident5. Median of the group’s estimate in the final round is then used as their estimate

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Advantages of Delphi

• Allows larger no. of participants than group or

committee meeting • Panelists can be geographically dispersed• Panelists can make estimates free from undue

pressures from group or dominant individuals• Avoids influence of potentially irrelevant factors

like status of person proposing an estimate• Anonymity means panelists can change estimates

between rounds without fear of losing face

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Rationale for Delphi

After feedback, improved accuracy is thought to result from:

• opinion changes in the ‘swingers’ who change less firmly grounded opinions and• opinion stability of the ‘holdouts’ who are assumed to be more accurate than the swingers

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Limitation of Delphi

There is little information sharing between panelists

-- this does not help individuals to construct an alternative theory or scenario in order to produce a revised estimate

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Decision conferencing

• Brings together group processes, decision analysis and IT in intensive 2-3 day session

• Involves small group of decision makers with a decision analyst (facilitator)

• Simple models often used so model is clear to all participants and shared understanding of problem generated

• Participants gain a sense of common purpose and commitment to action

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Why conferencing should avoid groupthink

• Participants are not on home ground

• The group is carefully composed of people from all perspectives

• The facilitator is a neutral outsider who is aware of the unhelpful affects of groupthink

• A decision analysis model is used to structure the discussion and make assumptions explicit