[EM] Friendly Approval

[Forest Simmons]

Remember Toby Nixon, a Washington State legislator who seriously consulted
with the EM List members to find the simplest decent Condorcet proposal
with a good chance of being adopted?

The method we settled on was Approval based Benham, which we called DMC for
Democratic Majority Choice (or Definite Majority Choice for Republicans).

The Benham elimination formulation was the first of several equivalent
descriptions: list the candidates in approval order and eliminate
candidates one by one from the bottom of the list, until some candidate
becomes undefeated among the remaining.

Jobst was the first to point out that Ranked Pairs, Beatpath CSSD, and
River were all equivalent to this method when defeat strength was gauged by
winning approval.

We came "that close" to getting DMC adopted, before some spoil sport
scuttled the project.

Another simple approval based Condorcet efficient method (even nicer than
DMC in some ways) is ASM, Approval Sorted Margins: sort the approval order
into a beatpath by transposing adjacent out-of-order-pairwise candidates,
giving priority to the pairs with smallest approval margins.

Another excellent one is approval based SPE (Sequential Pairwise
Elimination).

Another one is Approval Chain Climbing.

And finally approval based top two runoff, a truncated form of approval
based SPE, that we only mention because its score based STAR version has
gained some traction recently.

The only drawback is that these methods, without exception, in their
present forms have not been successfully adapted to Ranked Choice Voting
style ordinal preference ballots.

The closest thing to it has been RCV style ballots with optional approval
cutoffs, still very unsatisfactory for voters uncomfortable with the
decision of exactly where they should put that cutoff for optimal effect.

But now, finally we have a well-defined notion of approval in the Universal
Domain category (i.e. restricted to using only ordinal information from the
ballots) based on Kristofer's idea of "friendly" candidates. [This is my
adaptation of his idea.]

A candidate X is friendly to candidate Y if it does not directly defeat Y
pairwise.

And by extension we say that a ballot is friendly to Y if B's top ranked
candidate is friendly to Y.

We define candidate Y's friendly approval to be the number of ballots that
are friendly to Y.

Another way to say this is the total first place support of the candidates
that are friendly to Y.

This friendly version of approval suddenly opens up all of the wonderful
approval based methods mentioned above (and more) for inclusion in the
Universal Domain category!

Furthermore, it automatically confers Landau efficiency onto most of them,
because if  X covers Y, then X's friendly approval cannot be less than Y's.

Thus DMC based on friendly approval is Landau efficient.

We can expect Friendly Approval to have high Voter Satisfaction Efficiency,
because of the essential role of first place votes in its definition.

So now what's keeping us from proposing Friendly Approval based DMC?

-Forest
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