Analyzing Congress
2nd edition
Answer Key
, 2
Chapter 1: Problems
Question 1. The median voter in each case is the one whose ideal point is exactly in the middle
of all the ideal points in the group. The most direct way to identify the median voter is to sort the
voters in ascending order, according to ideal point. There are seven voters in all of these
questions. Therefore, the median member will be the fourth in order in each case.
Questions 1a and 1b are fairly straightforward, with the answers being G=57 and F=63,
respectively.
Question 1c is a little tricky. Compared to Question 1a, it moves member C to equal the
ideal point of member G. It is important to keep in mind that although this is a single point, it is
occupied by two people. Therefore, in counting from the left or right, you need to count both C
and G separately. When you do that, you will see that the point they occupy is the location of the
fourth voter from either the left or the right. The identity of the member, C or G, is immaterial.
What is important is the location of the point.
Question 2. Recall that under the circumstances specified in the problem — the utility curves are
symmetrical and that voting proceeds under majority rule — whenever two alternatives are pitted
against each other, the one closer to the median will prevail. Therefore, we arrive at the answer
for each part of the question by finding the distance from the median voter to X = 60 and then to
Y = 65. The one that is closer to the median wins:
Median |X - Median| |Y - Median| Winner
a. G = 57 3 8 X
b. F = 63 3 2 Y
c. G = C = 57 3 8 X
, 3
Question 3. The first step is to place the answers to the question on a single ideological
dimension. The second step is to identify the position held by the median respondent in the
survey.
To place the answers on an ideological scale, it is usually best to find the answers that are
the most extreme on both sides, to anchor the scale. Survey researchers usually help us in these
situations, because they tend to give the response categories in “ideological order,” to help the
respondent. In the case of Question 3a, the abortion question, one extreme is represented by the
most restrictive response (“by law, abortion should never be permitted”) and the other is
represented by the most permissive (“by law, a woman should always be able to obtain an
abortion”). The other two responses are clearly between the two, spatially, with the second
response more restrictive than the third.
We calculate the median by cumulating the percentage of respondents expressing a
preference for increasingly permissive abortion laws. The following table shows the cumulation:
Response Pct. Cumulative pct.
By law, abortion should never be permitted [most permissive] 12.2 12.2
The law should permit abortion only in case of rape, incest 28.6 40.8
The law should permit abortion for reasons other than rape 15.5 56.3
By law, a woman should always be able to obtain an abortion [most 43.8 100.1*
restrictive]
*The percentages do not cumulate to 100 because of rounding.
We see that 12.2% chose the most restrictive, (12.2% + 28.6% =) 40.8% chose one of the
two most restrictive options, and (12.2%+28.6%+15.5% =) 56.3% chose one of the three most
restrictive options. Because we go over 50% of the respondents with this third answer category,
we assume the median respondent must belong to the group that gave this answer, that the law
should permit abortion for reasons other than rape.
, 4
The logic of the explanation is the same for Question 3b. The following table provides
the accounting of the cumulative percentages:
Response Pct. Cumulative pct.
Much more important to protect environment even if lose jobs 14.5 14.5
[most pro-environment]
Environment somewhat more important 18.8 33.3
About the same 28.4 61.7
Economy somewhat more important 23.7 85.4
Much more important to protect jobs, even if environment is worse 14.6 100.0
[least pro-environment]
Because we go over 50% of the respondents with this third answer category, we assume
the median respondent must belong to the group that gave this answer, that the law should permit
abortion for reasons other than rape.
Question 4. Recall that a Condorcet winner is a point, such that if it is the status quo, it cannot
be replaced via a majority vote. When there are an odd number of voters with single-peaked
questions along a single dimension, the Condorcet winner will be the policy that is equal to the
median voter’s ideal point. When the number of voters is even, the Condorcet winner may lie
within an interval — several points could be resistant to being overturned via a majority vote.
Question 4a is a straightforward application of the median voter theorem with an odd
number of voters. The answer is arrived at by re-ordering the ideal point in ascending (or
descending) order and finding the median:
D = 16 E = 22 C = 25 B = 100 A = 200
Median
2nd edition
Answer Key
, 2
Chapter 1: Problems
Question 1. The median voter in each case is the one whose ideal point is exactly in the middle
of all the ideal points in the group. The most direct way to identify the median voter is to sort the
voters in ascending order, according to ideal point. There are seven voters in all of these
questions. Therefore, the median member will be the fourth in order in each case.
Questions 1a and 1b are fairly straightforward, with the answers being G=57 and F=63,
respectively.
Question 1c is a little tricky. Compared to Question 1a, it moves member C to equal the
ideal point of member G. It is important to keep in mind that although this is a single point, it is
occupied by two people. Therefore, in counting from the left or right, you need to count both C
and G separately. When you do that, you will see that the point they occupy is the location of the
fourth voter from either the left or the right. The identity of the member, C or G, is immaterial.
What is important is the location of the point.
Question 2. Recall that under the circumstances specified in the problem — the utility curves are
symmetrical and that voting proceeds under majority rule — whenever two alternatives are pitted
against each other, the one closer to the median will prevail. Therefore, we arrive at the answer
for each part of the question by finding the distance from the median voter to X = 60 and then to
Y = 65. The one that is closer to the median wins:
Median |X - Median| |Y - Median| Winner
a. G = 57 3 8 X
b. F = 63 3 2 Y
c. G = C = 57 3 8 X
, 3
Question 3. The first step is to place the answers to the question on a single ideological
dimension. The second step is to identify the position held by the median respondent in the
survey.
To place the answers on an ideological scale, it is usually best to find the answers that are
the most extreme on both sides, to anchor the scale. Survey researchers usually help us in these
situations, because they tend to give the response categories in “ideological order,” to help the
respondent. In the case of Question 3a, the abortion question, one extreme is represented by the
most restrictive response (“by law, abortion should never be permitted”) and the other is
represented by the most permissive (“by law, a woman should always be able to obtain an
abortion”). The other two responses are clearly between the two, spatially, with the second
response more restrictive than the third.
We calculate the median by cumulating the percentage of respondents expressing a
preference for increasingly permissive abortion laws. The following table shows the cumulation:
Response Pct. Cumulative pct.
By law, abortion should never be permitted [most permissive] 12.2 12.2
The law should permit abortion only in case of rape, incest 28.6 40.8
The law should permit abortion for reasons other than rape 15.5 56.3
By law, a woman should always be able to obtain an abortion [most 43.8 100.1*
restrictive]
*The percentages do not cumulate to 100 because of rounding.
We see that 12.2% chose the most restrictive, (12.2% + 28.6% =) 40.8% chose one of the
two most restrictive options, and (12.2%+28.6%+15.5% =) 56.3% chose one of the three most
restrictive options. Because we go over 50% of the respondents with this third answer category,
we assume the median respondent must belong to the group that gave this answer, that the law
should permit abortion for reasons other than rape.
, 4
The logic of the explanation is the same for Question 3b. The following table provides
the accounting of the cumulative percentages:
Response Pct. Cumulative pct.
Much more important to protect environment even if lose jobs 14.5 14.5
[most pro-environment]
Environment somewhat more important 18.8 33.3
About the same 28.4 61.7
Economy somewhat more important 23.7 85.4
Much more important to protect jobs, even if environment is worse 14.6 100.0
[least pro-environment]
Because we go over 50% of the respondents with this third answer category, we assume
the median respondent must belong to the group that gave this answer, that the law should permit
abortion for reasons other than rape.
Question 4. Recall that a Condorcet winner is a point, such that if it is the status quo, it cannot
be replaced via a majority vote. When there are an odd number of voters with single-peaked
questions along a single dimension, the Condorcet winner will be the policy that is equal to the
median voter’s ideal point. When the number of voters is even, the Condorcet winner may lie
within an interval — several points could be resistant to being overturned via a majority vote.
Question 4a is a straightforward application of the median voter theorem with an odd
number of voters. The answer is arrived at by re-ordering the ideal point in ascending (or
descending) order and finding the median:
D = 16 E = 22 C = 25 B = 100 A = 200
Median
