**Practice with election methods**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk__

Given the election below

Figure 1

Question 1:

i. Determine the* winner* of the election using:

a. Plurality

b. Run-off

c. Sequential run-off

d. Borda count (using as the number of points for a particular candidate the number of candidates below that candidate on the ballot)

e. Condorcet method (Is there a winner in this case?)

ii. If instead of picking a single winner you needed to select a ranking (perhaps with ties allowed) what ranking would you produce using the "spirit" of each of the methods above?

Question 2:

Redo Question 1 where the number of votes for each of the ballots in Figure 1 is increased by 1.

Question 3:

Redo Question 1 where the number of votes for each of the ballots in Figure 1 is decreased by 1.

Question 4

Redo Question 1 where the number of votes for each of the ballots in Figure 1 is doubled.

Question 5

In Figure 1 what fraction of voter ranked E in third place? In Figure 1 what percentage of voters ranked C in second place?

Question 6

How might one implement the "spirit' of approval voting using ranked ballots rather than an approval ballot?

Question 7

Did did you learn by doing Questions 2, 3, and 4? (Are there "theorems" lurking here somewhere?)