Transcript Voting Methods (4/27-4/28)

Many Ways to Pick a Winner


We are all used to voting for whoever we want
to win, with the person receiving the most
votes declared the winner. This system works
pretty well when there are only two
candidates, but when there are more it
creates some problems.
What is one problem that might happen when
more candidates run?

In order to get more information from voters,
a better way to hold an election is to allow
voters to rank order the candidates rather
than just pick their favorite. This shows not
only who you want to win, but also who you
want to lose (and everyone in-between).

A Preference Ballot would look something like
this:


When all of the preference ballots are
counted, the results are placed in a
preference table. The numbers at the top
represent the number of people who have a
ballot that looks like the one below that
number.
If the four candidates were Fred, Wilma,
Barney, and Dino…

A Preference Table would look something like
this:
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes
Who should win this election?

This is the method that many people are
most comfortable with. In this method, the
person with the most 1st place votes wins (so
only look at the 1st row to determine the
winner.

In this example, Fred has 210 votes, Wilma
has 185+90=275 votes, and Barney has 315
votes. Therefore, Barney wins the election.
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

In a Borda Count, the different places are
assigned different point values. Last place
gets 1 point, and it increases by 1 point every
time you go up one place (i.e. 2nd to last
equals 2 points, next best place equals 3
points, etc.) The person with the most total
points will win the election.
This is an example of
the Borda count in
action…





Here are the totals in this example:
Fred=4*210 +3*500 +2*90 = 2520 pts
Wilma = 4*275 + 3*210 + 2*315 = 2360 pts
Barney = 4*315 + 2*210 + 1*275 = 1955 pts
Dino = 3*90 + 2*185 + 1*525 = 1165 pts


Fred wins the election
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

P. 735-736; #2, 3, 5, 7, 8, 11, 12


In this method, you find the candidate with the
fewest number of 1st place votes and eliminate
them from the race. All the votes in that
column move up one place (the 2nd place votes
now become the 1st place votes)
This process continues until someone has a
majority (or there is a tie)

In this example, Dino has the fewest 1st place
votes, so he is removed from the race, and the
votes in that column move up one place.
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Fred now has the fewest first place votes, and
is the next to go.
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
F
3rd choice
B
B
W
B
Number of Votes
4th choice

Since Wilma now has 210+185+90 = 485 votes,
she has a majority and is declared the winner
of the election.
210
185
315
90
1st choice
W
W
B
W
2nd choice
B
B
W
B
Number of Votes
3rd choice
4th choice
Election-swaying.com. Slapupsidethehead.com


In this method, you compare candidates two at
a time and see who would win in each column.
The candidate who would be victorious with a
majority of the voters would win that
comparison.
Each comparison victory is worth 1pt. Each tie
is worth ½ pt. Whoever has the most points
wins the election.

In this example, there will be 6 different
comparisons. The number is determined by n(n1)/2, where n is the number of candidates.
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Between Fred & Wilma, Fred wins in 525 votes,
while Wilma wins in 275 votes, so Fred beats
Wilma (and gets 1 pt).
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Between Fred & Barney, Fred wins in 485 votes,
while Barney wins in 315 votes, so Fred beats
Barney (and gets 1 pt).
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Between Fred & Dino, Fred wins in 525 votes,
while Dino wins in 275 votes, so Fred beats
Dino (and gets 1 pt).
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Between Wilma & Barney, Wilma wins in 485
votes, while Barney wins in 315 votes, so Wilma
beats Barney (and gets 1 pt).
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Between Wilma & Dino, Wilma crushes Dino
with 800 votes to Dino’s none, so Wilma
defeats Dino soundly (and gets 1 pt).
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

Between Barney & Dino, Barney gets 525 votes
to Dino’s 275, so Barney defeats Dino (and
gets 1 pt).
210
185
315
90
1st choice
F
W
B
W
2nd choice
W
F
F
D
3rd choice
B
D
W
F
4th choice
D
B
D
B
Number of Votes

The final totals in this election are:

Fred = 3 pts
Wilma = 2 pts
Barney = 1 pt
Dino = 0 points

So Fred wins the election.



Hipster-election-2004.gif. Toothpastefordinner.com

P. 735-737; #16-17, 19-20, 23-24, 27-30