1. Social Choice Theory [Election Theory]
Voting Methods
Plurality, Majority, Borda Count, Runoff, Sequential Runoff, Condorcet

2. Preference Schedules
A list or table of all candidates/options ranked in order of preference, and the number of people who prefer them in that order
more preferred moving in the direction the arrow points A B C D B C D A C B D A D B C A 8 5 6 7

3. PLURALITY & MAJORITY
Plurality – winner chosen by most “1st place” votes
Majority – requires winner to get MORE than ½ of “1st place” votes A B C D B C D A C B D A D B C A 8 5 6 7

4. BORDA COUNT 8 5 6 7 Winner chosen using a point system A B C D B C B B
Common point assignments last place = 1 point, next to last = 2 points, etc…
One could also assign point values of 0, 1, 2, etc. to make the math easier A B C D B C D A C B D A D B C A 8 5 6 7

5. BORDA COUNT - work 8 5 6 7 A: 8(3) + 5(0) + 6(0) + 7(0) = 24
assign
points 3 2 1 A B C D B C D A C B D A D B C A 8 5 6 7

6. D is the winner by a vote of 18 to 8
RUNOFF
The two candidates receiving the most 1st place votes are put in a head-to-head match up to determine winner.
1st place vote totals
A: 8 eliminate candidates B & C
B: 5 b/c they have the
C: 6 fewest 1st place votes
D: 7 A B C D B C B B
Re-total the votes based on whether A or D was more preferred in each schedule
A: 8
D: = 18 C D D C D A A A 8 5 6 7
D is the winner by a vote of 18 to 8

7. C is the winner by a vote of 18 to 8
SEQUENTIAL RUNOFF
The candidate with the fewest first place votes is eliminated in round 1, votes are re-tallied without that candidate, and again the candidate with the fewest 1st place votes is eliminated; continue until only one candidate remains, who we declare the winner.
1st place vote totals
A: 8 eliminate candidate B (lowest #)
B: 5
C: 6
D: 7 A B C D B C B B
Re-total the votes based on whether A, C, or D was more preferred in each schedule
A: 8
C: = 11 eliminate candidate D
D: 7 C D D C D A A A
Re-total the votes based on whether A or C was more preferred in each schedule
A: 8
C: = 18 8 5 6 7
C is the winner by a vote of 18 to 8

8. CONDORCET METHOD
A Condorcet winner is the candidate that would defeat all other candidates in a runoff election (head-to-head matchup)
Condorcet Paradox – there is not always a Condorcet winner (rock, paper, scissors) A B C D B C D A C B D A D B C A 8 5 6 7

9. CONDORCET METHOD 8 5 6 7 A B C D B C D A C B D A D B C A Read
Row vs. Col. A B C D
A vs. B
8 to 18 L
A vs. C
A vs. D
B vs. A
18 to 8 W
B vs. C
20 to 6
B vs. D
19 to 7
C vs. A
C vs. B
6 to 20
C vs. D
D vs. A
D vs. B
7 to 19
D vs. C
7 to 19 L A B C D B C D A C B D A D B C A 8 5 6 7
Since B is more preferred over all other candidates when paired head-to-head, B is the Condorcet Winner