Near Clone Sets
Markus Schulze
schulze at sol.physik.tu-berlin.de
Wed Jun 10 10:09:18 PDT 1998
Dear Mike,
Tideman's method fails to meet Fishburn's "No-Show Criterion".
Fishburn's "No-Show Criterion" says:
Suppose, candidate X does not win the election.
Then: A set of additional voters, who vote identically and
who strictly prefer every other candidate to candidate X,
must not change the winner from another candidate to
candidate X.
Example 1:
37 voters vote C > A > B > D.
20 voters vote B > D > A > C.
18 voters vote A > D > C > B.
15 voters vote B > D > C > A.
07 voters vote D > A > C > B.
03 voters vote C > B > A > D.
A:B=62:38
A:C=45:55
A:D=58:42
B:C=35:65
B:D=75:25
C:D=40:60
Tideman's method:
(1) Lock B > D.
(2) Lock C > B.
(3) Lock A > B.
(4) Skip D > C.
(5) Lock A > D.
(6) Lock C > A.
Thus: Candidate C wins the election.
Example 2:
Suppose, that additional 6 voters vote
B > D > C > A. Then, we have:
37 voters vote C > A > B > D.
20 voters vote B > D > A > C.
18 voters vote A > D > C > B.
21 voters vote B > D > C > A.
07 voters vote D > A > C > B.
03 voters vote C > B > A > D.
A:B=62:44
A:C=45:61
A:D=58:48
B:C=41:65
B:D=81:25
C:D=40:66
Tideman's method:
(1) Lock B > D.
(2) Lock D > C.
(3) Skip C > B.
(4) Lock A > B.
(5) Skip C > A.
(6) Lock A > D.
Thus: Candidate A wins the election.
In short: By going to the poll and by strictly
prefering every other candidate to candidate A,
the additional 6 voters, who voted B > D > C > A,
changed the winner from candidate C to candidate A.
Markus
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