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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


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 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   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

				
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