Voting

Decision making in group





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

 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



 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

 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

 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







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

 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 forecasts 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 eLearning / MCDA

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 eLearning / MCDA

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 eLearning / MCDA

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 eLearning / MCDA

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 eLearning / MCDA

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 eLearning / MCDA

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



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 eLearning / MCDA

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 eLearning / MCDA

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?

Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

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





Plurality voting Run-off



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 B is the winner





Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

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 - 18,15 18,15

B 15,18 - 32,1  A is better than B by 18:15

C 15,18 1,32 -  A is the Condorcet winner



 Similarly, C is the Condorcet loser



Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

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 eLearning / MCDA

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 the winner!

C - - - - - - X - X 2









Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

The Condorcet paradox (1/2)

Consider the following comparison of the three alternatives



DM1 DM2 DM3

A 1 3 2

Every alternative

B 2 1 3

has a supporter!

C 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)



Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

The Condorcet paradox (2/2)

Three voting orders: DM1 DM2 DM3

A 1 3 2

1) (A-B)  A wins, (A-C)  C is the winner B 2 1 3

2) (B-C)  B wins, (B-A)  A is the winner C 3 2 1



3) (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.



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





Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

Coalitions



 If the voting procedure is known voters may

form coalitions that serve their purposes

 Eliminate an undesired alternative

 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



 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.

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 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 eLearning / MCDA

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





Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

Arrow’s theorem









There is no complete and transitive f

satisfying the conditions 1-6









Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

Arrow’s theorem - an example

Borda criterion:

DM1 DM2 DM3 DM4 DM5 total

x1 3 3 1 2 1 10

Alternative x2

x2 2 2 3 1 3 11

is the winner!

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

Alternative x1

is the winner!

x2 0 0 1 0 1 2





The fourth criterion is not satisfied!



Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

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.



Systems Analysis Laboratory

Helsinki University of Technology eLearning / MCDA

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 eLearning / MCDA

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