Near Clone Sets

[Markus Schulze]

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