Group decisions and voting
eLearning resources / MCDA team
Director prof. Raimo P. Hämäläinen
Helsinki University of Technology
Systems Analysis Laboratory
http://www.eLearning.sal.hut.fi
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Contents
 Group characteristics
 Group decisions - advantages and
disadvantages
 Improving group decisions
 Group decision making by voting
 Voting - a social choice
 Voting procedures
 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
 more information and
knowledge
 generates more alternatives
+ Several stakeholders involved
 increases acceptance
 increases legitimacy
- Time consuming
- Ambiguous responsibility
- Problems with group work
 Minority domination
 Unequal participation
- Group think
 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
Delphi technique
Computer assisted decision making
 GDSS = Group Decision Support System
 CSCW = Computer Supported Collaborative Work
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Improving group decisions
Brainstorming (1/3)
 Group process for gathering ideas pertaining a solution
to a problem
 Developed by Alex F Osborne to increase individual’s
synthesis capabilities
 Panel format
 Leader: maintains a rapid flow of ideas
 Recorder: lists the ideas as they are presented
 Variable number of panel members (optimum 12)
 30 min sessions ideally
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Improving group decisions
Brainstorming (2/3)
Step 1: Preliminary notice
 Objectives to the participants at least a day before the session
 time for individual idea generation
Step 2: Introduction
 The leader reviews the objectives and the rules of the session
Step 3: Ideation
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The leader calls for spontaneous ideas
Brief responses, no negative ideas or criticism
All ideas are listed
To stimulate the flow of ideas the leader may
 Ask stimulating questions
 Introduce related areas of discussion
 Use key words, random inputs
Step 4: Review and evaluation
 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)
+ Large number of ideas in a short time period
+ Simple, no special expertise or knowledge
required from the facilitator
- Credit for another person’s ideas may impede
participation
Works best when participants come from a wide
range of disciplines
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Improving group decisions
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
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
 Each member ranks 5 to 7 most important ideas from the flip chart and
records them on separate cards
 The 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 vote
 More sophisticated voting procedures may be used here
Step 8: Listing and agreement on the prioritised items
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Improving group decisions
Nominal group technique (4/4)
 Best for small group meetings
 Fact finding
 Idea generation
 Search of problem or solution
 Not suitable for
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Routine business
Bargaining
Problems with predetermined outcomes
Settings where consensus is required
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Improving group decisions
Delphi technique (1/8)
 Group process to generate consensus when decisive factors may
be subjective
 Used to produce numerical estimates, forecasts on a given
problem
 Utilises written responses instead of brining people together
 Developed by RAND Corporation in the late 1950s
 First use in military applications
 Later several applications in a number of areas
 Setting environmental standards
 Technology foresight
 Project prioritisation
 A Delphi forecast by Gordon and Helmer
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Improving group decisions
Delphi technique (2/8)
Characteristics:
 Panel of experts
 Facilitator who leads the process
 Anonymous participation
 Easier to express and change opinion
 Iterative processing of the responses in several rounds
 Interaction with questionnaires
 Same arguments are not repeated
 All opinions and reasoning are presented by the panel
 Statistical interpretation of the forecasts
Systems Analysis Laboratory
Helsinki University of Technology
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Improving group decisions
Delphi technique (3/8)
First round
 Panel members are asked to list trends and issues that
are likely to be important in the future
 Facilitator organises the responses
 Similar opinions are combined
 Minor, marginal issues are eliminated
 Arguments are elaborated
  Questionnaire for the second round
Systems Analysis Laboratory
Helsinki University of Technology
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Improving group decisions
Delphi technique (4/8)
Second round
 Summary of the predictions is sent to the panel
members
 Members are asked the state the realisation times
 Facilitator makes a statistical summary of the
responses (median, quartiles, medium)
Systems Analysis Laboratory
Helsinki University of Technology
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Improving group decisions
Delphi technique (5/8)
Third round
 Results from the second round are sent to the panel
members
 Members are asked for new forecasts
 They may change their opinions
 Reasoning required for the forecasts in upper or lower
quartiles
 A statistical summary of the responses (facilitator)
Systems Analysis Laboratory
Helsinki University of Technology
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Improving group decisions
Delphi technique (6/8)
Fourth round
 Results from the third round are sent to the panel
members
 Panel members are asked for new forecasts
 A reasoning is required if the opinion differs from the general
view
 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
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Improving group decisions
Delphi technique (7/8)
 Most applicable when an expert panel and
judgemental data is required
 Causal models not possible
 The problem is complex, large, multidisciplinary
 Uncertainties due to fast development, or large time
scale
 Opinions required from a large group
 Anonymity is required
Systems Analysis Laboratory
Helsinki University of Technology
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Improving group decisions
Delphi technique (8/8)
+ Maintain attention directly on the issue
+ Allow diverse background and remote locations
+ Produce precise documents
- Laborious, expensive, time-consuming
- Lack of commitment
 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
Improving group decisions
Computer assisted decision making
 A large number software packages available for
 Decision analysis
 Group decision making
 Voting
 Web based applications
 Interfaces to standard software; Excel, Access
 Advantages
 Graphical support for problem structuring, value and probability
elicitation
 Facilitate changes to models relatively easily
 Easy to conduct sensitivity analysis
 Analysis of complex value and probability structures
 Allow distributed locations
Systems Analysis Laboratory
Helsinki University of Technology
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Group decision making by voting
 In democracy most decisions are made in groups or by
the community
 Voting is a possible way to make the decisions
 Allows large number of decision makers
 All DMs are not necessarily satisfied with the result
 The size of the group doesn’t guarantee the quality of
the decision
 Suppose 800 randomly selected persons deciding on the
materials used in a spacecraft
Systems Analysis Laboratory
Helsinki University of Technology
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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
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Voting procedures
Plurality voting (1/2)
 Each voter has one vote
 The alternative that receives the most votes is the
winner
 Run-off technique
 The winner must get over 50% of the votes
 If the condition is not met eliminate the alternatives with the
lowest number of votes and repeat the voting
 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 states that A > B > C
3 states that B > C > A
2 states 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
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Helsinki University of Technology
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B is the winner
Voting procedures
Condorcet
 Each pair of alternatives is compared.
 The alternative which is the best in most comparisons is the
winner.
 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
32,1
B
15,18
-
C
15,18
1,32
-
 C got least votes (15+1=16), thus
it cannot be winner  eliminate
 A is better than B by 18:15
 A is the Condorcet winner
 Similarly, C is the Condorcet loser
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Helsinki University of Technology
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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 is the
winner.
 An example: 3 alternatives, 9 voters
4 states that A > B > C
A : 4·2 + 3·0 + 2·0 = 8 votes
3 states that B > C > A
B : 4·1 + 3·2 + 2·1 = 12 votes
2 states that C > B > A
C : 4·0 + 3·1 + 2·2 = 7 votes
B is the winner
Systems Analysis Laboratory
Helsinki University of Technology
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Voting procedures
Approval voting
 Each voter cast one vote for each alternative she / he
approves of
 The alternative with the highest number of votes is the
winner
 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
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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:
 A is preferred to B (2-1)
 B is preferred to C (2-1)
 C is preferred to A (2-1)
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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 voting order!
There is no socially best alternative*.
* Irrespective of the choice the majority of voters would
prefer another alternative.
Systems Analysis Laboratory
Helsinki University of Technology
eLearning / MCDA
Strategic 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 round
 B is the winner
 She avoids the least preferred alternative C
* If DM2 and DM3 vote according to their preferences
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Helsinki University of Technology
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Coalitions
 If the voting procedure is known voters may
form coalitions that serve their purposes
 Eliminate an undesired alternative
 Support a commonly agreed alternative
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Helsinki University of Technology
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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 the collective preference R should 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.
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Helsinki University of Technology
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Requirements on the
social choice function (1/2)
1) Non trivial
There are at least two DMs and three alternatives
2) Complete and transitive 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
what the individual preferences are
Systems Analysis Laboratory
Helsinki University of Technology
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Requirements on the
social choice function (2/2)
4) Independence of irrelevant alternatives
The group’s choice doesn’t change if we add an alternative that is
 Considered inferior to all other alternatives by all DMs, or
 Is a copy of an existing alternative
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
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Arrow’s theorem
There is no complete and transitive f
satisfying the conditions 1-6
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Arrow’s theorem - an example
Borda 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 x2
is the winner!
Suppose that DMs’ preferences do not change. A ballot between the
alternatives 1 and 2 gives
DM1
DM2
DM3
DM4
x1
1
x2
0
DM5
total
1
0
1
0
3
0
1
0
1
2
The fourth criterion is not satisfied!
Systems Analysis Laboratory
Helsinki University of Technology
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Alternative x1
is the winner!
Value aggregation (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.
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Value aggregation (2/2)
 In addition to the weak preference order also a scale
describing the strength of the preferences is required
DM1: beer > wine > tea
DM1: tea > wine > beer
Value
Value
1
1
beer
wine
tea
beer
wine
tea
 Value function describes also the strength of the
preferences
Systems Analysis Laboratory
Helsinki University of Technology
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Problems in value aggregation
 There is a function describing group preferences but it may be
difficult to define in practice
 Comparing the values of different DMs is not straightforward
 Solution:
 Each DM defines her/his own value function
 Group preferences are calculated as a weighted sum of the individual
preferences
 Unequal or equal weights?
 Should the chairman get a higher weight
 Group members can weight each others’ expertise
 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