Math and Politics Lecture 1:
Email of Professor: Andrew.firstname.lastname@example.org
TA- Katie Sulivan KJS227@cornell.edu
The winner of an election should be the candidate of the first choice of more votes than
Makes a parallel to Al Gore and Bush el
Prop: S. ONeil is the tallest man in the world.
Pf: ONeil is the tallest basketball player This is not a proof
Prop: S. ONeil is NOT the tallest man in the world.
Pf: Find someone taller! Counter example!
-More Yes-No voting time:
Conservative Convention: If for other player at their turn they have to decide between two bids
which lead to the same pay-off, then they will choose the smallest bid.
This is a sequential game.
1. There are tw
Individual HW: Q 23, 41
Group HW: Q 29, 33, 35, 37
Recap: Social Choice Procedure
Input [Voter Profile] Output
Voter profile Social Choice Set cfw_b
What is wrong with plurality?
-Minority leadership because more people can
Recall: A social choice procedure takes input: voter profile and gives an output: social choice set.
Example: Majority rule n voters. The social choice set will consist of any candidate who is at the top of at least
n/2 preference lists.
Math and Politics Lecture 2:
Reminder: Homework due in on Tuesday Groups of 3.
Office hours this week (511 Mallot) Mon 9-10 and 11:10-12:10
Individual- Q 4, 8
Group- 9, 12, 17, 18
Social Choice Procedure- Input Output it can le
Math 1340: Maths and Politics, Spring 2012
Annie gets: apartment lease (35), entertainment system (20), washer-dryer (15). Total: 70.
Ben gets: pool table (25), antique table (20). Total: 45.
Math 1340: Math and Politics (Spring 2012)
Please be concise in your answers. 1. If there were only two candidates running for President of the United States, (a) would majority rule dictate the winner of the election? Explain. (You might want
Math 1340: Maths and Politics, Spring 2012 Homework Solutions Homework 1 Problem 1 (a) Majority rule (whereby the person who receives more than 50% of the popular vote is elected) would not dictate the winner of the US presidential election in a two-way c
Prelim on Thursday PLS 233 Starts at 7:30PM
HW for 2nd AprilIndividual: Q21, 27
Group: Q24, 28
e.g. Tic-tac-toe, chess
Theory of Moves
1. An initial state is chosen ie a choice of strategy for each player
Definition: A minimal winning coalition is the smallest winning coalition that you can get. This
group exists if the condition satisfies the criterion that if any member of the coalition is removed
Mathematics and Politics Lecture 4: Finishing the Chart of SP criterion
Prelims are evenings of Feb 19, March 28
Email him if you have a conflict
Hare- A B D
Borda- B wins
The Donation Paradox
Total BPBI (A)- 9/19
BI (B)- 7/19
BI (C)- 1/19
A gives a vote to B
Individual HW: Q4, 8
Group: Ch1: Q39, 42
Ch2: Q1, 9
+ read The fairest vote of all
Consider the following SCP:
According to 2000 dates:
BI of California -11.4%
BI of NY- 5.6%
BI of DC- 0.5%
Pop of these states- BI/10,000,000 ppl
Cali= 33.8 million . 3.4%
NY= 18.9 million .2.9%
Game Theory Time:
This trend c
Yet another divorce settlementApartment
Rare Wine Collection
Note: There are their honest valuations.
Ann- 30+15+35+10= 90
Ann is the i
Office Hours: 511 Mallot. 9:30-12:00
HW: Ind: Q13,26
Group: Q17, 18, 19, 21
Will not be graded, but may appear on prelim
Prelim: Tuesday, starting promptly at 7:30pm. PLS 233 (Plant Sciences, Ag Quad)
State of Being
State of Emergency 33
New Los Florida
State of the Union
Calculate SSI for A, B, C:
List winning coalitionsA+C
AA B B C C
Therefore A is pivotal four times out of 6 possible options As SSI is 2/3
Odd because even though B has
Reminder: Us federal system has one president and VP and 100 Senators and 435 members of
Let x be a coalition. If x contains P, then it will be winning if it contains at least 51 senato
Mo Game Theory
Split or Steal!
This game is called chicken.
both lose face, but survive
Why Did Lance Armstrong Cheat?
Rivalry between Armstrong and Jan Ullrick. In 2002, Ullrick was caught cheating and tested
positive for performance enhancing drugs.
Armstrong has the choice to:
(Due Thursday February 9 in class) Math 1340: Math and Politics (Spring 2012)
Please be concise in your answers. The homework seems long but that's because there's a lot to read in problems 3 and 4. Courage! 1. Exercise 36 in Chapter 1 of the t
Math 1340: Maths and Politics, Spring 2012 Homework Solutions Homework 2
Problem 1 Paris would clearly lose in a winner-by-majority or plurality contest since it is not the first choice of most of Kate's friends. Nor is it the Condorcet winner. Kate could
(Due Thursday February 16 in class) Math 1340: Math and Politics (Spring 2012)
Only 2 pages this time, it even fits in one piece of paper if you print double-sided! Please be concise in your answers. 0. Read the proof of Arrow's theorem in the
(Due Thursday April 26 in class) Math 1340: Math and Politics (Spring 2012)
Please provide complete justifications in all your answers. 1. Exercises 33 in Chapter 4 of the textbook. 2. Exercise 34 in Chapter 4 of the textbook (you did the one
(Due Thursday May 3 in class) Math 1340: Math and Politics (Spring 2012)
Please provide complete justifications in all your answers. 1. Exercise 7 in Chapter 5 of the textbook, plus (c) Prove that the divide-and-choose procedure does not guara