[EM] Ordering defeats in Minimax

[Kristofer Munsterhjelm]

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:
>
> https://arxiv.org/ftp/arxiv/papers/1606/1606.04371.pdf
>

[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