[EM] Reversal Symmetry Criterion & Borda-Elimination

[Blake Cretney]

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