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
----
Election-Methods mailing list - see http://electorama.com/em for list info
