1.		               
							    
a. plurality voting.
	A – only first place votes are considered
b. the Hare system.
	B – repeatedly eliminate least preferred candidate
c. the Borda count.
	D – rank method where points for n positions are n-1, n-2, n-3, ...1,0
d. sequential pairwise voting with the agenda A, B, C, D.
	D – picks first two candidates against one another in a one-to-one race
e. sequential pairwise voting with the agenda B, A, D, C.
	C

2. a. Find the winner(s) under plurality.
   As the first choice, 10 people for vote A, 9 people vote for B, and 5 people vote for C.
   Thus, A is the winner under plurality.

   b. Use the agenda CDBA to determine the winner under the sequential pairwise system.  
   In the first one-to-one match between C and D, C wins by a score of 24 to 0.
   In the second match C- B, B wins by a score of 19 to 5.
   In the third match B-A, A wins by a score of 13 to 11.
   Thus, A is the winner under the sequential pairwise system using the agenda CDBA.

   c. Determine the winner under the Hare system.

First choice: A: 10, B: 9, C: 5, D:0. Thus, we need to eliminate D. The preference list will become:

                 Number of Voters	
	10	9	3	2	
First choice	A	B	C	C	
Second choice	B	C	A	B	
Third choice	C	A	B	A	

First choice: A: 10, B: 9, C: 5. C will be eliminated next. The preference list will become:

                 Number of Voters	
	10	9	3	2	
First choice	A	B	A	B	
Second choice	B	A	B	A	

First choice: A: 13, B: 11. B will be eliminated next and A becomes the winner
Thus, A is the winner under the Hare system.

3. 
a.  Who wins under the Borda count?

The Borda score of A is: 
The Borda score of B is: 
The Borda score of C is: 
The Borda score of D is: 

A is the winner under the Borda count.

b.  
The Borda score of A is: 
The Borda score of B is: 
The Borda score of C is: 
The Borda score of D is: 

B is the winner under the Borda count.

c. Yes, this example shows that IIA is violated by the Borda count. B has gone from being a non-winner to being a winner; even though no one changed his/her mind about whether B is preferred to A or vice versa.

4. a. the Pareto Condition, This can happen in sequential pairwise voting, if Renee French was defeated earlier in the agenda by a candidate who was later defeated by the winner.

   b. Condorcet Winner Criterion, This can happen in plurality voting.	

   c. Independence of Irrelevant Alternatives, This can happen with the Borda Count. The new winner may gain enough points to obtain a higher score than the previous 	winner without being moved ahead of the previous winner on any voters list.

   d.  Monotonicity, This can happen using the Hare system. The previous winner’s new position can benefit candidates other than him/herself by eliminating the wrong opponent.

5. candidate C wins the election