[EM] Post-mortem on wikimedia's recent approval-with-abstention election

[Kristofer Munsterhjelm]

On 07/05/2013 12:29 AM, Jameson Quinn wrote:
> https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections_2013/Post_mortem
>
> I think it would be worthwhile to bring some expertise to the section at
> the end. But let's keep it on-topic and try to keep from getting too
> deep into the election theory weeds.

I don't have a user on Wikipedia, but I'll comment here about my first 
impressions.

It seems there are three main issues being raised here:

- That Schulze is not a multiwinner method but the Wikipedia election is 
a multiwinner election[1],
- that Schulze is really complicated and the results are hard to parse,
and
- that it is not intuitive that unranked means bottom rank.

-

That the Schulze method is not multiwinner is very true, but nor is the 
average approval method. Both of these methods can elect a long string 
of clones if the voters behave in a particularly partisan manner. 
However, there are really no very simple set-proportional (i.e. Droop 
proportional or analogous) voting methods. The simplest one is STV (or 
possibly Benham's recent method), but if you want Condorcet logic, it 
gets very hairy very quickly.


Complexity is a significant downside to Schulze, and there seems to be 
two two objections on the Wikimedia page. First, that who wins (and his 
margin) is not obvious; second, that the actual matrix is hard to parse. 
Now, there are ways to make Schulze continuous (so that it would say, 
for instance, "Chen, 31.5%")[2], but this would make the method itself 
extremely complex. So I don't think we can have a more "justified" way 
of showing the quality of the winners without paying for it with 
significant complexity.

If the objection that "who wins is not obvious" instead regards the 
method, then we're not so quite out of luck. Other Condorcet methods may 
seem more intuitive: I think the Ranked Pairs method is moreso, for 
instance. On the one hand, this is a distraction. Whether or not the 
algorithm itself goes through intuitive-seeming steps doesn't matter 
from a game theory/social choice point of view - the results matter. On 
the other hand, I understand how some would prefer a more 
intuitive-sounding method: it grants some confidence that the method 
won't sneak up on them, do weird things with their ballots, and 
subsequently provide a very wrong result. So if the method seems opaque, 
well, then perhaps a less opaque method would be better.

As for the Condorcet matrix, one shouldn't have to parse it directly. 
There is a lot of information there, and it's not really relevant to 
examinations of the result, I think. But I further suppose that the 
matrix could be made more visual by coloring victories in different 
shades of green and losses in different shades of red - as long as that 
doesn't produce more confusion than insight[3].


Finally, it may or may not be obvious that unranked means "worse than 
the rest". Here we have the same "does unranked mean disapproval or just 
no opinion?" question that I mentioned when talking about the Plurality 
criterion. Either can be defended, but I think at its extreme, average 
(i.e. unranked means no opinion) has a dangerous edge case where only a 
few supporters rank/rate a certain candidate and he then wins. So, at 
least to me, it seems that pointing the "Approval-style" interpretation 
of the ranked ballot in Schulze would suffice. Make it clear what the 
ballot *means* and then link to reasons why it's defined that way for 
the voters that would like more details.

----

[1] Oddly, on the 2011 page about this, Rob Richie said: "The Schulze 
method is a very defensible voting method to use when electing one 
person ...". Huh. There was no signature, though, so we can't be sure it 
really was him.

[2] E.g. http://arxiv.org/abs/0912.2190 and http://arxiv.org/abs/0912.2195 .

[3] Here's an example of a gradient-colored matrix: 
http://www.koth.org/lcgi-bin/hugetable.pl?hill