Kevin, Let's call the method that elects the candidate with the max (non-negative) difference between IA and MPO, "IA-MPO."
This method satisfies FBC, Plurality, Monotonicity, and the Mono-Add-Top version of Participation. In addition it has the property that if a ballot that does not truncate the current winner is added, the new winner (if any) will be someone not truncated on the added ballot. IA-MPO fails the Majority Criterion, but the following variant satisfies the MC and therefore should be more proposable: 1. Eliminate all candidates that have greater MPO than IA. 2. Elect from among the remaining candidates one with the least MPO (not recalculating MPO's). Here's a short proof that step one does not eliminate the Implicit Approval winner: Let A be the candidate with max IA, and suppose that this max value is IA(A). Let MPO(A) be the max pairwise opposition against A, and let B be a candidate that is ranked above A on MPO(A) ballots. Then B's IA is at least MPO(A), which cannot be greater than the approval winner's IA. Therefore MPO(A) is no greater than IA(A). In other words the Implicit Approval winner is never eliminated by step one above. If I am not mistaken, this MC compliant method still satisfies the FBC, Plurality, etc. and even satisfies Mono-Add-Plump, but not Mom-Add-Top. What do you think? Forest On Fri, Oct 11, 2013 at 6:53 AM, Kevin Venzke <step...@yahoo.fr> wrote: > Hi Forest, > > > > De : Forest Simmons <fsimm...@pcc.edu> > > > >On Thu, Oct 10, 2013 at 9:23 AM, Kevin Venzke <step...@yahoo.fr> wrote: > > > >Hi Forest, > > > (....) > Well, if the elimination in step 1 recalculates MPO for step 2, you > probably lose FBC. > > Important reason to not re-calculate the MPO's > 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 >
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