The Meta Election is taking nominations.
David Catchpole
s349436 at student.uq.edu.au
Wed Oct 7 01:06:56 PDT 1998
On Tue, 6 Oct 1998, Charles Fiterman wrote:
> At 11:42 AM 10/6/98 +1000, you wrote:
> >I nominate:
> >
> >1) Voting truthfully will advantage and not disadvantage you (where
> >possible)
> >
> >2) It should be hard for any candidates to split the vote
>
> Please add explanations and brief nominating speeches.
>
>
1) VOTING TRUTHFULLY SHOULD ADVANTAGE AND NOT DISADVANTAGE A VOTER (where
possible)
Voting methods should always strive to be such that the votes that
they process are the sincere expression of preferences by each voter, for
several reasons-
-Reflection on other goals of the election
Such goals will not be met properly if the sincerity which they
assume from the voters does not exist.
-Possibility of disadvantage under risk
Considering again the other goals of the election, and the reality
and necessity of the secret ballot, voters behave under risk, and while
voting insincerely may benefit one most of the time there may be a
significant likelihood of a real and drastic loss.
-Inequity with regards to voting power
It is very rare for all voters to uniformly benefit from the
possibility of an advantage from insincerity. Different preferences (and
different behaviour) mean that some voters' effectiveness is eroded by
others where the opportunity exists. If insincerity will benefit someone
no matter what the outcome of the election is (which is sometimes the
case) the potential for insincerity benefitting should as widely spread
over the election as possible, and as mild as possible.
-Charles' point
It is the mark of a civil democratic society that an expectation
is made of the voters to be honest, and often a compulsion to dishonesty
means disillusionment.
2) IT SHOULD BE HARD TO "SPLIT" THE VOTE
It should be as difficult as possible for the retraction of irrelevant
candidates from an election to change the outcome of an election (which in
reverse, could be perceived to be "splitting the vote". Reasons for this-
-Participation
No candidate should feel proscribed from an election simply because they
will damage the interests of their voters.
-Honesty
There should be no reason for "dummy candidates" to deflect the votes for
a rival.
Striving for honesty relates also to the insincere voting principle
above: Voters should not have to protect their interests by voting only
for "major candidates."
From election-methods-list-request at eskimo.com Wed Oct 7 03:56:57 1998
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Date: Wed, 07 Oct 1998 12:54:51 +0200
To: election-methods-list at eskimo.com
From: Markus Schulze <schulze at sol.physik.tu-berlin.de>
Subject: Re: Regretted Turnout. Insincere = ranking.
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Dear participants,
the aim of this email is to prove, that the Condorcet Criterion
and the No-Punishment Criterion are incompatible. [You can also
find this proof in "Condorcet's Principle Implies the No Show
Paradox" by Herve Moulin (Journal of Economic Theory, vol. 45,
p. 53-64, 1988).]
Condorcet Criterion:
Candidate A is a Condorcet Winner if & only if: For every other
candidate B, the number of voters, who strictly prefer candidate A
to candidate B is strictly larger than the number of voters, who
strictly prefer candidate B to candidate A.
An election method meets the Condorcet Criterion if & only if:
If there is a Condorcet Winner, then this Condorcet Winner must
be elected.
No-Punishment Criterion:
Suppose, that candidate X is elected. Then a set of additional
voters, who vote identically and who strictly prefer candidate X
to candidate Y, must not make Y win the election.
******
To prove the incompatibility, I consider an explicite example and
I will demonstrate that -independently on who is elected- it is
always possible to add voters such that either the Condorcet Criterion
or the No-Punishment Criterion is violated.
******
Example:
3 voters vote A > D > C > B.
3 voters vote A > D > B > C.
5 voters vote D > B > C > A.
4 voters vote B > C > A > D.
The matrix of pairwise defeats looks as follows:
A:B=6:9
A:C=6:9
A:D=10:5
B:C=12:3
B:D=4:11
C:D=4:11
***
Case 1: Suppose, that candidate D is elected.
If additional 4 voters vote D > A > B > C, the matrix
of pairwise defeats looks as follows:
A:B=10:9
A:C=10:9
A:D=10:9
B:C=16:3
B:D=4:15
C:D=4:15
Due to the No-Punishment Criterion, candidate D must
be elected. But due to the Condorcet Criterion,
candidate A must be elected.
***
Case 2: Suppose, that candidate B is elected.
If additional 6 voters vote B > D > A > C, the matrix
of pairwise defeats looks as follows:
A:B=6:15
A:C=12:9
A:D=10:11
B:C=18:3
B:D=10:11
C:D=4:17
Due to the No-Punishment Criterion, candidate B must
be elected. But due to the Condorcet Criterion,
candidate D must be elected.
***
Case 3: Suppose, that candidate C is elected.
If additional 8 voters vote C > B > D > A, the matrix
of pairwise defeats looks as follows:
A:B=6:17
A:C=6:17
A:D=10:13
B:C=12:11
B:D=12:11
C:D=12:11
Due to the No-Punishment Criterion, candidate C must
be elected. But due to the Condorcet Criterion,
candidate B must be elected.
***
Case 4: Suppose, that candidate A is elected.
If additional 4 voters vote C > A > B > D, the matrix
of pairwise defeats looks as follows:
A:B=10:9
A:C=6:13
A:D=14:5
B:C=12:7
B:D=8:11
C:D=8:11
Due to the No-Punishment Criterion, candidate A or C
must be elected.
***
Case 4a: Suppose, that candidate A is elected in case 4.
If additional 6 voters vote A > C > B > D, the matrix
of pairwise defeats looks as follows:
A:B=16:9
A:C=12:13
A:D=20:5
B:C=12:13
B:D=14:11
C:D=14:11
Due to the No-Punishment Criterion, candidate A must
be elected. But due to the Condorcet Criterion,
candidate C must be elected.
***
Case 4b: Suppose, that candidate C is elected in case 4.
If additional 4 voters vote C > B > A > D, the matrix
of pairwise defeats looks as follows:
A:B=10:13
A:C=6:17
A:D=18:5
B:C=12:11
B:D=12:11
C:D=12:11
Due to the No-Punishment Criterion, candidate C must
be elected. But due to the Condorcet Criterion,
candidate B must be elected.
******
Summary: I have demonstrated, that -independently on
who is elected- I can always add voters, such that either
the Condorcet Criterion or the No-Punishment Criterion
is violated.
In other words: If an election method, that meets the
Condorcet Criterion, is used, it can always happen, that
voters are punished for going to the polls.
Markus Schulze
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