Here's the upshot of my explorations on this topic:

Let R(X) be the Range total for alternative X, and let MPO(X) be its Max Pairwise Opposition ...

Elect the alternative that maximizes the ratio of R(X) to MPO(X).

For ranked preference ballots, replace R(X) with the average of the definite and implicit approvals.

The implicit approval IA(X) is the number of ballots on which X is ranked. The definite approval DA(X) is the number of ballots on which X is ranked top or equal top plus the number of ballots on which X is marked as definitely approved.

If a voter is not sure about definite approval, then it is not definite approval, so this sidesteps the high stakes dilemma of the approval cutoff in standard Approval.

But like standard approval this stable approval method satisfies the FBC; there is no risk in voting favorite in the equal top position on a ballot.

How about Condorcet efficiency? Somebody should run some simulations.

In summary, the methodÂ elects the alternative X that maximizes the ratio...

(IA(X)+DA(X))/2)/MPO(X).

The greater the ratio the more impervious to manipulation!

----

Election-Methods mailing list - see

https://electorama.com/em for list info