Looney Labs Icehouse Mailing list Archive

RE: [Icehouse] IGDC Summer 2007 Rankings

  • FromDoug Orleans <dougorleans@xxxxxxxxx>
  • DateWed, 26 Sep 2007 15:38:41 -0400
Dale Sheldon writes:
 > I don't find the system to be unintuitive.

Perhaps "unintuitive" is the wrong word.  It makes perfect sense in
theory, but looking at a table of votes and figuring out the results
is far from obvious.

 > The complication comes, and this vote has some great examples, of what do 
 > to when A beats B, B beats C, and C beats A, as happened, when Subdivision 
 > beat Zamboni Wars, Zamboni Wars beat Moonshot, and Moonshot beat 
 > Subdivision.
 > The base Condorcet method doesn't address how to handle so-called 
 > "Condorcet ties", but the Ranked Pairs method, which was used for this 
 > vote, breaks the tie by, essentially, ignoring the "weaker" wins; ZW beat 
 > MS by 15, and SD beat ZW by 4, while MS beat SD by only 2.  (It's 
 > explained a bit more wordily for precision's sake, but that's the meat of 
 > it.)

And here's that URL again:  http://condorcet.org/rp/

Unfortunately, the Ranked Pairs method does not say what to do when
all the wins in a tied group are equal[1], which also happened here:
Pylon beat Zamboni Wars by 2, Zamboni Wars beat Penguin Soccer by 2,
and Penguin Soccer beat Pylon by 2.  This is where Zarf's tiebreaker
(which is not part of the standard Ranked Pairs method) comes in, by
looking at which games beat more other games, or lost to fewer, but
I'm still a little fuzzy about exactly how and when this tiebreaker is
applied.  And the fact that Zarf's new program gives slightly
different results from his old program, and Timothy Hunt's procedure
appears to be slightly different from either of Zarf's programs, makes
me think that there are still some kinks to work out (even though they
did all give the same result here).

I'm also a little worried about problems that could result from
allowing incomplete ballots.  For example, suppose Trip Away had only
appeared on one ballot (because, say, no one else could figure out how
to play from the rules), but it was ranked first on that ballot, above
all the other games.  It would then win the competition, because its
margin over every other game would be 1, and there would be no
inconsistencies.  In practice, I highly doubt that anything like this
would happen.  But I think it shows that it's important to have enough
players play every game (or, more precisely, to have every game played
by enough players).  Perhaps a game should be required to appear on
some minimum percentage of ballots or be disqualified?

 > That said, it was a _very_ close contest, and there's no such thing as a 
 > "perfect" voting system; but Condorcet Ranked Pairs is a fair sight better 
 > than most, in my opinion.

Perhaps, but the issue here is Condorcet Ranked Pairs With Incomplete
Ballots And Zarf's Tiebreaker.  I'm sure we can either show that it's
sound or tweak it until it is, but I'm not quite there yet.

(By the way, my reservations about this method do not at all apply to
using it in "real-life" elections, where the ratio of voters to
candidates is several orders of magnitude higher, and where you only
need one winner instead of a total ordering.  The issues discussed
here would practically never occur in that situation, and I'm fully in
favor of advocating for preference voting as a vast improvement over
our current broken electoral systems.)


[1] Actually, the ranked pairs website does say what to do in the case
of ties: resolve them randomly.  http://condorcet.org/rp/details.shtml
Obviously that's unsatisfactory here.