Math 116 Winter 06

Assignment 2 due Thursday, January 12

Chapter 1, Exercises #15, 16, 17, 18, 25, 26, 20, 22, 28, 29, 30, 34,

Exercises 25, 26 appear to be
out of order, but they are related to the parts that are added to #18.

In Exercise #18, add some
parts as follows:

#18(c) Make a second tabulation of the same
votes by building the following table

1st
place (votes) 2nd
place votes 3rd
place 4th place

candidate A

candidate B

candidate C

candidate D

Do you prefer calculating the
Borda counts for the candidates
using the original tabulations or the 2nd one? Why?

(d) In the 2nd tabulation the numbers in each column add up to
1240. Why? (If they don't, you've
made an error in tabulating them.)
In the 2nd tabulation the numbers in each column also add up to
1240. Why?

(e) The total of the Borda counts for all of the candidates add
up to 12400. Why?

(f) If C drops out, is it easier to recompute
the Borda counts by making a new 2nd tabulation based on the original tabulation
or by making a new 2nd tabulation directly from the one that you made in part
(c)?

(g) For the new 2nd
tabulation made after C drops out, do you find behavior similar
to that in parts (d), (e), (f) above?