Social Choice Theory Election Theory Voting Methods Plurality

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

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

Preference Schedules • A list or table of all candidates/options ranked in order of

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 B B C D D C D A A A 8 5 6 7

PLURALITY & MAJORITY • Plurality – winner chosen by most “ 1 st place”

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

BORDA COUNT • Winner chosen using a point system • Common point assignments last

BORDA COUNT • Winner chosen using a point system • 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 B B C D D C D A A A 8 5 6 7

BORDA COUNT - work A: B: C: D: assign points 8(3) 8(2) 8(1) 8(0)

BORDA COUNT - work A: B: C: D: assign points 8(3) 8(2) 8(1) 8(0) + + 5(0) 5(3) 5(2) 5(1) + + 6(0) 6(2) 6(3) 6(1) + + 7(0) 7(2) 7(1) 7(3) 3 A B C D 2 B C B B 1 C D D C 0 D A A A 8 5 6 7 = = 24 57 43 32

RUNOFF • The two candidates receiving the most 1 st place votes are put

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

SEQUENTIAL RUNOFF • The candidate with the fewest first place votes is eliminated in

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 1 st place votes is eliminated; continue until only one candidate remains, who we declare the winner. 1 st place vote totals A: B: C: D: 8 5 6 7 eliminate candidate B (lowest #) Re-total the votes based on whether A, C, or D was more preferred in each schedule A: 8 C: 5 + 6 = 11 D: 7 eliminate candidate D Re-total the votes based on whether A or C was more preferred in each schedule A: 8 C: 5 + 6 + 7 = 18 A B C D B C B B C D D C D A A A 8 5 C is the winner by a vote of 18 to 8 6 7

CONDORCET METHOD • A Condorcet winner is the candidate that would defeat all other

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 B B C D D C D A A A 8 5 6 7

CONDORCET METHOD Read Row vs. Col. A A B C D A vs. B

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