Negotiation Analytics 30C02000 Jyrki Wallenius Lecture 6: Guest Lecture by Johanna Bragge and Negotiating with more than two parties -- Voting Original lecture slides: Pirkko Lahdelma

Today’s objectives Johanna Bragge’s guest lecture: pseudo-mock negotiations, with a case about energy taxation dispute in Finland See Raiffa pages 379-380 What are pseudo-mock negotiations and why are they sometimes useful Real-world application To learn how different voting procedures work 2

Voting When people disagree but must act collectively, they often resort to various voting mechanisms to resolve their conflict.

Vote for the best If there are two candidates, the candidate who gets the most votes, wins If there are more than two candidates, the situation is not as clear any more: 21 voters, 4 candidates {a,b,c,d}, and one vote per a voter (i.e. each voter votes one candidate) Candidate “a”: 8 votes Candidate “b”: 7 votes Candidate “c”: 6 votes Candidate “d”: 0 votes Candidate “a” wins Or we could vote again between the two candidates who received most votes

Ranking – more information Assume voters rank all the candidates; the distribution of votes is: Number of voters 3 5 7 6 Best a a b c 2. choice b c d b 3. choice c b c d Worst d d a a The candidate “a” is the best for 8 voters, but the worst for 13 voters More comparisons: a vs b: b better than a according to 13 persons b vs c: c better than b according to 11 persons c vs d: c better than d according to 14 persons  Now, the winner is the candidate “c”

Majority rule: most common voting scheme Many candidates: someone who gets majority in first round, wins If nobody gets majority in first round, conduct second round between the two who received most votes Wyzard, Inc. Wysocki, Yarosh, and Zullo Joint owners of Wyzard, Inc. A proposal to start construction of a new factory in the next year Debate about where the new factory should be located: Allston Brockton Cohasset

Majority rule continued Wysocki Yarosh Zullo First choice C A B Second choice Third choice Here, majority rule generates intransitives in paired comparisons: majority prefer A over B, and B over C; yet majority prefers C over A!

Ranking, with two more alternatives Mr. Pumper (the realtor) has found two more options: Dedham Essex Each one ranks all the choices by giving points (from 1 to 5, where 5 is the best) Allston wins Individual ranking (5 = best)   Wysocki Yarosh Zullo Total Allston 5 2 12 Brockton 3 11 Cohasset 1 4 7 Dedham 6 Essex 9

Wyzard, Inc. – strategic voting? Mr. Pumper tells that Essex is not available any more The comparison table will be corrected in the following way: Oops, now Brockton has won “Has Zullo voted insincerely in order not to get Allston to be chosen?” “Can we change our rankings and manipulate the results?” Individual ranking (4 = best)   Wysocki Yarosh Zullo Total Allston 4 1 9 Brockton 3 10 Cohasset 2 6 Dedham 5

Approval Voting Due to Fishburn Each person eligible to vote indicates who/which project she would approve Can indicate more than one person/project The winner is the one who has most approval votes Several scientific associations use this when choosing their officers Subject to manipulation

About Voting: Arrow’s impossibility theorem There is a group of N (N at least 2) individuals, who wish to give a group ranking (ordinal) for a set of alternatives ranked by individuals (according to the conditions of the Arbitration Rule: 5 different conditions)? Can you do it? No, there does not exist such a group ranking

Conditions of the Arbitration Rule (Group Ordering) Condition 4: Citizen’s Sovereignty For each pair of alternatives (x and y) there is some profile of individual orderings such that the group prefers x to y (i.e. individual votes count) Condition 5: Non-dictatorship There is no individual with the property that whenever he or she prefers x to y, the group also prefers x to y Condition 1 There are at least 3 alternatives There are at least 2 individuals The group ordering is defined for all possible combinations Condition 2: Positive Association If, in any individual ordering, an alternative x is pushed up and all else remain fixed, then x should not be pushed down in the group ordering Condition 3: Independence of Irrelevant Alternatives The group ordering of any two alternatives, x and y, should depend only on the individual orderings of x and y. Arrow’s impossibility theorem: There exists no such arbitration rule which meets all these conditions = There is no rank order based voting system that is fair according to these conditions.

A way to get around Strength of preference John Kyle Lisa Utility A B C + C B A A B - C 12/2/2018

Examples of courses which can deepen your knowledge Business Decisions 1 /27C01000 Juuso Liesiö Linear programming, Integer programming, Goal programming, Nonlinear programming, and Decision Analysis with Excel Solver Business Decisions 2 /30C00400 Decision Analysis, Multiple Criteria Decision Making, Waiting Line Models and Simulation The emphasis is on probabilistic aspects Decision Making and Choice Behavior (masters course) Eeva Vilkkumaa Rational DM axioms, their criticism, Prospect Theory, Biases

About the exam… It might include: Problems to be solved (calculations but without Excel) Short essay questions If there are restrictions on e.g. the length of the answer, you should follow them An essay is not a bulleted list but consists of complete sentences Definitions If you fail in the exam OR if you pass the exam but are dissatisfied with your grade, you can retake it in Fall 2018 I strongly recommend participating in the exam this spring

Recap – about the theory Fundamentals Negotiations in general (typical situations, skills) Decision Analysis: Expected monetary and utility values Decision traps and prediction anomalies Game theory Basic concepts for win-lose negotiations (RVs, ZOPA, etc) and complications for 2-party win-loose negotiations Uncertainty (decision trees) Time Hardball tactics Win-win integrative negotiations (phases) Efficient and extreme-efficient solutions Fair division Behavioral realities Third party intervention (different types, reasons to use, reasons not to use) Multi-party negotiations Fair division with/without monetary transactions between many parties Coalitions Voting