Math 116 Spring 06

*Please see "Updated
Websites" on the course website for election system materials.*

* *

*Our final exam room has
been changed to Hitchcock 131. Do
not show up to Postle Hall for the final exam.*

Assignment 7 due Thursday, June
1

No late papers.
This is the last assignment.

You may do this assignment as
a group assignment if you wish. No
more than four persons to a group, and if your GTA does not assign you to
groups, you may form your own.

This assignment is on
election systems.

1. Check that the total popular vote for each party in scenario
0 as shown on acetate 206 is correct.

2. Calculate the total popular vote for each party in scenario
1 (scenario 1 is on acetate 207).

3. (a) For scenario 2 (acetate 208) tabulate the vote in each
of the 7 districts. For each
district be sure to total the tabulation to make sure it comes out to be the
population of the district.

(b)
How many seats does each party get in scenario 2? Which party forms the government?

(c)
In scenario 2 tabulate the total popular vote for each party.

4. (a) In scenario 3 (acetates 210-212) calculate how many
candidates from each party are elected in each district if each party fields
exactly as many candidates as there are seats to be filled in that district. Then calculate how many total seats
each party gets in the national assembly (which now has 17 members). If you need to apportion the seats
between the parties, use Hamilton's method. Which party forms the government? Can you draw any generalizations from this result?

(b) Same as 4(a) except that in
district U_{1}
party A fields 6 candidates. Can
you draw any generalizations from this result?

(c) Same as 4(a) except that in district U_{1}
party A fields only 1 candidate.
Can you draw any generalizations from this result.

5. (a) Suppose the districts are the multimember districts as
in scenario 3, but that the voting is the proportional representation voting
system called party list voting, using closed lists. There is no list from party E in district R_{7}. The proportion of voters that vote for
each party is given by the table on acetate 203. How many representatives are elected by each party? Use
Hamilton's method if you need to.
Which party forms the government?

(b)
Suppose that the entire nation is viewed as a single 7-member district
and the voting system is party list voting with closed lists. Each voter in the
nation gets the same party lists, and each voter casts one vote (for a party,
not for a candidate). The voters
in each of the seven former districts cast their votes according to the
percents in the table on acetate 203.
How many candidates are elected from each party? Use Hamilton's method
if you need to. Which party forms
the government?

Note: In the study of electoral
systems the Hamilton method usually goes under the name The Largest Remainder
Method Using The Hare Quota.