[EM] Approval versus Ranked methods

[Simmons, Forest]

Rep. Nixon rightly opined that Approval would not be favored as a proposal because people want to be able to distinguish their favorite from their lesser evil compromise.
 
Although Approval satisfies the weak Favorite Betrayal Criterion (FBC), what people really want is the Strong FBC which allows them to rank their Favorite strictly above Compromise, without hurting Compromise's chances in the event that Favorite is not strong enough to win.
 
Some of the ranked ballot methods, including IRV  (at first blush) give the illusion of satisfying the Strong FBC, when in reality they do not even statisfy the weak FBC that Approval satisfies.
 
However, in a race that isn't too close IRV, Schulze, DMC, and other ranked methods allow voters to get away with ranking Favorite strictly above Compromise.
 
I would like to point out that although Approval beats Shulze(wv) which beats Shulze(margins) with respect to the weak FBC,  wv is no better than margins when it comes to the Strong FBC that everybody covets so strongly.
 
How does DMC fit in here?  I believe that, like wv, it is better than margins, when it comes to the weak FBC, and on a par with winning votes.  I believe DMC slightly beats wv when is comes to the Strong FBC, because (among other reasons) in at least some cases where ranking Compromise equal with  Favorite is required in wv methods, under DMC it suffices to approve Compromise without ranking it equal to Favorite.
 
In a recent posting I have detailed the precise conditions for a violation of the Strong FBC in DMC, and have explained why they are very unlikely to be met in practice.  It would be helpful if someone could do a similar analysis for Shulze(wv).
 
[I'm assuming that most people will not consider equal approval as a violation of Strong FBC as long as they can still distinguish by rank.]
 
A simple method that completely satisfies the weak FBC, and comes close to satisfying the Strong FBC is Majority Choice Approval (MCA).  Voters specify a favorite as well as other acceptable candidates.  If no candidate is listed as favorite on more than fifty percent of the ballots, then the most acceptable candidate is elected.
 
That said, an even simpler method comes closer to satisfying the Strong FBC than any of these other more complicated methods:  Asset Voting:
 
Voters vote for their favorite, who represents them by proxy in an election completion convention.  Write-ins are allowed.  In the completion convention the proxies (i.e. the candidates including write-ins) get as many votes (their "assets") as they were granted by the voters.  In other words, whatever ballots they cast in the election completion method (some reliable method like Approval, DMC, or Shulze) are given weights equal to their "assets."
 
This method is called asset voting because if these proxies diappoint their supporters, then after the election they will be kicked out into the street and be left sitting on their assets.
 
I think that we should go for Asset Voting, MCA, or DMC.  If we are going to get more complicated than DMC, we should go for Approval Weighted Pairwise, which is Schulze with defeat strength measured by Approval Opposition, which is a great improvement (with respect to Strong FBC) over wv at negligible cost.
 
Forest
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