Deck 8: Voting and Social Choice

Question 1

In a group of 50 voters, each person has one vote, and the quota is a simple majority. What is the Banzhaf power index for each voter?

A)1/2
B)13/50
C)13/25
D)1/50

Answer 1

D

Question 2

Suppose a country consists of 35 states, each of which is assigned a certain number of electoral votes. How many possible coalitions (each coalition including at least one state) are there?

A)
B)
C)
D)35! - 1

Answer 2

D

Question 3

Suppose there are only two voters. Arnold controls 160 votes, and the quota is 145 votes. What is Arnold's Shapley-Shubik index?

A)2/3
B)2/2
C)1/2
D)0/2

Answer 3

B

Question 4

Suppose there are five voters, A, B, C, D, and E, with 7, 6, 5, 4, and 3 votes, respectively. Suppose that a simple majority is required to win. What is the quota?

A)15
B)14
C)13
D)12

Question 5

A set of voters with enough votes to determine the outcome of an election is a:

A)determining coalition.
B)winning coalition.
C)powerful coalition.
D)dominating coalition.

Question 6

Suppose there are only two voters. Arnold controls 160 votes and the quota is 145 votes. What is Arnold's Banzhaf power index?

A)2/3
B)2/2
C)1/2
D)0/2

Question 7

Suppose there are three delegates to a county convention: Adam has 4 votes from his precinct, Bob has 3 votes, and Cathy has 1 vote. A simple majority wins. Which of the following is not a winning coalition?

A)Adam, Bob, and Cathy
B)Adam and Bob
C)Adam and Cathy
D)Bob and Cathy

Question 8

Suppose there are five voters, A, B, C, D, and E, with 7, 6, 5, 4, and 3 votes, respectively. Suppose that a simple majority is required to win. How many winning coalitions are there?

A)31
B)17
C)13
D)8

Question 9

In a group of 50 voters, each person has one vote, and the quota is a simple majority. What is the Shapley-Shubik index for each voter?

A)1/2
B)13/50
C)13/25
D)1/50

Question 10

Suppose that there are only three hypothetical states with a distribution of popular and electoral votes as shown in the table below. Find the Shapley-Shubik index for state A using the electoral vote. Assume that a simple majority is required.

A)1/6
B)1/3
C)2/3
D)5/6

Question 11

Suppose there are five voters, A, B, C, D, and E, with 7, 6, 5, 4, and 3 votes, respectively. Suppose that a simple majority is required to win. Find the swing voter when voters are in the following order: A, B, C, D, E.

A)A
B)B
C)C
D)D

Question 12

In a collection of six voters, how many different permutations are possible?

A)720
B)600
C)128
D)64

Question 13

In the system of _______________ voting, the candidate receiving more votes than any other candidate wins.

A)alternate
B)proportional
C)plurality
D)sequential

Question 14

In a voting system, the number of votes necessary to win the election is called the:

A)victor.
B)successor.
C)quota.
D)coalition.

Question 15

In a collection of four voters, how many different coalitions are possible?

A)24
B)16
C)15
D)12

Question 16

Suppose there are three delegates to a county convention: Adam has 14 votes from his precinct, Bob has 13 votes, and Cathy has 11 votes. A simple majority wins. What is the quota?

A)38
B)19
C)20
D)30

Question 17

Suppose that there are only three hypothetical states with a distribution of popular and electoral votes as shown in the table below. Find the ordering of the Shapley-Shubik indexes for states using the popular vote. Assume that a simple majority is required.

A)A < B < C
B)A = B < C
C)A < B = C
D)A = B = C

Question 18

The number of times that a voter is critical in some winning coalition divided by the total number of instances of critical voters is:

A)critical power index.
B)Banzhaf power index.
C)Shapley-Shubik index.
D)winning power index.

Question 19

A member of a winning coalition is said to be a _______________ for that coalition if the coalition is no longer a winning one when that voter is removed.

A)winning voter
B)critical voter
C)necessary voter
D)swing voter

Question 20

Suppose a country consists of 35 states, each of which is assigned a certain number of electoral votes. How many vote orders would we need to consider in order to calculate the Shapley-Shubik index for each state?

A)
B)
C)
D)35! - 1

Question 21

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)14
B)27
C)47
D)50

Question 22

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 23

In an election, a _______________ winner is a candidate who beats each of the other candidates in a one-on-one election.

A)Borda
B)Banzhaf
C)Shapely-Shubik
D)Condorcet

Question 24

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 25

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 26

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 27

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 28

The vote tally of ranked ballots for a slate of four candidates is as follows: Is there a Condorcet winner?

A)Yes, candidate C.
B)Yes, candidate D.
C)Yes, candidates C and D
D)No, there is no Condorcet winner.

Question 29

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 30

The Borda count assigns how many points to the choice ranked last?

A)0
B)1
C)2
D)3

Question 31

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)B, C, B
B)A, C, D
C)B, B, D
D)A, B, D

Question 32

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 33

In the elimination runoff system, if no candidate receives a majority then there is a new election with only the two highest vote-getters.

Question 34

If there are three or more candidates, there is no voting system (other than a dictatorship) for which both the Condorcet winner criterion and the independence of irrelevant alternatives hold.

Question 35

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 36

A(n) _______________ is a candidate who has no realistic chance of winning but whose presence in the election affects the outcome.

A)dark horse
B)spoiler
C)outlier
D)anomaly

Question 37

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 38

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 39

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 40

The vote tally of ranked ballots for a slate of four candidates is as follows:

A)A
B)B
C)C
D)D

Question 41

In the _______________ procedure, one person divides the items into two parts and the other person chooses which part he or she wants.

A)adjusted winner
B)divide-and-conquer
C)divide-and-choose
D)Knaster

Question 42

In the _______________ procedure, two people assign points to bid on each item, assigning a total of 100 points.

A)adjusted winner
B)divide-and-conquer
C)divide-and-choose
D)Knaster

Question 43

Adam and Brandy divide an art collection using the initial bids: What is the critical item?

A)Drawings
B)Paintings
C)Art supplies
D)No critical item.

Question 44

In the 1948 presidential election, the official popular vote tallies were as follows: Let's treat these results as voting blocks. Assume that the quota is determined by a majority vote. What is the Banzhaf index for each block?

A)1/6
B)2/6
C)3/6
D)4/6

Question 45

brother and sister divide an inheritance using the initial bids: What is the critical item?

A)Jewelry
B)Car
C)Cash
D)Library

Question 46

Amber and Matthew divide household items using the initial bids: Using the adjusted winner procedure, who is the leader?

A)Amber
B)Cooking utensils
C)Crockery
D)Furniture

Question 47

Adam and Brandy divide an art collection using the initial bids: Using the adjusted winner procedure, who initially receives the drawings?

A)Adam
B)Brandy
C)Each receives a share.
D)Neither

Question 48

To find the ideal size of a congressional district, we divide the U.S. population by the:

A)state's population.
B)state's quota.
C)House size.
D)Senate size.

Question 49

A brother and sister divide an inheritance using the initial bids: Using the adjusted winner procedure, what percentage of the library is transferred to the sister?

A)20%
B)25%
C)30%
D)35%

Question 50

Abby, Cody, Evelyn, and Ingrid inherent a house and wish to divide it. Using the Knaster procedure with the given bids, what is the size of the kitty?

A)$235,000
B)$265,000
C)$250,000
D)$210,000

Question 51

In the adjusted winner procedure, the person with the highest score is the __________, while the person with the lowest score is the ____________.

A)leader; loser
B)leader; trailer
C)winner; loser
D)winner; trailer

Question 52

The Knaster procedure is a method for dividing items among several parties, and it doesn't require dividing ownership of the items.

Question 53

Alice, Bobby, Cathy, and David wish to divide a business property. Using the Knaster procedure with the given bids, what is the size of the kitty?

A)$30,000
B)$32,000
C)$36,000
D)$38,000

Question 54

Amber and Matthew divide household items using the initial bids: Using the adjusted winner procedure, what percentage of the dishes is transferred to Amber?

A)40%
B)50%
C)56%
D)74%

Question 55

Adam and Brandy divide an art collection using the initial bids: Using the adjusted winner procedure, what percentage of the paintings is transferred to Brandy

A)26.7%
B)30.5%
C)33.2%
D)40.0%

Question 56

In the adjusted winner procedure, the first item whose transference would change the lead is the critical item.

Question 57

Adam and Brandy divide an art collection using the initial bids: Using the adjusted winner procedure, who is the leader?

A)Adam
B)Brandy
C)They are tied.
D)Neither

Question 58

There are four candidates in an election. The table shows a part of the winner of one-on-one election. Which of the following is correct?

A)Candidate A is the Condorcet winner.
B)Candidate B is the Condorcet winner.
C)Candidate D is the Condorcet winner.
D)There is no Condorcet winner.

Question 59

Amber and Matthew divide household items using the initial bids: Using the adjusted winner procedure, who is the leader?

A)Amber
B)Matthew
C)They split the dishes.
D)Neither

Question 60

Amber and Matthew divide household items using the initial bids: Using the adjusted winner procedure, who initially receives the dishes?

A)Amber
B)Matthew
C)They split the dishes
D)Neither

Question 61

Suppose that California, Arizona, and Nevada form a Board of Representatives to attract business to the region. There are to be 125 members of the board, and the membership from each state is determined by its population in 2010, given in the table below. Find the ideal district size for the coalition.

A)319,636.2
B)349,168.2
C)370,772.2
D)463,465.3

Question 62

The U.S. population in 1860 was 31,443,321 and the House size was set at 238. What was the ideal congressional district size in 1860?

A)238
B)31,443
C)16,905
D)132,115

Question 63

Apportionment methods that do not stay within quota are said to violate quota.

Question 64

The congressional district size in 1860 was 132,115. The population of New York was 805,658. What was New York's quota in 1860?

A)433.1
B)71.0
C)6.1
D)4.7

Question 65

The U.S. Constitution states that the minimum size of a congressional district is 30,000 people. The U.S population in 1990 was 248,709,873. If each district size were 30,000 people, how many House members would there have been in 1990?

A)2487
B)3000
C)5678
D)8290

Question 66

A small town elects a total of 12 board members from four districts, North, South, East, and West. The populations of each district are shown below.

A)82.75
B)83.33
C)83.89
D)84.25

Question 67

Which of the following shows a state's quota?

A)
B)
C)
D)

Question 68

A small town elects a total of 15 board members from four districts, North, South, East, and West. The populations of each district are shown below. Find the South's quota.

A)2.4
B)3.0
C)3.6
D)4.8

Question 69

A desirable trait of any apportionment method is to make the final apportionment for each state be ______________ the quota.

A)exactly the same as
B)within one of
C)within two of
D)within three of

Question 70

In 1990, the U.S. population was 248,709,873. There were 435 members of the House of Representatives. The population of Texas in 1990 was 17,044,714. What was Texas' quota in 1990?

A)24.5
B)43.5
C)17.0
D)29.8