[EM] election strategy paper, alternative Smith, web site relaunch

[James Green-Armytage]

Hello. This is James Green-Armytage, replying to Chris Benham.

>> I focus on the nine single-winner voting rules that I consider to be the
>> most widely known, the most widely advocated, and the most broadly
>> representative of single-winner rules in general:
>> these are plurality, runoff, alternative vote, minimax, Borda, Bucklin,
>> Coombs, range voting, and approval voting8.
>
> I would think that Schulze(Winning Votes) is more "widely advocated" than
> "minimax", aka MinMax(Margins).

Well, I analyze the vulnerability of beatpath (and ranked pairs) to a  
simple burying-and-compromising combination strategy, but so far I  
haven't written an algorithm to exhaustively determine when it is and  
isn't vulnerable to strategic voting. Perhaps I should say that I'm  
focusing on minimax because it's one of the simplest and most obvious  
Condorcet methods. To me, this is somewhat implied by saying that I'm  
focusing on 'broadly representative' methods, as minimax is probably  
the most 'generic' Condorcet method around.

The exhaustive voting analysis code for minimax is already very  
complicated. (Have a look at section 4.1 in general and 4.1.9 in  
particular, and then the minimax code at  
http://www.econ.ucsb.edu/~armytage/codes.pdf ). I'm sure that it's  
possible to do the same thing for beatpath, but I'm guessing that it  
would be a headache, and judging by the results of simple strategy  
analysis, it would end up in a very similar result anyway. (That is,  
we know from this analysis that beatpath and ranked pairs aren't  
substantially less vulnerable than minimax, and I see no reason to  
think that they would be substantially more vulnerable.)

I really don't think that using winning votes rather than symmetric  
completion would make a substantial difference to my analysis. Just  
about any group of votes that a strategic coalition can produce given  
symmetric completion, can also be produced given winning votes.  
Likewise, I don't think that casting truncated ballots as allowed by  
winning votes opens up any useful strategic possibilities.

I've written in the past about the advantage of winning votes  
Condorcet methods over margins methods in allowing for more stable  
counter-strategies. As far as I know, that analysis is still valid,  
but it doesn't apply here, because I don't get into counter-strategy  
in this paper. I'm trying to answer the question of which methods  
allow people to simply not worry about strategy at all, with the  
greatest frequency.

> I find these "assumptions" about ballots that are truncated or have
> equal-ranking to be very unsatisfactory.
> It means that the version of Bucklin you are considering is a strange one
> (advocated by no-one) that fails the
> Favorite Betrayal criterion. It would also fail Later-no-Help, which is met
> by normal Bucklin.

I make that assumption as a way of treating the different methods  
equally. It makes little to no difference for most of the methods that  
I look at. It makes a very tiny difference for Borda, and it makes  
coding substantially more straightforward. It actually does make a  
major difference for Bucklin, as I note in subsection 4.1.8. Bucklin  
without symmetric completion is strictly more vulnerable to strategy  
(and I'd imagine, by a noticeable amount) than the version I use in  
the paper. I can run some simulations on the other version for you, if  
you like (the version without symmetric completion) -- actually, the  
coding for this version is monumentally easier than the coding for the  
version I used. I'm quite sure that it would be bad to put two Bucklin  
versions in the paper, because people don't care that much about  
Bucklin to begin with. It's possible that I chose the symmetrically  
completed Bucklin in part because I didn't want to shrink away from  
the intellectual challenge involved. Have a look at 4.1.8 and the  
Bucklin code -- it's tricky!

>> Coombs
> Surely this is a museum curiosity that no-one currently advocates?

Yeah, I don't know anyone who advocates Coombs, but it appears quite  
often in the academic literature on voting strategy and comparative  
voting systems in general. It also generates some interesting  
comparisons, and rounds out the group a bit, so I'm glad that it's in  
there.

Sincerely,
James