Re: [EM] Ordering defeats in Minimax
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
After All") is very interesting:
https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
There are many papers where some author makes presumptions
about the distribution of the voters and the candidates,
about the used strategies, about how the performance of an
election method is measured in concrete test cases, etc..
The author then proves that his favorite election method
performs better than every other known election method.
However, this is not surprising. The purpose of an
election method is to find the best candidate according
to some heuristic. So you can always use test cases where
this election method's heuristic happens to be met exactly
and then claim that you have proven with random simulations
that your favorite method is the best.
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.
Markus Schulze
To follow up on this, the method implemented by CIVS is Darlington's T3
method, described in the paper Markus mentions. The main criterion by
which he judges methods is minimum change; that is, the candidate who
is closest to becoming a Condorcet winner if some votes are changed.
This criterion is attractive because it makes the results tend to be
stable with respect to adding or subtracting voters. The biggest
downside is that, as he demonstrates in Section 1.2, a Condorcet loser
can be the candidate who is closest being a Condorcet winner. His
corresponding example can be found here:
http://civs.cs.cornell.edu/cgi-bin/results.pl?id=E_e5c3c20972af0ab5
-- Andrew
Markus Schulze wrote:
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
After All") is very interesting:
https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
There are many papers where some author makes presumptions
about the distribution of the voters and the candidates,
about the used strategies, about how the performance of an
election method is measured in concrete test cases, etc..
The author then proves that his favorite election method
performs better than every other known election method.
However, this is not surprising. The purpose of an
election method is to find the best candidate according
to some heuristic. So you can always use test cases where
this election method's heuristic happens to be met exactly
and then claim that you have proven with random simulations
that your favorite method is the best.
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.
Markus Schulze
On 05/06/2017 11:33 AM, Markus Schulze wrote:
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
After All") is very interesting:
[snip]
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.
If the best method ends up being Minmax, wouldn't the second best
presumably be the most Minmax-ish of what's left? If so, which method
ends up being second best might not be all that more interesting than
which method ends up being best.
I also find this comment of Darlington's somewhat surprising:
Green-Armytage (2014) compared 8 electoral systems
on 5 forms of strategic manipulability. He
found that all 8 were somewhat manipulable, but Borda
was worst while minimax was one of the less
manipulable systems.
Page 17 of that paper shows that there are broadly speaking three
classes of strategy resistance. The least resistant methods (Borda,
Approval, Range), general Condorcet methods (and Plurality), and then
Hare and the Hare hybrids.
Minmax belongs to the middle class, so it's only "one of the less
manipulable" in that it's not in the least resistant class
Some quick observations on the paper.
I agree that those criteria that do not allow electing the Minmax winner D of the example should not be considered as criteria that should always be true.
The paper aimed at using continuous and appropriately monotonic functions as preference functions. They fall within the families of natural preference functions that I described in a recent post. Or actually in the smaller family (W-L)(W+L)^k or (W-L)/(W+L)(W+L)^k. I.e. methods in a continuous range from proportions/ratio to the proposed square root based approach, and finally to Minmax, but not beyond that point, although methods beyond that point might be interesting too.
The approach of using the second preferences as tie breakers may be problematic because of problems with having or not having clones. Also the approach of using e.g. a square root based method to solve the ties of basic Minmax is a bit ad hoc. One simple approach to solving most of the ties in Minmax is simply to compare the W+L values of the tied candidates (to break ties in pairwise comparisons). That's what k values very close to 0 (e.g. -0,0001) would do anyway in (W-L)*(W+L)^k.
Don't take these comments too seriously since I skimmed the paper already few days ago, and this is about as much as I can remember of the comments that I had then :-).
Juho
On 06 May 2017, at 12:33, Markus Schulze markus.schulze@alumni.tu-berlin.de wrote:
Hallo,
Darlington's paper ("Minimax is the Best Electoral System
After All") is very interesting:
https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
There are many papers where some author makes presumptions
about the distribution of the voters and the candidates,
about the used strategies, about how the performance of an
election method is measured in concrete test cases, etc..
The author then proves that his favorite election method
performs better than every other known election method.
However, this is not surprising. The purpose of an
election method is to find the best candidate according
to some heuristic. So you can always use test cases where
this election method's heuristic happens to be met exactly
and then claim that you have proven with random simulations
that your favorite method is the best.
Therefore, a more interesting question is which election
method performs the second best. Here, Darlington writes
that the Schulze method performs the second best, only
slightly worse than his favorite method.
Markus Schulze
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