MATH 131--Homework--Spring 08

Homework 7: Due Friday 04/04/08.

Problem 1:

# of voters	14	10	8	4	1
1st choice	A	C	D	B	C
2nd choice	B	B	C	D	D
3rd choice	C	D	B	C	B
4th choice	D	A	A	A	A

a) Who is the Borda Count winner?

b) Who is the Borda Count winner if candidate D drops out?

c) What criterion does this example speak to?

Problem 2: Write up the STV procedure for the election of two candidates given the following preference list:

	# OF VOTERS
	14	10	8	4	2	2	2	2	2	2	1
1st choice	A	C	D	B	E	E	E	E	E	E	C
2nd choice	B	B	C	D	B	C	B	C	D	D	D
3rd choice	C	D	B	C	C	B	D	D	B	C	B
4th choice	D	E	A	E	D	D	C	B	C	B	A
5th choice	E	A	E	A	A	A	A	A	A	A	E

Clearly explain each step!

Homework 6: Due Friday 03/14/08.

1) Give and example that shows that the Borda Count violates the Majority Criterion and explain why your examples shows what it is supposed to show.

2) Give an argument why the Borda Count NEVER violates the Monotonicity Criterion.

3) Give an example that shows that the Borda Count violates the Condorcet criterion and explain why your examples shows what it is supposed to show.

4) Give an example that shows that the Borda Count violates IIA and explain why your examples shows what it is supposed to show.

5) Consider the following voting method: The winner of the election is the candidate with the fewest last place votes. Show by giving appropriate examples that this method violates all 4 criteria.

Homework 5: Due Friday 03/07/08.

1) Determine the winner of the election given the following set of preference lists

# of voters	12	7	20	18	23	25
1st	A	A	C	B	E	D
2nd	B	E	B	C	B	E
3rd	C	B	D	E	C	A
4th	D	C	A	A	D	B
5th	E	D	E	D	A	C

Using

a) straight plurality

b) plurality with runoff

c) plurality with sequential elimination

d) Borda count

e) Copeland’s method, aka the method of pairwise comparison

2) Some voting methods can be “inverted”. Instead of counting first place votes, we can count last place votes, etc.. E.g., we can invert the plurality method by declaring the winner to be the candidate with the fewest last place votes. Invert the first 3 methods from Problem 1 and find the winner of the election in each case.

3) Check out the article “Are we using the worst voting procedure?” at Science News Online. Give two arguments from the article against currently voting methods. (You only need to read the article. You may skip the letters that follow it.)

Homework 4: Due Friday, 02/29/08.

1. A hospital has to assign its 100 nurses to 5 different departments based on the average weekly

case load during the last year in each department. The numbers are as follows.

Department	Average weekly case load during last year
ICU	65
General surgery	218
Maternity	187
Oncology	141
Emergency/Urgent Care	139
Total	750

1. Use HAM to apportion the 100 nurses.
2. JAM with a divisor 7.3 also apportions the 100 nurses (Trust me!). Carry out JAM with divisor 7.3.
3. What does “district size” mean in the context of nurses and patients?
4. What does “representative share” mean in the context of nurses and patients?
5. If you were a patient which apportionment method would you prefer? Why? Think about your

answer to part d.

6. If you were a nurse which apportionment method would you prefer? Why? Think about your

answer to part c.

2. The 1840 census determined the population of MI to be 5,256,106 and the

population of AR to be 1,949,387.

1. For apportionment 1 (MI 17 and AR 7) and apportionment 2 (MI 18 and AR 6)

find the representative shares.

Representative shares

	pop	App 1	App2
		Rep share	Rep share
MI
AR
Abs. Diff
Rel. diff

2. Which apportionment is better if we use absolute difference of representative

shares as our measure? Why?

3. Which apportionment is better if we use relative difference of representative

shares as our measure? Why?