Question 1

The Condorcet paradox
A)proved that the Arrow impossibility theorem is wrong.
B)was proved wrong by the Arrow impossibility theorem.
C)serves as an example of the Arrow impossibility theorem.
D)pertains to voting systems, whereas Arrow's Impossibility Theorem does not.

Accepted Answer

The Condorcet paradox serves as an example of the Arrow impossibility theorem. The paradox shows that when there are three or more options to choose from, it becomes impossible to satisfy all the criteria for a fair and consistent collective decision-making process, which is the central idea behind Arrow's Impossibility Theorem.

Question 2

The Condorcet voting paradox applies to situations in which voters
A)decide between exactly two possible outcomes.
B)decide among more than two possible outcomes.
C)as a group have transitive preferences.
D)choose the inferior candidate even though the majority preferred the better candidate.

Accepted Answer

The Condorcet voting paradox, also known as Condorcet's paradox, occurs when voters have transitive preferences (i.e., if A is preferred over B, and B is preferred over C, then A is preferred over C), but when a group is asked to choose between more than two possible outcomes, there is no clear winner because different outcomes win in pairwise comparisons (i.e., if A is compared to B, more people may prefer A, but if B is compared to C, more people may prefer B, and if C is compared to A, more people may prefer C). This paradox only applies to situations with more than two possible outcomes, making choice B the correct answer.

Question 3

Table 22-1
Three friends -- Linda, Stephanie, and Jamie -- are deciding where to go together for vacation. They all agree that they should go to one of three places: France, Greece, or Italy. They also agree that they will have two pairwise votes to determine where to go on vacation, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below. 
-Refer to Table 22-1. If the first vote pits France against Greece and the second vote pits Italy against the winner of the first vote, then the outcome is as follows:
A)France wins the first vote and Italy wins the second vote, so they go to Italy.
B)France wins the first vote and France wins the second vote, so they go to France.
C)Greece wins the first vote and Greece wins the second vote, so they go to Greece.
D)Greece wins the first vote and Italy wins the second vote, so they go to Italy.

Accepted Answer

The answer of Table 22-1
Three friends -- Linda, Stephanie, and...

Question 4

The Condorcet paradox demonstrates that the result of a majority vote may be affected by
A)moral hazard.
B)adverse selection.
C)the order of the votes.
D)All of the above are correct.

Accepted Answer

The Condorcet paradox demonstrates that the outcome of a majority vote can be influenced by the order of the votes. This paradox occurs when a group of individuals vote on three or more choices, and no single choice is the clear winner. Instead, different voting orders lead to different outcomes, which makes it difficult to determine a clear winner. Moral hazard and adverse selection are not directly related to the Condorcet paradox.

Question 5

Table 22-1
Three friends -- Linda, Stephanie, and Jamie -- are deciding where to go together for vacation. They all agree that they should go to one of three places: France, Greece, or Italy. They also agree that they will have two pairwise votes to determine where to go on vacation, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below. 
-Refer to Table 22-1. Depending on the order of the pairwise voting,
A)the friends could go to either France, Italy, or Greece.
B)the friends could go to either France or Italy, but they will not go to Greece.
C)the friends could go to either Italy or Greece, but they will not go to France.
D)the friends could go to either France or Greece, but they will not go to Italy.

Accepted Answer

Since there are three possible destinations and two pairwise votes, there are three possible outcomes:

1. France vs. Italy
2. Winner of vote 1 vs. Greece

No matter what order the votes are taken in, the friends could end up going to any of the three destinations, as each destination has the potential to be a winner in at least one pairwise vote. Therefore, choice A is the best answer.

Question 6

The Condorcet paradox shows that
A)allocations of resources based on majority rule are always inefficient.
B)problems in counting votes can negate legitimate democratic outcomes.
C)the order on which things are voted can affect the result.
D)transitive preferences are inconsistent with rationality.

Accepted Answer

The Condorcet paradox highlights that the order in which alternatives are voted upon can affect the result. This paradox occurs when there is no clear majority winner between three or more alternatives, even though each alternative may have a majority preference over one or more others in pairwise comparisons. The paradox shows that transitive preferences, which are consistent with rationality, may not result in a rational and clear overall outcome. Therefore, choice C is the best answer.

Question 7

Table 22-1
Three friends -- Linda, Stephanie, and Jamie -- are deciding where to go together for vacation. They all agree that they should go to one of three places: France, Greece, or Italy. They also agree that they will have two pairwise votes to determine where to go on vacation, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below. 
-Refer to Table 22-1. If the first vote pits France against Italy and the second vote pits Greece against the winner of the first vote, then the outcome is as follows:
A)France wins the first vote and Greece wins the second vote, so they go to Greece.
B)France wins the first vote and France wins the second vote, so they go to France.
C)Italy wins the first vote and Italy wins the second vote, so they go to Italy.
D)Italy wins the first vote and Greece wins the second vote, so they go to Greece.

Accepted Answer

The answer of Table 22-1
Three friends -- Linda, Stephanie, and...

Question 8

Table 22-1
Three friends -- Linda, Stephanie, and Jamie -- are deciding where to go together for vacation. They all agree that they should go to one of three places: France, Greece, or Italy. They also agree that they will have two pairwise votes to determine where to go on vacation, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below. 
-Refer to Table 22-1. If the first vote pits Greece against Italy and the second vote pits France against the winner of the first vote, then the outcome is as follows:
A)Greece wins the first vote and France wins the second vote, so they go to France.
B)Greece wins the first vote and Greece wins the second vote, so they go to Greece.
C)Italy wins the first vote and Italy wins the second vote, so they go to Italy.
D)Italy wins the first vote and France wins the second vote, so they go to France.

Accepted Answer

The answer of Table 22-1
Three friends -- Linda, Stephanie, and...

Question 9

Which of the following is a lesson from the Condorcet paradox?
A)If voters are choosing a point along a line, then majority rule will pick the most preferred point of the median voter.
B)Under certain conditions, there is no scheme for aggregating individual preferences.
C)When there are more than two options, deciding the order in which to vote can have a powerful influence over the outcome of an election.
D)Majority voting always indicates what outcome a society really wants.

Accepted Answer

The answer of Which of the following is a lesson...

Question 10

Suppose that residents of a town are asked to vote on the best day to improve the safety of an intersection. The three choices are: a stoplight, a 4-way stop, and a 2-way stop. The mayor asks the residents to assign 3 points to their first choice, 2 points to their second choice, and 1 point to their last choice. The intersection will be controlled by the method that receives the most points. This voting scheme is called
A)Arrow's impossibility theorem.
B)the Condorcet paradox.
C)a Borda count.
D)the median voter theorem.

Accepted Answer

This is a Borda count, where voters rank choices and assign points based on those rankings. The choice with the most points will be selected as the winner. Therefore, the best choice(s) are those that receive the most points overall, which could be any combination of the three choices based on the voters' preferences.

Question 11

One implication of the Condorcet paradox is
A)that the order in which things are voted on can affect the result.
B)that the order in which things are voted on is irrelevant.
C)that you do not want to be in charge of arranging which items are voted upon first.
D)that when there are only two items being voted on the order matters.

Accepted Answer

The Condorcet paradox shows that the order in which options are voted on can affect the outcome of the vote, as demonstrated by the cyclical preferences that can arise. This means that the order in which things are voted on should be carefully considered to ensure a fair and unbiased outcome.

Question 12

Suppose that residents of a town are asked to vote on the best way to improve the safety of an intersection. The three choices are: a stoplight, a 4-way stop, and a 2-way stop. When the mayor asks the residents to choose between a stoplight and a 4-way stop, the residents choose a 4-way stop. Then, when the mayor asks them to choose between a 4-way stop and a 2-way stop, they choose a 2-way stop. However, if the mayor firsts asks the residents to choose between a 4-way stop and a 2-way stop, they choose a 2-way stop. Then, when the mayor asks the residents to choose between a 2-way stop and a stoplight, they choose a stoplight. What does this example illustrate?
A)Arrow's impossibility theorem
B)the Condorcet paradox
C)a Borda count
D)the median voter theorem

Accepted Answer

This example illustrates the Condorcet paradox, where the outcome of a vote can depend on the order of choices presented to voters. In this case, when the choices are presented as stoplight versus 4-way stop, the majority prefers the 4-way stop. Then, when the choices are presented as 4-way stop versus 2-way stop, the majority prefers the 2-way stop. However, when the choices are presented as 4-way stop versus 2-way stop first, the majority prefers the 2-way stop. This inconsistency in preferences highlights the flaws in relying solely on majority rule in elections. Therefore, there is no "best" choice in this scenario.

Question 13

The Condorcet paradox
A)demonstrates that the order in which one votes on options may influence the outcome.
B)demonstrates that majority voting by itself may not reveal the outcome that society wants.
C)disproves Arrow's impossibility theorem.
D)Both a and b are correct.

Accepted Answer

The Condorcet paradox shows how the order in which one votes on options can influence the outcome, while also demonstrating that majority voting by itself may not reveal the outcome that society wants. Therefore, both option A and B are correct. However, it does not disprove Arrow's impossibility theorem.

Question 14

As an alternative to pairwise majority voting, each voter could be asked to rank the possible outcomes, giving 1 point to her lowest choice, 2 points to her second-lowest choice, 3 points to her third-lowest choice, and so on. This voting method is called a(n)
A)median vote.
B)pairwise minority vote.
C)Borda count.
D)Arrow count.

Accepted Answer

The described voting method is the Borda count, where rankings are used to assign each outcome a score and the outcome with the highest total score wins.

Question 15

Which of the following sets of preferences can not satisfy the property of transitivity?
A)Plan A is preferred to plan D. Plan D is preferred to plan B. Plan C is preferred to plan B.
B)Plan A is preferred to plan B. Plan B is preferred to plan C. Plan A is preferred to plan C.
C)Plan C is preferred to plan A. Plan B is preferred to plan A. Plan C is preferred to plan B.
D)Plan D is preferred to plan C. Plan C is preferred to plan B. Plan B is preferred to plan D.

Accepted Answer

In this set of preferences, there is a cycle where plan D is preferred to plan C, which is preferred to plan B, which is preferred back to plan D. This violates the property of transitivity, as transitivity requires that if A is preferred to B and B is preferred to C, then A must be preferred to C.

Question 16

Under majority rule, the order in which items are voted on is
A)unimportant, and this is a lesson of the Condorcet paradox.
B)unimportant, and this is a lesson of Arrow's impossibility theorem.
C)important, and this is a lesson of the Condorcet paradox.
D)important, and this is a lesson of Arrow's impossibility theorem.

Accepted Answer

The Condorcet paradox states that, under certain conditions, majority rule can lead to inconsistent or intransitive preferences. This means that the order in which items are voted on can be important, as it can affect the outcome of the vote. For example, in a three-way race where each candidate is preferred by a third of the voters, the outcome will depend on which candidate is voted on first. This highlights the importance of considering the order in which items are voted on in majority rule.

Question 17

Table 22-1
Three friends -- Linda, Stephanie, and Jamie -- are deciding where to go together for vacation. They all agree that they should go to one of three places: France, Greece, or Italy. They also agree that they will have two pairwise votes to determine where to go on vacation, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below. 
-Refer to Table 22-1. If the friends change their minds and decide to choose a vacation destination using a Borda count, then
A)the friends will go to France.
B)the friends will go to Greece.
C)the friends will go to Italy.
D)A Borda count will not result in a single winner in this case.

Accepted Answer

A Borda count assigns point values to each person's first, second, and third choices and then adds up the points for each destination. In this case, each person's first choice receives 3 points, their second choice receives 2 points, and their third choice receives 1 point. Adding up the points, we get:

France: 7 points (Linda 3 + Stephanie 2 + Jamie 2)
Greece: 6 points (Linda 1 + Stephanie 3 + Jamie 2)
Italy: 7 points (Linda 2 + Stephanie 1 + Jamie 4)

Since both France and Italy have 7 points, there is a tie using the Borda count and a single winner cannot be determined. Therefore, option D is the correct choice.

Question 18

Table 22-2
Three longtime friends-Allen, Brian, and Cody-are deciding how they will spend their Sunday afternoon. They all agree that they should do one of three things: go to a movie, play golf, or go to a baseball game. They also agree that they will have two pairwise votes to determine how to spend their afternoon, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below. 
-Refer to Table 22-2. If (1) the first vote pits "baseball game" against "movie," and (2) the second vote pits "golf" against the winner of the first vote, then the outcome is as follows:
A)"Baseball game" wins the first vote and "baseball game" wins the second vote, so they go to a baseball game.
B)"Baseball game" wins the first vote and "golf" wins the second vote, so they go to the golf.
C)"Movie" wins the first vote and "movie" wins the second vote, so they go to a movie.
D)"Movie" wins the first vote and "golf" wins the second vote, so they play golf.

Accepted Answer

According to the first vote, "movie" would not be the majority choice, as both Allen and Cody prefer "baseball game" and Brian prefers "golf." Therefore, "baseball game" wins the first vote. Then, in the second vote, "golf" is pitted against "baseball game," and since Brian and Cody both prefer "golf" over "baseball game," "golf" wins the second vote. Therefore, they will play golf.

Question 19

Which of the following is not correct?
A)Pairwise voting never produces transitive preferences.
B)The order of pairwise voting can affect the result.
C)Majority voting by itself does not tell us what outcome a society really wants.
D)No voting system can satisfy all of the following properties: unanimity, transitivity, independence of irrelevant alternatives, and no dictators.

Accepted Answer

Pairwise voting can produce transitive preferences, but it is not always guaranteed to do so. For example, if three candidates A, B, and C are being voted on and the results of pairwise voting are A > B, B > C, and C > A, then transitive preferences have not been produced.

Question 20

The Condorcet voting paradox demonstrates that democratic outcomes do not always obey the property of
A)narrowness of preferences.
B)concavity of preferences.
C)asymmetry of preferences.
D)transitivity of preferences.

Accepted Answer

The Condorcet voting paradox is a situation where, in a group of voters, a candidate can be defeated by another candidate in a one-on-one comparison, but when compared to all other candidates, they come out as the most preferred candidate. This violates transitivity of preferences, which states that if a voter prefers candidate A to candidate B, and candidate B to candidate C, then they must prefer candidate A to candidate C. Therefore, the best choice is D, which identifies transitivity of preferences as the property that is not always obeyed in democratic outcomes.

Quiz 22: Frontiers in Microeconomics

The Condorcet paradox

The Condorcet voting paradox applies to situations in which voters

The Condorcet paradox demonstrates that the result of a majority vote may be affected by

The Condorcet paradox shows that

Which of the following is a lesson from the Condorcet paradox?

One implication of the Condorcet paradox is

The Condorcet paradox

As an alternative to pairwise majority voting, each voter could be asked to rank the possible outcomes, giving 1 point to her lowest choice, 2 points to her second-lowest choice, 3 points to her third-lowest choice, and so on. This voting method is called a(n)

Which of the following sets of preferences can not satisfy the property of transitivity?

Under majority rule, the order in which items are voted on is

Which of the following is not correct?

The Condorcet voting paradox demonstrates that democratic outcomes do not always obey the property of