On Wed, 26 Sep 2007, Dale Sheldon wrote:
On Wed, 26 Sep 2007, Doug Orleans wrote:
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.
This is why standard ranked-pairs is to have all unranked candidates lose to
any ranked candidates on a ballot; honestly, that's probably how voting aught
to be done for this, because counting partial ballots the way we do /does/
break the algorithm, just as you described. Does doing so change the outcome
in this case?
I don't think it's a matter of "breaking the algorithm". In the
(hypothetical) situation Doug describes, one person thinks TA is the best
game, and nobody has gone on record to say that any game is better than
TA. It is not unreasonable to look at that situation and say, okay, TA is
on top of the list. Weakly, I admit! You have to drop the intuition that
"winner" means "most strongly voted for". But I think Condorcet wants you
to get rid of that intuition anyway.
(You can get the same situation even with complete ballots, anyhow. It's
just less likely. Imagine fifty people rank TA on top, and forty-nine
rank it on the bottom. Forty-nine of the stated preferences cancel out,
leaving TA the overall winner... it's still a weak outcome, just due to
being hotly contested, rather than apathy.)
I don't have the IGDC#5 ballots in front of me, but I'm positive that
changing them to "unlisted entries tie for last" would change the outcome.
It's not a fair comparison, though. The contest was run under the
instruction that leaving a entry off neither helps nor hurts it. If you
change how you interpret the ballots, you have to tell people in advance;
it changes how they'll vote.
The solution I'd actually recommend is to say: any game which is listed on
fewer than N ballots is eliminated.
(Note that this solution is not just for Condorcet elections. The IFComp
uses a simple "give each game a score from 1 to 10, then we find the
average" rule. It *also* has this elimination rule, and for basically the
same reason! If game X is listed on just one ballot, and gets a 10, then
its average is 10 and it wins the IFComp. But we can't require that
everybody play every game -- and it seems deeply wrong to say "If you
don't list a game, that counts as a 1.")
"And Aholibamah bare Jeush, and Jaalam, and Korah: these were the borogoves..."
It used to be that "conservatives" were in favor of smaller government,
fiscal responsibility, and tighter constraints on the Man's ability to
monitor you, arrest you, and control your life.