[EM] Inclusion/Exclusion Multiwinner Approval Idea

[Forest Simmons]

Here's an idea that has nothing to do with Binomial STV except that it
popped into my head while puzzling over clues patiently provided by Richard
Lung:

Voted ballots mark some candidates as definitely approved, others as
definitely disapproved, with the unmarked considered to be indifferent
"abstentions."

Each possible slate of candidates is given both an inclusion score and an
exclusion score by each ballot. The inclusion score is the sum
1+1/2+...1/j, where j is the number of slate members marked definitely
approved by the ballot. Similarly, the exclusion score is the harmonic
series truncated at the k_th term, where k is the number of definitely
disapproved candidates excluded from the slate.

For each slate, both ballot scores (inclusive and exclusive) are summed
over all ballots.

Finally, the geometric mean of the two sums becomes the final score for the
slate under consideration.

The slate with the highest score is elected.

Those familiar with proportional approval voting (PAV), will recognize this
method as a combination of ordinary PAV applied to both the slate and its
complement.

There are only nCm possible slates of m candidates chosen from among n
candidates, so not exponentially hard.

For manual counts you would need to stick to nominated slates.
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