Positive Involvement; No-Show

[Markus Schulze]

Dear Participants,

Smith//Condorcet[EM] violates
"Positive Involvement".

"Positive Involvement" means:

   Suppose, candidate X is the unique winner. Then a
   set of additional voters, who vote identically and
   who strictly prefer candidate X to every other
   candidate, cannot make candidate X lose the
   election.

Example 1a:

   35 voters vote D > A > B > C.
   32 voters vote C > A > B > D.
   20 voters vote B > C > A > D.
   13 voters vote D > B > C > A.

   Smith//Condorcet(EM) chooses candidate A.

Example 1b:

   Additional 6 voters vote A > D > C > B.
   Now, we have:

   35 voters vote D > A > B > C.
   32 voters vote C > A > B > D.
   20 voters vote B > C > A > D.
   13 voters vote D > B > C > A.
   06 voters vote A > D > C > B.

   Smith//Condorcet(EM) chooses candidate D.

********

Smith//Condorcet(EM) violates
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 2a:

   34 voters vote D > A > B > C.
   31 voters vote C > A > B > D.
   18 voters vote B > C > A > D.
   12 voters vote D > B > C > A.
   05 voters vote A > D > B > C.

   A:B=70:30
   A:C=39:61
   A:D=54:46
   B:C=69:31
   B:D=49:51
   C:D=49:51

   Smith//Condorcet(EM) chooses candidate D.

Example 2b:

   Suppose, that additional 3 voters vote
   B > C > D > A. Then I got:

   34 voters vote D > A > B > C.
   31 voters vote C > A > B > D.
   18 voters vote B > C > A > D.
   12 voters vote D > B > C > A.
   05 voters vote A > D > B > C.
   03 voters vote B > C > D > A.

   A:B=70:33
   A:C=39:64
   A:D=54:49
   B:C=72:31
   B:D=52:51
   C:D=52:51

   Smith//Condorcet(EM) chooses candidate A.

Markus