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


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

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.


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...

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


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


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



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



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



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 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




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




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



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

http://www.rand.org/

http://www.mcda.hut.fi/voting/theory/Gordon.html

http://www.mcda.hut.fi/voting/theory/Gordon.html



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




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




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)




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)




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




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



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



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


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


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


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


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


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


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


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!


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!


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


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


Coalitions

If the voting procedure is known voters may form coalitions that serve their purposes Eliminate an undesired alternative Support 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 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.


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


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


Arrow’s theorem

There is no complete and transitive f satisfying the conditions 1-6


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!


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.


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


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

Group decisions and voting

Documents

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