Near Clone Sets
Markus Schulze
schulze at sol.physik.tu-berlin.de
Wed Jun 10 04:58:42 PDT 1998
Dear Mike,
I have a question: Many election methods have the problem,
that they sometimes "punish" voters for going to the poll.
Example 1:
35 voters vote B > A > C > D.
30 voters vote C > D > B > A.
20 voters vote A > C > D > B.
15 voters vote D > B > A > C.
The matrix of wins and defeats looks as follows:
A:B=20:80
A:C=70:30
A:D=55:45
B:C=50:50
B:D=35:65
C:D=85:15
As B > A > C > D > B, every candidate is in the Smith Set.
The winner of Smith//Condorcet(EM) is candidate B.
Example 2:
Suppose, that 6 additional voters go to the poll, who
vote D > B > C > A. Then we have:
35 voters vote B > A > C > D.
30 voters vote C > D > B > A.
20 voters vote A > C > D > B.
15 voters vote D > B > A > C.
6 voters vote D > B > C > A.
The matrix of wins and defeats looks as follows:
A:B=20:86
A:C=70:36
A:D=55:51
B:C=56:50
B:D=35:71
C:D=85:21
As B > A > C > D > B, every candidate is in the Smith Set.
The winner of Smith//Condorcet(EM) is candidate C.
In other words: By going to the poll, the 6 additional
voters change the winner from candidate B to candidate C,
although they rank candidate B higher than candidate C.
The additional 6 voters are "punished" for going to the
poll.
If Tideman or Schulze were used, the effect would
be the same: The winner would be changed from
candidate B to candidate C. Thus, this seems to me to be
a problem for many election methods.
Is it possible (maybe in a very simple way) to "patch"
the currently discussed election methods in such a way,
that it is not possible for them to "punish" voters for
going to the poll?
It is possible (maybe in a very simple way) to prove,
that every election method, that meets some other
desirable criteria, necessarily "punishes" voters for
going to the poll in some situations?
Markus
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