1. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

2. eLearning / MCDA Systems Analysis Laboratory Helsinki 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

3. eLearning / MCDA Systems Analysis Laboratory Helsinki 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.

4. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 thinkGroup think  Pressures to conformity...

5. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

6. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

7. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

8. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

9. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

10. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

11. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

12. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

13. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 1950sRAND Corporation  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 A Delphi forecasts by Gordon and Helmer

14. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

15. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

16. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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)

17. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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)

18. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

19. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

20. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

21. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

22. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

23. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Voting - a social choice  N alternatives x 1, x 2, …, x n  K decision makers DM 1, DM 2, …, DM k  Each DM has preferences for the alternatives  Which alternative the group should choose?

24. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

25. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

26. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 ABCABC A B C -18,1518,15 15,18 -32,1 15,181,32 -  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

27. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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

28. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 DM 1 DM 2 DM 3 DM 4 DM 5 DM 6 DM 7 DM 8 DM 9 total ABCABC X - - X - X - X - 4 X X X X X X - X - 7 - - - - - - X - X 2 the winner!

29. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology The Condorcet paradox (1/2) Consider the following comparison of the three alternatives A B C DM 1 DM 2 DM 3 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!

30. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 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 DM 1 DM 2 DM 3 1 3 2 2 1 3 3 2 1

31. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Strategic voting  DM 1 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 DM 2 and DM 3 vote according to their preferences

32. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Coalitions  If the voting procedure is known voters may form coalitions that serve their purposes  Eliminate an undesired alternative  Support a commonly agreed alternative

33. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Weak preference order The opinion of the DM i about two alternatives is called a weak preference order R i : The DM i thinks that x is at least as good as y  x R i 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(R 1,…,R k )?  Voting procedures are potential choices for social choice functions.

34. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Requirements on the social choice function (1/2) 1) Non trivial There are at least two DMs and three alternatives 2) Complete and transitive R i :s If x  y  x R i y  y R i x (i.e. all DMs have an opinion) If x R i y  y R i z  x R i z 3) f is defined for all R i :s The group has a well defined preference relation, regardless of what the individual preferences are

35. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 DM i such that x R i y  x R y

36. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Arrow’s theorem There is no complete and transitive f satisfying the conditions 1-6

37. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Arrow’s theorem - an example Borda criterion: DM 1 DM 2 DM 3 DM 4 DM 5 total x 1 33121 10 x 2 22313 11 x 3 11200 4 x 4 00032 5 Suppose that DMs’ preferences do not change. A ballot between the alternatives 1 and 2 gives DM 1 DM 2 DM 3 DM 4 DM 5 total x 1 11010 3 x 2 00101 2 The fourth criterion is not satisfied! Alternative x 2 is the winner! Alternative x 1 is the winner!

38. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Value aggregation (1/2) Theorem (Harsanyi 1955, Keeney 1975): Let v i (·) be a measurable value function describing the preferences of DM i. There exists a k-dimensional differentiable function v g () with positive partial derivatives describing group preferences > g in the definition space such that a > g b  v g [v 1 (a),…,v k (a)]  v g [v 1 (b),…,v k (b)] and conditions 1-6 are satisfied.

39. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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 winetea Value beer 1 winetea DM 1 : beer > wine > teaDM 1 : tea > wine > beer

40. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology 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