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eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology

Group Decision Making


Contents

Group decision makingGroup characteristics Advantages and disadvantages

Methods for supporting groupsNominal Group TechniqueDelphi method Voting procedures

Aggregation of values


Group characteristics

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


Group decisions: advantages and disadvantages

+ Pooling of resourcesaccess to more information and knowledgetends to generate more alternatives

+ Several stakeholders involvedmay increase acceptance and legitimacy

--

Time consumingResponsibilities sometimes ambiguous

- Problems with group work Minority dominationUnequal participation

- Group thinkPressures to conformity...

http://www.cedu.niu.edu/~fulmer/groupthink.htm


Methods for improving group decisions

BrainstormingNominal Group Technique (NGT)Delphi techniqueComputer assisted decision making

GDSS = Group Decision Support SystemCSCW = Computer Supported Collaborative Work

Improving group decisions


Brainstorming (1/3)

Group process for generating possible solutions to a problemDeveloped by Alex F. Osborne to increase individual capabilities for synthesis

Panel formatLeader: maintains a rapid flow of ideasRecorder: lists the ideas as they are presentedVariable number of panel members (optimum about 12)

30 min sessions ideally



Brainstorming (2/3)Step 1: Prior notification

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

Step 2: IntroductionThe leader reviews the objectives and the rules of the session

Step 3: Idea generation The leader calls for spontaneous ideasBrief responses, no negative ideas or criticism allowed All ideas are listedTo stimulate the flow of ideas the leader may

Ask stimulating questionsIntroduce related areas of discussionUse key words, random inputs

Step 4: Review and evaluationA list of ideas is sent to the panel members for further study



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



Nominal group technique (1/4)

Organised group meetings for problem identification, problem solving, program planning

Used to eliminate the problems encountered in small group meetings

Balances interests

Increases participation

2-3 hours sessions

6-12 members

Larger groups divided in subgroups




Step 1: Silent generation of ideasThe leader presents questions to the groupIndividual responses in written format (5 min)Group work not allowed

Step 2: Recorded round-robin listing of ideasEach member presents an idea in turnAll ideas are listed on a flip chart

Step 3: Brief discussion of ideas on the chartClarifies the ideas ⇒ common understanding of the problem Max 40 min




Step 4: Preliminary vote on prioritiesEach member ranks 5 to 7 most important ideas from the flip chart and records them on separate cardsThe leader counts the votes on the cards and writes them on the chart

Step 5: Break

Step 6: Discussion of the vote Examination of inconsistent voting patterns

Step 7: Final voteMore sophisticated voting procedures may be used here

Step 8: Listing of and agreement on the prioritised items




Best for small group meetingsFact findingIdea generationSearch of problem or solution

Not suitable for Routine businessBargaining Problems with predetermined outcomes Settings where consensus is required



Delphi technique (1/8)

A group process which helps aggregates viewpoints in settings where subjective information has to be relied on Produces numerical estimates and forecasts on selected statements Depends on written feedback (instead of bringing people together)Developed by RAND Corporation in the late 1950s First uses in military applications Subsequently numerous applications in a variety of areas

Setting of environmental standardsTechnology foresight Project prioritisation

A Delphi forecasts by Gordon and Helmer

http://www.rand.org/



Delphi technique (2/8)Characteristics

Panel of expertsFacilitator who leads the process (‘manager’)Anonymous participation

Makes it easier to change opinionIterative processing of the responses in several rounds

Interaction through questionnairesSame arguments are not repeatedEstimates and associated arguments are generated by and presented to the panel

Statistical interpretation of the forecasts




First roundPanel members are asked to list trends and issues that are likely to be important in the futureFacilitator organises the responses

Similar issues are combinedMinor, marginal issues are eliminatedArguments are elaborated

⇒ Questionnaire for the second round




Second roundA list of relevant events (topics) is sent to all panel membersPanelists are requested to

(1) estimate when the events will take place (2) provide arguments in supports of their estimates

Facilitator develops a statistical summary of the responses (median, quartiles, medium)




Third roundResults from the second round are sent to the panelists

Events - realisation times - supporting argumentsPanelists are asked for revised estimates

Changes of opinion are allowed For any change, arguments are requested Arguments are also required for if the estimate lies within the lower or upper quartiles

Facilitator produces a revised statistical summary




Fourth roundResults from the third round are sent to the panelistsPanel members are asked for revised estimates

Arguments are asked for if the estimate differs markedly from the views expressed by most

Facilitator summarises the results

Forecast = median from the fourth roundUncertainty = difference between the upper and lower

quartile




Suitable when subjective expertise and judgementalinputs must be relied on Complex, large, multidisciplinary problems with considerable uncertainties

Possibility of unexpected breakthroughs Causal models cannot be built or validatedParticularly long time frames

Opinions required from a large groupAnonymity is deemed beneficial



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

Partly due the anonymity

- Systematic errorsDiscounting the future (current happenings seen as more important) Illusory expertise (expert may be poor forecasters)Vague questions and ambiguous responsesSimplification urge Desired events are seen as more likelyExperts too homogeneous ⇒ skewed data


Group decision making by voting

In democracies, most decisions are taken by groups or by the larger community

Voting is one possible way to make the decisionsAllows for a (very) large number of decision makersAll DMs are not necessarily satisfied with the result

The size of the group doesn’t guarantee the quality of the decisionSuppose 800 randomly selected persons were to decide what materials should be used in a spacecraft


Voting - a social choice

N alternatives x1, x2, …, xn

K decision makers DM1, DM2, …, DMk

Each DM has preferences for the alternativesWhich alternative the group should choose?

Voting procedures


Plurality voting (1/2)

Each voter has one voteThe alternative which receives the most votes wins Run-off technique

The winner must get over 50% of the votesIf the condition is not met eliminate alternatives with the lowest number of votes and repeat the votingContinue until the condition is met

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

Plurality voting

4 votes for A

3 votes for B

2 votes for C

A is the winner

Run-off

4 votes for A

3+2 = 5 votes for B

B is the winner

Voting procedures


Condorcet

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

B

C

A B C

- 18,15 18,15

15,18 - 32,1

15,18 1,32 -

C got least votes (15+1=16), thusit cannot be winner ⇒ eliminate

A is better than B by 18:15

⇒ A is the Condorcet winner

Similarly, C is the Condorcet loser

Voting procedures


Borda

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

3 state that B > C > A

2 state that C > B > A

A : 4·2 + 3·0 + 2·0 = 8 votes

B : 4·1 + 3·2 + 2·1 = 12 votes

C : 4·0 + 3·1 + 2·2 = 7 votes

B is the winner

Voting procedures


Approval voting

Each voter cast one vote for each alternative that she approvesThe alternative with the highest number of votes is the winnerAn example: 3 alternatives, 9 voters

DM1 DM2 DM3 DM4 DM5 DM6 DM7 DM8 DM9 total

A

B

C

X - - X - X - X - 4

X X X X X X - X - 7

- - - - - - X - X 2

the winner!


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

ABC

DM1 DM2 DM3

1 3 22 1 33 2 1

Every alternative has a supporter!

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


The Condorcet paradox (2/2)

Three voting orders:1) (A-B) ⇒ A wins, (A-C) ⇒ C is the winner2) (B-C) ⇒ B wins, (B-A) ⇒ A is the winner3) (A-C) ⇒ C wins, (C-B) ⇒ B is the winner

DM1 DM2 DM3

A 1 3 2B 2 1 3

3 2 1C

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.


Tactical voting

DM1 knows the preferences of the other voters and the voting order (A-B, B-C, A-C)

Her favourite A cannot win*

If she votes for B instead of A in the first roundB is the winnerShe avoids the least preferred alternative C

* If DM2 and DM3 vote according to their true preferences


Coalitions

If the voting procedure is known voters may form coalitions that serve their purposes

Eliminate an undesired alternativeSupport a commonly agreed alternative


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

How should the collective preference R be determined when there are k decision makers?

What is the social choice function f that gives R=f(R1,…,Rk)?

Voting procedures are potential choices for social choice functions.


Requirements on the social choice function (1/2)

1) Non trivialThere are at least two DMs and three alternatives

2) Complete and transitive R and Ri:sIf 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:sThe group has a well defined preference relation, regardless of individualpreferences


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 principleIf all group members prefer x to y, the group should choose the alternative x

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


Arrow’s theorem

There is no complete and transitive social choice function f such that the

conditions 1-6 are always satisfied


Arrow’s theorem - an exampleBorda criterion:

DM1 DM2 DM3 DM4 DM5 total

x1 3 3 1 2 1 10

x2 2 2 3 1 3 11

x3 1 1 2 0 0 4

x4 0 0 0 3 2 5

Alternative x2is the winner!

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

DM1 DM2 DM3 DM4 DM5 total

x1 1 1 0 1 0 3

x2 0 0 1 0 1 2

Alternative x1is the winner!

The fourth criterion is not satisfied!


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.


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

Value function also captures the DMs’ strength of preferences

Value

beer

1

wine tea

Value

beer

1

wine tea

DM1: beer > wine > tea DM1: tea > wine > beer


Problems in value aggregationThere is a function describing group preferences but in practice it may be difficult to elicit Comparing the values of different DMs is not straightforwardSolution:

Each DM defines her/his own value functionGroup preferences are calculated as a weighted sum of the individual preferences

Unequal or equal weights? Should the chairman get a higher weightGroup members can weight each others’ expertiseDefining the weight is likely to be politically difficult

How to ensure that the DMs do not cheat?See value aggregation with value trees



Computer assisted decision making

A large number software packages available forDecision analysisGroup decision makingVoting

Web based applicationsInterfaces to standard software; Excel, AccessAdvantages

Graphical support for problem structuring, value and probabilityelicitationFacilitate changes to models relatively easilySensitivity analyses can be easily conductedAnalysis of complex value and probability structuresPossibility to carry out analysis in distributed mode

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