Group Decision Making

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
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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
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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
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Objectives communicated to the participants at least one day ahead of time
⇒ time for individual idea generation
Step 2: Introduction
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The leader reviews the objectives and the rules of the session
Step 3: Idea generation
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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
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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
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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
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Each member presents an idea in turn
All ideas are listed on a flip chart
Step 3: Brief discussion of ideas on the chart
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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
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Partly due the anonymity
- Systematic errors
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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
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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
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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
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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
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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