[EM] Reversal Symmetry Criterion & Borda-Elimination
Blake Cretney
bcretney at postmark.net
Wed Nov 7 19:42:39 PST 2001
On Tue, 6 Nov 2001 19:30:25 -0800 (PST)
Steve Barney <barnes992001 at yahoo.com> wrote:
> I don't believe the Borda-Elimination method fails the Reversal
Symmetry
> Criterion, as claimed on the "Electoral Methods: Standards and
Criteria"
> webpage (which is listed in the EM list's bookmarks in Yahoo
Groups).
That's my site. I have been known to be wrong, but not this time.
> According to _Chaotic Elections_, the recent voting theory book by
UC-Irvine
> professor Donald Saari, all methods based on pairwise rankings and
tallies
> satisfy this condition. Saari ought to know, as he is probably the
original
> source of this criterion. I asked Dr. Saari about this, and he said
"...they
> are wrong in the comment about Borda elimination. If all individual
rankings
> are reversed, then the Borda ranking is reversed. (This is in
Chaotic
> elections.) Thus, if X was top-ranked before, X is bottom ranked
now. As
> such, X is the first candidate to be eliminated."
Although a Borda winner cannot win for the reversed ballots using
Borda-elimination, that's beside the point. The question is whether a
Borda-elimination winner can win for the reversed votes using
Borda-elimination.
Here's an example where it does. This is the input and output for my
VoteEngine. I notice that it still incorrectly prints the name as
Nanson, even though I stopped using that name to avoid confusion with
Nanson's other method. I'll have to fix that.
./voteengine.py -m borda-elim -cands A B C
40: A B C
35: B C A
25: C A B
VOTES 100
A B C
A X 65 40
B 35 X 75
C 60 25 X
Nanson
Cand Borda count
A 105.0
B 110.0
C 85.0
Cand Borda count
A 65.0
B 35.0
Winner A
./voteengine.py -m borda-elim -cands A B C
40: C B A
35: A C B
25: B A C
VOTES 100
A B C
A X 35 60
B 65 X 25
C 40 75 X
Nanson
Cand Borda count
A 95.0
B 90.0
C 115.0
Cand Borda count
A 60.0
C 40.0
Winner A
---
Blake Cretney
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