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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. Contents. Group characteristics Group decisions - advantages and disadvantages

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Group decisions and voting l.jpg

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


Contents l.jpg
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


Group characteristics l.jpg
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


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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


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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

  • 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


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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


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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


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Improving group decisions

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


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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


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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

    • Routine business

    • Bargaining

    • Problems with predetermined outcomes

    • Settings where consensus is required


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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


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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


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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


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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)


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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)


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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


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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


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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

  • 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


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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


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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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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 - a social choice


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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


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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

3+2 = 5 votes for B

4 votes for A

3 votes for B

2 votes for C

A is the winner

B is the winner


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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 B C

  • 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

A

B

C

- 18,15 18,15

15,18 - 32,1

15,18 1,32 -


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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

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


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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

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

the winner!


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Consider the following comparison of the three alternatives

DM1 DM2 DM3

A

1 3 2

B

2 1 3

C

3 2 1

The Condorcet paradox (1/2)

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)


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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.


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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 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


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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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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

DM1 DM2 DM3 DM4 DM5 total

x11 1 0 1 0 3

x2 0 0 1 0 1 2

Arrow’s theorem - an example

Borda criterion:

Alternative x2is the winner!

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

Alternative x1is the winner!

The fourth criterion is not satisfied!


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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

DM1: beer > wine > tea

DM1: tea > wine > beer

Value

Value

1

1

beer

wine

tea

beer

wine

tea


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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


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