[EM] BTR-like phrasing of Benham

Kristofer Munsterhjelm km_elmet at t-online.de
Fri Dec 6 15:09:08 PST 2019

Here's a BTR-IRV-like phrasing of Benham. The ballot counters would
probably not appreciate the extra work, but there's a benefit that it
can easily be used in STV as well:

- When choosing a candidate to eliminate, consider the two candidates A
and B with fewest first preference votes (A having fewer than B). If A
wins a runoff against every other remaining candidate, eliminate B;
otherwise, eliminate A.

This works because if, after some eliminations, X is the CW among the
remaining candidates, then X will never be eliminated after that point.
Thus the candidate who remains until the end is the Benham winner. It
works in STV as well because as long as the election and surplus
distribution based on first preferences work the way they do in STV, the
method passes Droop proportionality, no matter what candidates are

Similarly, transplanting the BTR elimination mechanism onto STV will
preserve Droop proportionality. I think Rob suggested that the
eliminated candidate for STV-ME (BTR-IRV's STV analog) should be the
loser of a Condorcet method's election among the (s+1) candidates with
the fewest votes, where s is the number of seats remaining to elect
candidates to. That strikes me as a little too complex, though.

Just basing the method on globally preserving the CW is easier, although
it might produce somewhat of a centrist bias within each solid
coalition. Then again, it might not, given how the surplus distribution
works. E.g. the first solid coalition would elect a global CW if there
is one among it; but then everybody who voted for this global CW in
first place after eliminations would be deweighted, so that later "CWs"
would be biased in the opposite direction, somewhat. It's hard to tell.

Even if it's centrist-biased, that might not be a bad thing. See e.g.
arguments for deliberately giving the center greater weight in an
otherwise proportional system to limit unfair kingmaker scenarios.

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