[EM] Another approach to declonification, clone-liberation, or whatever you want to call it.

[Forest Simmons]

We need a good connotation-neutral word for "nfluentiality" or
"impactfullness" ... two very awkward, unsatisfactory neologisms.

On each ranked preference ballot give each voter the option of putting a
check mark next to the name of the candidates tied for being most
influential/impactful with regard to the issues at stake in the election.

Explain that you mean the candidates most distant from zero on a scale of
negative infinity to positive infinity ... i.e. the candidates tied for
least neutral.

The impactfullness/importance/influentiality score Im(X) for candidate X is
the number of ballots (counted fractionally) on which X is among the
check-marked. So if X is one of k candidates check-marked on ballot B, then
ballot B contributes a fraction 1/k to X's Im(X) total.

De-cloned Copeland becomes ...

For each candidate X, let W(X) and L(X) be the respective sums given by ...

W(X)=Sum{Im(Y)| X pairwise defeats Y},

and

L(X)=Sum{Im(Z)| Z pairwise defeats X}.

Elect the candidate X with the greatest difference W(X) - L(X).

The lack of any positive or negative connotation of Im(X) makes
monotonicity easy to prove;  because of this presumed neutrality of Im(X),
raising X on a ballot has no ipso facto expected effect on Im(X).

Counting the check-marked contributions to Im(X) fractionally is the key to
clone independence.

That said, for simulation purposes, on each ballot you could put a default
check-mark next to the name of each candidate that is ranked equal top or
equal bottom.

[... which also shows how to bring this method fully into the Universal
Domain tent.]

By the way, if X covers Y, then the W-L score of X will be at least as
great as the W-L score for Y, which shows that (like ordinary clone
infested Copeland) the method elects from Landau.

-Thanks!
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