1 voting methods chapter 1 preliminaries 1.1 preference schedules 2 preference schedules section 1.1

1

Voting Methods

Chapter 1

Preliminaries

1.1 Preference Schedules 2

Preference Schedules

Section 1.1


“Majority” means

1. 50%

2. More than 50%

3. 50% or more

4. More than anyone else

Think, Murmur, Vote


Two Types of Elections

1. Two – Candidate

2. Multi – Candidate


Your (hypothetical) Grade

Tests = 50% Participation = 10% How would you like to determine the

remaining 40%?

1. 3 short papers2. 15-minute class

presentation


Pie-chart of last vote

“Majority rules”

Option 1

Option 2

is the . winner


2006 - Connecticut Congressional Race

121,248 votes121,157 votes

Courtney won with a 50.00188% majority

Rob Simmons

Joe Courtney


A Dead Heat in Jackson Hole

• In 1994 Independent Larry Call and Republican Randall Luthi tied for a seat in the Wyoming House of Representatives

• State voting law required “ping pong ball” solution

Luthi

Mr. LuthiMr. Call

Call


In this course – No ties!


Summary of Two-Candidate Elections


Multi-Candidate ElectionsCandidates = A, B, C

Which is the best answer?

1. Some candidate must get a majority of the votes

2. Two candidates will each get a majority of the votes

3. No candidate might get a majority of the votes


Presidential Election

George H. W. Bush

(Republican Incumbent)

Bill Clinton

(Democratic Challenger)

H. Ross Perot

(Independent)

43%37%

1992

19.8 %

Clinton wins


There are 4 candidates - A, B, C, D - in an election. 65 people vote. Who

wins?

1. A

2. B

3. C

4. D

20 19 15 11

A B C DD C B CC D D AB A A B


Stem Cell Policy12-person Presidential Commission

1. Allow unrestricted use of federal funds

2. Ban all federal support

3. Compromise by using federal funds only when no harm is done to an embryo


Each of the 12-members on the commission lists (in order from top to bottom) their 1st, 2nd and 3rd choices

B

C

A

These are called .

Cartoon


CBA

CBA

ACB

ACB

ACB

ACB

BCA

ACB

BCA

BCA

CBA

BCA

Mathematical Model

Better

Preference Schedule


Rewrite the last preference schedule one row at a time

2nd place votes

3rd place votes

5 34

A CB

C BC

B AA

1st place votes


Why we need this mathematical model- 50 voters -

CBA

CBA

ACB

ACB

BAC

ABC

BCA

ACB

BAC

BCA

CBA

BCA

CBA

CBA

CAB

ACB

ABC

CAB

BCA

BCA

BAC

BCA

CBA

BAC

CBA

CBA

ABC

BCA

ACB

ACB

BCA

ACB

CBA

BCA

CBA

BCA

CAB

CBA

ACB

ACB

ABC

CAB

CBA

ACB

BCA

BAC

CBA

BAC

ACB

BCA


Better 1

312

11

6 4 4

C B A B C A

B C C A A B

A A B C B C1. What does each column mean?

2. All possible types of ballots for 3 candidates?


How many different types of preference ballots are possible for 4 candidates – A, B, C, D?

1. 4

2. 10

3. 16

4. 24

5. 30


End of 1.1


Grading

• 4 Exams 80%

• Final Project 20%

• No final exam

• No extra credit at end of semester


Exams

• Miss an exam? Contact me within 24 hours to qualify for a make-up

• Make-up policy: last day of classes - 7 a.m. – here

• Exams 2 - 4 may cover earlier material


Final Project

• PowerPoint Presentation - last week of classes

• More info later

• Team projects okay (no more than 2 per team)


Homework

• On “Blackboard”

• Not collected

• Answers in text

• Test questions


• Expected

• Limit = 3 (T/TH) 4 (MWF) missed classes

• Miss a class? Your responsibility to get the material

Attendance


Miscellaneous

• TI-83+ (or TI-84) graphing calculator

• I’ll distribute handouts for each chapter

• Read e-mail. Notify me if you're not receiving it.

• Please, no attachments with your email

28

My Teaching Style

• Graphics >

Text

• QED’s

• P. I.

• Clickers


M116 Mantra

Murmur

Vote

Think

30

Overview of Course

• Contemporary Mathematics

• Higher level mathematics that you

can do

• Good news

– 4 unrelated topics

– Applications

So - what do you need to know?

31

NOGeometry?

NOPrecalculus?

Algebra?

NO

32

Think?

YES!


You are enrolled in

1. College of Arts and Sciences

2. College of Education

3. Hartford Art School

4. Hartt School

5. Other


You are a

1. Freshman

2. Sophomore

3. Junior

4. Senior

5. Other


Your favorite presidential candidate was

(in alphabetical order)

1. Bob Barr

2. John McCain

3. Ralph Nader

4. Barack Obama

5. None of the above


Your home state is

1. CT

2. MA

3. Other New England State

4. NY

5. NJ

6. Other


Favorite baseball team

1. Red Sox2. Mets3. Other4. Yankees

5. Couldn’t care less


Your interest in mathematics

1. 1

2. 2

3. 3

4. 4

5. 5

1 = low

5 = high


Your ability in mathematics

1. 1

2. 2

3. 3

4. 4

5. 5

1 = low

5 = high


Your expected grade in this course

1. A

2. B

3. C

4. D

5. Pass


On average how many times a day do you use Facebook?

1. 0

2. 1 - 10

3. 11 - 20

4. 21 - 50

5. More than 50


On average how many times a day do you text message?

1. 0

2. 1 - 10

3. 11 - 20

4. 21 - 50

5. More than 50


Each day you use this medium the most

1. Cell phone calls

2. E-mail

3. Facebook

4. Text messaging

5. None. I’m a Luddite

Chapter 1

Voting Methods

45

Why Study Voting?

• Math not covered in high

school

• Surprising results

• Nobel Prize involved

• Major influence on our

lives


“President” Tom Dobbs as played by Robin

Williams in the movie Man of the Year

“Politicians are like diapers.

They ought to be changed

frequently and for the same

reason”


Meta-Material

1 voting methods chapter 1 preliminaries 1.1 preference schedules 2 preference schedules section 1.1

Documents

preference schedules

vote slide

preliminaries slide

embryo slide

winner slide

cartoon slide

multi candidate slide

rd choices bcabca