1 / 40

Group decisions and voting

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

rosina
Download Presentation

Group decisions and voting

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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. 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. 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...

  5. 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. 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. 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. 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. 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. 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. 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. 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. 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

  14. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

  24. 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. 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

  26. 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 -

  27. 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. 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!

  29. 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)

  30. 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.

  31. 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

  32. 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. 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.

  34. 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

  35. 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

  36. Arrow’s theorem There is no complete and transitive f satisfying the conditions 1-6

  37. 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!

  38. 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.

  39. 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

  40. 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

More Related