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?