1. 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

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

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

4. 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

5. Ranking – more information
Assume voters rank all the candidates; the distribution of votes is:
Number of voters
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”

6. 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

7. 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!

8. 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

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

10. 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

11. 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

12. 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.

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

14. 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

15. 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

16. 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