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| inputs profiles and outputs results |
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| In a Two candidate elections... (4) |
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vote either A or B
List of candidated understood
List of voters of understood
Every balle chooses A or B |
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| who ever gets the most votes wins |
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| doesn't treat everyone equally |
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| One candidate wins no matter what |
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| The vote of one voter determines the outcome |
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| who ever gets an odd number of votes wins |
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| Anenemity, Neutrality, Monotone, Decisive, Nearly Decisive |
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| all voters are treated equal and anonymous |
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| candidates are treated equal. |
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| you can not hurt a candidate by voting for him or her |
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| If there is always a winner, either A or B |
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| Only way to get a tie is for A and B to have the same amount of votes. Not always a defined winner. |
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can not be decisive
if searching for a good method one must give up decisiveness. |
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Definition
1. The only SCF that is Anon., Neutral, and Almost Decisive is Super Majority
2. If Anon., Neutral, and Monotone you must have Simple or Super Majority |
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| Winner is the candidate with the most first place votes (more then half) |
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| award points for each candidate from bottom to top and then count up points to determine winner. |
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If there is majority winner then that candidate wins.
If not then eliminate the candidate with the fewest first place votes and proceed (elminate the least favored... top to bottom with numbers across the top) |
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Term
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| if there is no majority winner then eliminate candidates with the most last place votes (eleminate the most hated cand... bottom to top) |
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| the winner has the most H2H wins (make the chart A to B, B to C, B to D, etc.) |
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| What Criterion do we insist on for in MCE? |
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| Anon, Neutrality, Unanemity |
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| if every candidate prefers A to B then B is a loser.. but A might not be the winner |
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| 3rd party candidate can not effect the race between the major candidates. |
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| Candidate that beats every other candidated H2H |
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| Candidate that loses H2H everytime. |
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Term
| What Function satisfies Condorcet and Independence |
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Definition
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Definition
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| Independence + Pareto = Dictator |
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| State the Arrow Method Theorem... |
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Definition
| The only SCF with 3+ Candidates that satisfies pareto and indepence are dictatorships. |
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| What are the 3 steps of Arrows Theorem? |
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Definition
1. SCF must be decisive cant choose more than one winner)
2. Given 2 candidates A and B. there is a voter V who has dictatorial power of A over B. if V puts A over B... B loses
3. The voter of part 2 is the same for any pair of candidates
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Term
Step 3 of Arrows Theorem (Part 1) |
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Definition
If V has dictorial power of A over B
If W has dictorial power of B over A
V = A B others
W = B A others
Others = A B others
Then there is no winner, V=W
A loses = W has power B over A
B loses = V has power A over B
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Term
| Step 3 of Arrows Theorem (Part 2) |
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Definition
If V has power of A over B
If W has power of B over C
then V=W
V = C A B
W = B C A
O = C A B
no winner
A loses because (pareto with C)
B loses (V power over A over B )
C loses (W power over B over C) |
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Term
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Definition
expresses preferences by listing candidates by descending of preference
Ex.
123
ABC
BCA
CAB |
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