Discussing Public Voting in the Web as a Measure to Democratize Award Decisions
Group decisions and voting
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Transcript of Group decisions and voting
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Group decisions and voting
eLearning resources / MCDA teamDirector prof. Raimo P. HämäläinenHelsinki University of Technology
Systems Analysis Laboratoryhttp://www.eLearning.sal.hut.fi
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
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
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Group characteristics
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.
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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...
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Methods for improving group decisions
Brainstorming Nominal group technique Delphi technique Computer assisted decision making
GDSS = Group Decision Support System CSCW = Computer Supported Collaborative Work
Improving group decisions
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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
Improving group decisions
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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 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
Improving group decisions
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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
Improving group decisions
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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
Improving group decisions
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Nominal group technique (2/4)
Step 1: Silent generation of ideas 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 Each member presents an idea in turn All ideas are listed on a flip chart
Step 3: Brief discussion of ideas on the chart Clarifies the ideas common understanding of the problem Max 40 min
Improving group decisions
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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
Improving group decisions
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Nominal group technique (4/4)
Best for small group meetings Fact finding Idea generation Search of problem or solution
Not suitable for Routine business Bargaining Problems with predetermined outcomes Settings where consensus is required
Improving group decisions
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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
Improving group decisions
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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
Improving group decisions
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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
Improving group decisions
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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)
Improving group decisions
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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)
Improving group decisions
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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 roundUncertainty = difference between the upper and lower
quartile
Improving group decisions
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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
Improving group decisions
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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 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
Improving group decisions
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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
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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
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Voting - a social choice
N alternatives x1, x2, …, xn
K decision makers DM1, DM2, …, DMk
Each DM has preferences for the alternatives Which alternative the group should choose?
Voting procedures
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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
Voting procedures
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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
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
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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
B
C
A B C
- 18,15 18,15
15,18 - 32,1
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
Voting procedures
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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
3 states that B > C > A
2 states 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
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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
B
C
X - - X - X - X - 4
X X X X X X - X - 7
- - - - - - X - X 2
the winner!
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The Condorcet paradox (1/2)Consider the following comparison of the three alternatives
ABC
DM1 DM2 DM3
1 3 2 2 1 3 3 2 1
Paired comparisons: A is preferred to B (2-1) B is preferred to C (2-1) C is preferred to A (2-1)
Every alternative has a supporter!
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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
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.
A
B
C
DM1 DM2 DM3
1 3 2
2 1 3
3 2 1
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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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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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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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Requirements on the social choice function (1/2)
1) Non trivialThere are at least two DMs and three alternatives
2) Complete and transitive 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 what the individual preferences are
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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 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
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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 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
Suppose that DMs’ preferences do not change. A ballot between the 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
The fourth criterion is not satisfied!
Alternative x2
is the winner!
Alternative x1
is the winner!
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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
Value function describes also the strength of the preferences
Value
beer
1
wine tea
Value
beer
1
wine tea
DM1: beer > wine > tea DM1: tea > wine > beer
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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