Positive Involvement; No-Show
Markus Schulze
schulze at sol.physik.tu-berlin.de
Tue Jun 16 02:51:02 PDT 1998
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
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