[EM] IA/MPO

[Kevin Venzke]

Hi Forest,


> De : Forest Simmons <fsimmons at pcc.edu>
>
>On Thu, Oct 10, 2013 at 9:23 AM, Kevin Venzke <stepjak at yahoo.fr> 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