Looney Labs Icehouse Mailing list Archive

RE: [Icehouse] IGDC Summer 2007 Rankings

  • FromAndrew Plotkin <erkyrath@xxxxxxxxxx>
  • DateWed, 26 Sep 2007 16:15:33 -0400 (EDT)
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.")


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