1 voting methods chapter 1 preliminaries 1.1 preference schedules 2 preference schedules section 1.1
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1
Voting Methods
Chapter 1
Preliminaries
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1.1 Preference Schedules 2
Preference Schedules
Section 1.1
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1.1 Preference Schedules 3
“Majority” means
1. 50%
2. More than 50%
3. 50% or more
4. More than anyone else
Think, Murmur, Vote
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1.1 Preference Schedules 4
Two Types of Elections
1. Two – Candidate
2. Multi – Candidate
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1.1 Preference Schedules 5
Your (hypothetical) Grade
Tests = 50% Participation = 10% How would you like to determine the
remaining 40%?
1. 3 short papers2. 15-minute class
presentation
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Pie-chart of last vote
“Majority rules”
Option 1
Option 2
is the . winner
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1.1 Preference Schedules 7
2006 - Connecticut Congressional Race
121,248 votes121,157 votes
Courtney won with a 50.00188% majority
Rob Simmons
Joe Courtney
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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
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1.1 Preference Schedules 9
In this course – No ties!
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1.1 Preference Schedules 10
Summary of Two-Candidate Elections
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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
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1.1 Preference Schedules 12
Presidential Election
George H. W. Bush
(Republican Incumbent)
Bill Clinton
(Democratic Challenger)
H. Ross Perot
(Independent)
43%37%
1992
19.8 %
Clinton wins
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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
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1.1 Preference Schedules 14
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
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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
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1.1 Preference Schedules 16
CBA
CBA
ACB
ACB
ACB
ACB
BCA
ACB
BCA
BCA
CBA
BCA
Mathematical Model
Better
Preference Schedule
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1.1 Preference Schedules 17
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
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1.1 Preference Schedules 18
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
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1.1 Preference Schedules 19
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?
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1.1 Preference Schedules 20
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
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1.1 Preference Schedules 21
End of 1.1
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Grading
• 4 Exams 80%
• Final Project 20%
• No final exam
• No extra credit at end of semester
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1.1 Preference Schedules 23
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
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1.1 Preference Schedules 24
Final Project
• PowerPoint Presentation - last week of classes
• More info later
• Team projects okay (no more than 2 per team)
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1.1 Preference Schedules 25
Homework
• On “Blackboard”
• Not collected
• Answers in text
• Test questions
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• Expected
• Limit = 3 (T/TH) 4 (MWF) missed classes
• Miss a class? Your responsibility to get the material
Attendance
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1.1 Preference Schedules 27
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
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My Teaching Style
• Graphics >
Text
• QED’s
• P. I.
• Clickers
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1.1 Preference Schedules 29
M116 Mantra
Murmur
Vote
Think
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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?
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NOGeometry?
NOPrecalculus?
Algebra?
NO
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Think?
YES!
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1.1 Preference Schedules 33
You are enrolled in
1. College of Arts and Sciences
2. College of Education
3. Hartford Art School
4. Hartt School
5. Other
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1.1 Preference Schedules 34
You are a
1. Freshman
2. Sophomore
3. Junior
4. Senior
5. Other
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1.1 Preference Schedules 35
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
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1.1 Preference Schedules 36
Your home state is
1. CT
2. MA
3. Other New England State
4. NY
5. NJ
6. Other
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1.1 Preference Schedules 37
Favorite baseball team
1. Red Sox2. Mets3. Other4. Yankees
5. Couldn’t care less
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1.1 Preference Schedules 38
Your interest in mathematics
1. 1
2. 2
3. 3
4. 4
5. 5
1 = low
5 = high
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1.1 Preference Schedules 39
Your ability in mathematics
1. 1
2. 2
3. 3
4. 4
5. 5
1 = low
5 = high
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1.1 Preference Schedules 40
Your expected grade in this course
1. A
2. B
3. C
4. D
5. Pass
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1.1 Preference Schedules 41
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
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1.1 Preference Schedules 42
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
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1.1 Preference Schedules 43
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
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Chapter 1
Voting Methods
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Why Study Voting?
• Math not covered in high
school
• Surprising results
• Nobel Prize involved
• Major influence on our
lives
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1.1 Preference Schedules 46
“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”
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1.1 Preference Schedules 47
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1.1 Preference Schedules 48
Meta-Material