# 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

```