Math 2000 - Assignment 10

Spring 2001

Due May 3

Do not wait until the last minute to start the assignment! It’s best to get an early start and work on it in several steps. Do not hesitate to ask for help before the assignment is due! Office hours are on Tuesdays and Thursdays immediately before and after class in Science 132 or by arrangement. Email also works at wbriggs@math.cudenver.edu.

A. We will have covered two new topics during the last two weeks: mathematics and music (Unit 10B) and the mathematics of voting (Units 11D and 11E).

B. Please do the following problems. Be sure do additional problems if necessary to master an idea. Remember to show your work, state all assumptions, and please write clearly!

1. Make a table showing the frequencies of the notes of the scale that starts at the G above middle C, which has a frequency of 390 cycles per second.

2. Consider the following preference schedule for four candidates:

First	B	D	C	A	D	C
Second	D	A	D	D	A	A
Third	C	C	A	C	B	B
Fourth	A	B	B	B	C	D
	20	15	10	8	7	6

a. How many votes were cast in the survey?

b. Find the plurality winner. Did the plurality winner also receive a majority? Explain.

c. Find the winner by a runoff of the top two candidates.

d. Find the winner of a sequential run-off.

e. Find the winner by a Borda count.

f. Find the winner, if any, by the method of pairwise comparisons.

g. Summarize the results of the various methods of determining a winner. Based on these results, is there a clear winner? If so, why? If not, which candidate would select as the winner, and why?