Voting

Review Material

Walking

Voting - Review 3

How many people voted in this election?

13 9 12 11

A B C D

B C A C

D D D B

C A B A

1. 13

2. 35

3. 45

4. 55

5. Can’t tell

Voting - Review 4

How many different preference ballots are there for an election with 6 candidates?

1. 6

2. 21

3. 36

4. 120

5. 720

6. None of the above

Voting - Review 5

A preference schedule can have a row in which the same candidate appears twice

1. True

2. False

3. Can’t tell

Voting - Review 6

What’s wrong with this preference schedule?

1. Column 1

2. Column 2

3. Column 3

4. Nothing

5 2 3

A B C

B C B

C A C

Voting - Review 7

“Plurality” means

1. Most number of votes

2. 50% of the votes

3. More than 50% of the votes

4. More votes than most of the candidates

Voting - Review 8

Who wins using Plurality?

1. A

2. B

3. C

4. D

13 9 12 11

A B C D

B C A B

D D B C

C A D A

Voting - Review 9

Who wins using IRV?

1. A

2. B

3. C

4. D

13 9 12 11

A B C D

B C A B

D D B C

C A D A

Voting - Review 10

Who wins using Hare?

1. A

2. B

3. C

4. D

13 9 12 11

A B C D

B C A B

D D B C

C A D A

Voting - Review 11

Who wins using Borda?

1. A

2. B

3. C

4. D

13 9 12 11Pts

A B C D 3

B C A B 2

D D B C 1

C A D A 0

Voting - Review 12

Who wins using Condorcet?

1. A

2. B

3. C

4. D

13 9 12 11

A B C D

B C A B

D D B C

C A D A

Voting - Review 13

Who wins using Approval?(Voters approve of the candidates in

RED)

1. A

2. B

3. C

4. D

13

912

11

A B C D

B C A B

D D B C

C A D A

Jogging

Voting - Review 15

An election involves three candidates. The preference schedule has two columns. So, there must be a majority winner.

1. True

2. False

3. Can’t tell

Voting - Review 16

A Plurality winner

1. Must be a majority winner

2. Can be a majority winner

3. Cannot be a majority winner

Voting - Review 17

The greatest flaw of Plurality voting is

1. Time consuming

2. A small plurality could win

3. Encourages voter apathy

4. Costly

5. Difficult to carry out

Voting - Review 18

The greatest flaw of IRV is

1. A strong 3rd place finisher would be eliminated on 1st round

2. A small plurality could win

3. Time consuming

4. Costly

5. Difficult to explain

Voting - Review 19

An IRV winner always winds up with

1. A plurality

2. A majority

3. Neither

Voting - Review 20

If there are three candidates in an election IRV and Hare

1. Never choose the same candidate

2. Sometimes choose the same candidate

3. Always choose the same candidate

Voting - Review 21

Suppose that A is favored by a majority of the voters. Then the IRV method

1. Must choose A

2. May not choose A

3. Cannot choose A

Voting - Review 22

Suppose that A is favored by a majority of the voters. Then the Hare method

1. Must choose A

2. May not choose A

3. Cannot choose A

Voting - Review 23

On each re-tally, the Hare method eliminates the candidate with

1. The least number of first place votes

2. The most number of last place votes

3. Neither

13 9 12 11

A B C D

B C A C

D D D B

C A B A

Voting - Review 24

Suppose that A is favored by a majority of the voters. Then the Borda method

Must

choos

e A

May

not

choos

e...

Can

not c

hoose

...

0% 0%0%

1. Must choose A

2. May not choose A

3. Cannot choose A

0 of 5

Voting - Review 25

The Condorcet Method

Nev

er p

roduce

s a

wi...

Alw

ays

produ

ces

a w...

May

not

pro

duce

a w...

Can

pro

duce

two d

iff...

0% 0%0%0%

1. Never produces a winner

2. Always produces a winner

3. May not produce a winner

4. Can produce two different winners

0 of 5

Voting - Review 26

Using the Condorcet method, if A beats B, and B beats C, then

A m

ust b

eat C

A c

an’t

beat C

A m

ay b

eat C

0% 0%0%

1. A must beat C

2. A can’t beat C

3. A may beat C

0 of 5

Voting - Review 27

In the Approval method you

1. Can vote for any number of candidates

2. Cannot vote for all candidates

3. Must vote for at least 2 candidates

Voting - Review 28

Some voters exhibited irrational behavior when voting using the Approval method. How many columns contain highly suspicious entries?

1 c

olum

n

2 c

olum

ns

3 c

olum

ns

4 c

olum

ns

None

0% 0% 0%0%0%

1. 1 column

2. 2 columns

3. 3 columns

4. 4 columns

5. None

13

912

11

A B C D

B C A CD D D BC A B A

0 of 5

Voting - Review 29

Who wins?

A B C D

Can

’t te

ll

0% 0% 0%0%0%

1. A

2. B

3. C

4. D

5. Can’t tell

13 912

11

A B C D

B D D C

D C A B

C A B A

0 of 5

Running

Voting - Review 31

A student club has 10 members. They will use the Borda method (3 – 2 – 1 – 0) to elect A, B, C, or D president. A gets 19 points, B gets 20, and C gets 18. How many points does D get?

1. 3

2. 6

3. 9

4. 15

5. Can’t tell

Voting - Review 32

The Borda method will pick the same winner regardless of how the points are assigned to each preference level

1. True

2. False

Voting - Review 33

To show that Approval voting violates the Majority Criterion we must show

1. If a candidate wins using Approval, that candidate has a majority

2. If a candidate has a majority that candidate wins using Approval

Voting - Review 34

To show that Hare voting violates the Condorcet criterion we must show

1. There is a Condorcet winner but Hare doesn’t pick that candidate

2. The Hare winner is not a Condorcet winner.

Voting - Review 35

To show that Borda violates the Irrelevant Alternative criterion we must show that

1. C wins the 1st election but H wins the 2nd

2. C wins the 1st election but Me wins the 2nd

3. Me wins the 1st election but H wins the 2nd

End

Voting - Review 37

A candidate having a majority of the votes may not win using

1. Plurality and IRV

2. Plurality and Hare

3. Borda and Approval

4. Borda and Condorcet