[EM] Ordering defeats in Minimax

[Andrew Myers]

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
>
>