Group Decision Making

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Contents ƒ Group decision making ƒ Group characteristics ƒ Advantages and disadvantages

ƒ Methods for supporting groups ƒ Nominal Group Technique ƒ Delphi method ƒ Voting procedures

ƒ Aggregation of values

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Group characteristics ƒ ƒ ƒ ƒ

DMs with a common decision making problem Shared interest in a collective decision All members have an opportunity to influence the decision For example: local governments, committees, boards etc.

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Group decisions: advantages and disadvantages + Pooling of resources

ƒ access to more information and knowledge ƒ tends to generate more alternatives + Several stakeholders involved ƒ may increase acceptance - Time consuming - Responsibilities sometimes and legitimacy ambiguous - Problems with group work ƒ Minority domination ƒ Unequal participation - Group think ƒ Pressures to conformity...

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Methods for improving group decisions ƒ ƒ ƒ ƒ

Brainstorming Nominal Group Technique (NGT) Delphi technique Computer assisted decision making ƒ GDSS = Group Decision Support System ƒ CSCW = Computer Supported Collaborative Work

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Brainstorming (1/3) ƒ Group process for generating possible solutions to a problem ƒ Developed by Alex F. Osborne to increase individual capabilities for synthesis ƒ Panel format ƒ Leader: maintains a rapid flow of ideas ƒ Recorder: lists the ideas as they are presented ƒ Variable number of panel members (optimum about 12) ƒ 30 min sessions ideally

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Brainstorming (2/3) Step 1: Prior notification ƒ

Objectives communicated to the participants at least one day ahead of time ⇒ time for individual idea generation

Step 2: Introduction ƒ

The leader reviews the objectives and the rules of the session

Step 3: Idea generation ƒ ƒ ƒ ƒ

The leader calls for spontaneous ideas Brief responses, no negative ideas or criticism allowed All ideas are listed To stimulate the flow of ideas the leader may ƒ Ask stimulating questions ƒ Introduce related areas of discussion ƒ Use key words, random inputs

Step 4: Review and evaluation ƒ

A list of ideas is sent to the panel members for further study

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Brainstorming (3/3) + A large number of ideas can be generated in a short period of time + Simple - no special expertise or knowledge required from the facilitator - Credit for another person’s ideas may impede participation Works best when participants represent a wide range of disciplines

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Nominal group technique (1/4) ƒ Organised group meetings for problem identification, problem solving, program planning ƒ Used to eliminate the problems encountered in small group meetings ƒ Balances interests ƒ Increases participation ƒ 2-3 hours sessions ƒ 6-12 members ƒ Larger groups divided in subgroups

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Nominal group technique (2/4) Step 1: Silent generation of ideas ƒ ƒ ƒ

The leader presents questions to the group Individual responses in written format (5 min) Group work not allowed

Step 2: Recorded round-robin listing of ideas ƒ ƒ

Each member presents an idea in turn All ideas are listed on a flip chart

Step 3: Brief discussion of ideas on the chart ƒ ƒ

Clarifies the ideas ⇒ common understanding of the problem Max 40 min

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Nominal group technique (3/4) Step 4: Preliminary vote on priorities ƒ Each member ranks 5 to 7 most important ideas from the flip chart and records them on separate cards ƒ The leader counts the votes on the cards and writes them on the chart

Step 5: Break Step 6: Discussion of the vote ƒ Examination of inconsistent voting patterns

Step 7: Final vote ƒ More sophisticated voting procedures may be used here

Step 8: Listing of and agreement on the prioritised items

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Nominal group technique (4/4) ƒ Best for small group meetings ƒ Fact finding ƒ Idea generation ƒ Search of problem or solution ƒ Not suitable for ƒ Routine business ƒ Bargaining ƒ Problems with predetermined outcomes ƒ Settings where consensus is required

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (1/8) ƒ A group process which helps aggregates viewpoints in settings where subjective information has to be relied on ƒ Produces numerical estimates and forecasts on selected statements ƒ Depends on written feedback (instead of bringing people together) ƒ Developed by RAND Corporation in the late 1950s ƒ First uses in military applications ƒ Subsequently numerous applications in a variety of areas ƒ Setting of environmental standards ƒ Technology foresight ƒ Project prioritisation

ƒ A Delphi forecasts by Gordon and Helmer Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (2/8) Characteristics ƒ Panel of experts ƒ Facilitator who leads the process (‘manager’) ƒ Anonymous participation ƒ Makes it easier to change opinion ƒ Iterative processing of the responses in several rounds ƒ Interaction through questionnaires ƒ Same arguments are not repeated ƒ Estimates and associated arguments are generated by and presented to the panel ƒ Statistical interpretation of the forecasts

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (3/8) First round ƒ Panel members are asked to list trends and issues that are likely to be important in the future ƒ Facilitator organises the responses ƒ Similar issues are combined ƒ Minor, marginal issues are eliminated ƒ Arguments are elaborated ⇒ Questionnaire for the second round

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (4/8) Second round ƒ A list of relevant events (topics) is sent to all panel members ƒ Panelists are requested to (1) estimate when the events will take place (2) provide arguments in supports of their estimates ƒ Facilitator develops a statistical summary of the responses (median, quartiles, medium)

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (5/8) Third round ƒ Results from the second round are sent to the panelists ƒ Events - realisation times - supporting arguments ƒ Panelists are asked for revised estimates ƒ Changes of opinion are allowed ƒ For any change, arguments are requested ƒ Arguments are also required for if the estimate lies within the lower or upper quartiles ƒ Facilitator produces a revised statistical summary

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (6/8) Fourth round ƒ Results from the third round are sent to the panelists ƒ Panel members are asked for revised estimates ƒ Arguments are asked for if the estimate differs markedly from the views expressed by most ƒ Facilitator summarises the results

Forecast = median from the fourth round Uncertainty = difference between the upper and lower quartile

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (7/8) ƒ Suitable when subjective expertise and judgemental inputs must be relied on ƒ Complex, large, multidisciplinary problems with considerable uncertainties ƒ Possibility of unexpected breakthroughs ƒ Causal models cannot be built or validated ƒ Particularly long time frames

ƒ Opinions required from a large group ƒ Anonymity is deemed beneficial

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Delphi technique (8/8) + Maintains attention directly on the issue + Allows for diverse background and remote locations + Produces precise documents - Laborious, expensive, time-consuming - Lack of commitment ƒ

Partly due the anonymity

- Systematic errors ƒ ƒ ƒ ƒ ƒ ƒ

Discounting the future (current happenings seen as more important) Illusory expertise (expert may be poor forecasters) Vague questions and ambiguous responses Simplification urge Desired events are seen as more likely Experts too homogeneous ⇒ skewed data

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Group decision making by voting ƒ In democracies, most decisions are taken by groups or by the larger community ƒ Voting is one possible way to make the decisions ƒ Allows for a (very) large number of decision makers ƒ All DMs are not necessarily satisfied with the result ƒ The size of the group doesn’t guarantee the quality of the decision ƒ Suppose 800 randomly selected persons were to decide what materials should be used in a spacecraft

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Voting - a social choice

ƒ ƒ ƒ ƒ

N alternatives x1, x2, …, xn K decision makers DM1, DM2, …, DMk Each DM has preferences for the alternatives Which alternative the group should choose?

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Voting procedures

Plurality voting (1/2) ƒ Each voter has one vote ƒ The alternative which receives the most votes wins ƒ Run-off technique ƒ The winner must get over 50% of the votes ƒ If the condition is not met eliminate alternatives with the lowest number of votes and repeat the voting ƒ Continue until the condition is met

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Voting procedures

Plurality voting (2/2) Suppose, there are three alternatives A, B, C, and 9 voters. 4 state that A > B > C 3 state that B > C > A 2 state that C > B > A Run-off

Plurality voting 4 votes for A

4 votes for A

3 votes for B

3+2 = 5 votes for B

2 votes for C A is the winner

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

B is the winner

Voting procedures

Condorcet ƒ ƒ ƒ

Each pair of alternatives is compared. The alternative which is the best in most comparisons wins There may be no solution.

Consider alternatives A, B, C, 33 voters and the following voting result

A A

-

B

C

18,15

18,15

B

15,18

-

32,1

C

15,18

1,32

-

ƒ C got least votes (15+1=16), thus it cannot be winner ⇒ eliminate ƒ A is better than B by 18:15 ⇒ A is the Condorcet winner ƒ Similarly, C is the Condorcet loser

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Voting procedures

Borda ƒ

ƒ ƒ

Each DM gives n-1 points to the most preferred alternative, n-2 points to the second most preferred, …, and 0 points to the least preferred alternative. The alternative with the highest total number of points wins. An example: 3 alternatives, 9 voters

4 state that A > B > C

A : 4·2 + 3·0 + 2·0 = 8 votes

3 state that B > C > A

B : 4·1 + 3·2 + 2·1 = 12 votes

2 state that C > B > A

C : 4·0 + 3·1 + 2·2 = 7 votes

B is the winner Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Voting procedures

Approval voting ƒ Each voter cast one vote for each alternative that she approves ƒ The alternative with the highest number of votes is the winner ƒ An example: 3 alternatives, 9 voters

DM1 DM2 DM3 DM4 DM5 DM6 DM7 DM8 DM9 total A

X

-

-

X

-

X

-

X

-

4

B

X

X

X

X

X

X

-

X

-

7

C

-

-

-

-

-

-

X

-

X

2

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

the winner!

The Condorcet paradox (1/2) Consider the following comparison of the three alternatives

DM1 A B C

1 2 3

DM2

DM3

3 1 2

2 3 1

Paired comparisons: ƒ A is preferred to B (2-1) ƒ B is preferred to C (2-1) ƒ C is preferred to A (2-1)

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Every alternative has a supporter!

The Condorcet paradox (2/2) Three voting orders: 1) (A-B) ⇒ A wins, (A-C) ⇒ C is the winner 2) (B-C) ⇒ B wins, (B-A) ⇒ A is the winner 3) (A-C) ⇒ C wins, (C-B) ⇒ B is the winner

DM1 DM2 DM3 A

1

3

2

B

2

1

3

C

3

2

1

The voting result depends on the order in which votes are cast! There is no socially ‘best’ alternative*. * Irrespective of the result the majority of voters would prefer another alternative. Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Tactical voting ƒ DM1 knows the preferences of the other voters and the voting order (A-B, B-C, A-C) ƒ Her favourite A cannot win* ƒ If she votes for B instead of A in the first round ƒ B is the winner ƒ She avoids the least preferred alternative C

* If DM2 and DM3 vote according to their true preferences Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Coalitions ƒ If the voting procedure is known voters may form coalitions that serve their purposes ƒ Eliminate an undesired alternative ƒ Support a commonly agreed alternative

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Weak preference order The opinion of the DMi about two alternatives is called a weak preference order Ri:

The DMi thinks that x is at least as good as y ⇔ x Ri y ƒ How should the collective preference R be determined when there are k decision makers? ƒ What is the social choice function f that gives R=f(R1,…,Rk)? ƒ Voting procedures are potential choices for social choice functions.

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Requirements on the social choice function (1/2) 1) Non trivial There are at least two DMs and three alternatives

2) Complete and transitive R and Ri:s If x ≠ y ⇒ x Ri y ∨ y Ri x (i.e. all DMs have an opinion) If x Ri y ∧ y Ri z ⇒ x Ri z

3) f is defined for all Ri:s The group has a well defined preference relation, regardless of individual preferences

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Requirements on the social choice function (2/2) 4) Binary relevance The group’s choice doesn’t change if we remove or add an alternative such that that the DM’s preferences among the remaining alternatives do not change.

5) Pareto principle If all group members prefer x to y, the group should choose the alternative x

6) Non dictatorship There is no DMi such that x Ri y ⇒ x R y

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Arrow’s theorem

There is no complete and transitive social choice function f such that the conditions 1-6 are always satisfied

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Arrow’s theorem - an example Borda criterion: DM1

DM2

DM3

x1

3

3

1

x2

2

2

x3

1

x4

0

DM4

DM5

total

2

1

10

3

1

3

11

1

2

0

0

4

0

0

3

2

5

Alternative x2 is the winner!

Suppose that DMs’ preferences do not change. A ballot between alternatives 1 and 2 gives DM1

DM2

DM3

x1

1

1

0

x2

0

0

1

DM4

DM5

total

1

0

3

0

1

2

The fourth criterion is not satisfied! Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Alternative x1 is the winner!

Aggregation of values (1/2) Theorem (Harsanyi 1955, Keeney 1975): Let vi(·) be a measurable value function describing the preferences of DMi. There exists a k-dimensional differentiable function vg() with positive partial derivatives describing group preferences >g in the definition space such that a >gb ⇔ vg[v1(a),…,vk(a)] ≥ vg[v1(b),…,vk(b)] and conditions 1-6 are satisfied. Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Aggregation of values (2/2) ƒ In addition to the weak preference order also a scale describing the strength of the preferences is required

Value

DM1: beer > wine > tea

1

Value

DM1: tea > wine > beer

1

beer

wine

tea

beer

wine

tea

ƒ Value function also captures the DMs’ strength of preferences Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Problems in value aggregation ƒ ƒ ƒ

ƒ

ƒ ƒ

There is a function describing group preferences but in practice it may be difficult to elicit Comparing the values of different DMs is not straightforward Solution: ƒ Each DM defines her/his own value function ƒ Group preferences are calculated as a weighted sum of the individual preferences Unequal or equal weights? ƒ Should the chairman get a higher weight ƒ Group members can weight each others’ expertise ƒ Defining the weight is likely to be politically difficult How to ensure that the DMs do not cheat? See value aggregation with value trees

Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA

Improving group decisions

Computer assisted decision making ƒ A large number software packages available for ƒ Decision analysis ƒ Group decision making ƒ Voting

ƒ Web based applications ƒ Interfaces to standard software; Excel, Access ƒ Advantages ƒ Graphical support for problem structuring, value and probability elicitation ƒ Facilitate changes to models relatively easily ƒ Sensitivity analyses can be easily conducted ƒ Analysis of complex value and probability structures ƒ Possibility to carry out analysis in distributed mode Systems Analysis Laboratory Helsinki University of Technology

eLearning / MCDA