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 • 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...
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
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
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
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
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
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
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
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
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
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
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)
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)
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
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
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
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
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
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
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 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
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 -
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
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!
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)
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.
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 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
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
Arrow’s theorem There is no complete and transitive f satisfying the conditions 1-6
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!
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 DM1: beer > wine > tea DM1: tea > wine > beer Value Value 1 1 beer wine tea beer wine tea
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