Hi Forest,
> De : Forest Simmons <[email protected]> > >On Thu, Oct 10, 2013 at 9:23 AM, Kevin Venzke <[email protected]> wrote: > >Hi Forest, > >>Unfortunately, I realized that an SFC problem is possibly egregious: >> >>51 A>B >>49 C>B >> >>B would win easily, contrary to SFC (which disallows both B and C). But more >>alarmingly it's a majority favorite problem. >> > >So it is non-majoritarian in the same sense that Approval is. In this case >the count is too close for approval voters to drop their second preferences, >so B will be the Approval winner. Of course with perfect information, they >would bullet, and A would win. Philosophically, in this situation I >sympathize with electing the candidate broader support (the "consensus >candidate") over the mere majority favorite, which is why Approval's failure >of (one version of) the Majority Criterion has never bothered me. > Well, as an Approval scenario this is pretty inexplicable. It suggests to me that the pre-election polling is not working. There should generally be two frontrunners, but both A and C factions are voting as though their favorite is not one of the two. That's odd to the point that I don't know how to say who should win based purely on the ballots. In a rank ballot setting, where you can see the majority, I think there's a risk of that majority complaining about the outcome and asking for a different method to be adopted. > >Jobst and I have gone to a lot of trouble to contrive methods that make B the >game theoretic winner in the face of such preferences. I'm sure you remember >his challenge to find a method that makes B the perfect information game >theoretic winner when utilities are given by (say) > > >60 A(100), B(70) > >40 C(100), B(50) > > >It seems that only lottery methods can solve this challenge in a satisfactory >way. We co-authored a paper with the double entendre title of "Some Chances >for Consensus" on this topic for the benefit of people who take the "tyranny >of the majority" problem seriously. > Yes, I read that paper. It was very interesting. It doesn't fit my perception of a proposable method, which is fine. It's just that IA/MPO, at first glance, seems pretty proposable. Not just the properties but the fact that the name is also the definition. > >In light of this fact I propose the following variation on our method: > > >1. Eliminate all candidates that have higher MPO than IA. > > >2. Elect the remaining candidate with the greatest difference between its IA >and its MPO. > > >I like differences better than ratios in this context, but I used ratios in >IA/MPO because I worried about people who couldn't easily agree that (25 - 30) >> (72 - 90) , for example. But now that we know eliminating all of the >negative differences is possible without eliminating all of the candidates, >let's switch to differences. > Well, if the elimination in step 1 recalculates MPO for step 2, you probably lose FBC. Hrm. MDDA's approach (i.e. for satisfying Majority Favorite, and SFC more broadly) is that if your MPO >.5 then you mostly can't win. MAMPO's approach is that if your IA is >.5 then only your MPO is considered, not your IA. I wonder if there are any other options. Both of these approaches are kind of drastic, and I don't think a method "needs" to completely satisfy SFC. Kevin Venzke ---- Election-Methods mailing list - see http://electorama.com/em for list info
