[EM] MUMA with runoffs?

Jameson Quinn jameson.quinn at gmail.com
Sat Oct 1 04:52:32 PDT 2016

It is my opinion that runoffs are in some cases a healthy addition to a
voting system. You shouldn't waste time with a runoff if the winner is
clear, but if it's a close race, focussing attention on only the
most-viable seems like a good idea.

So, how should runoffs interact with MUMA?

-If there are any candidates with majority upvotes, then the most-upvoted
should win, and there's no need for a runoff.
-If there is only one non-eliminated candidate (that is, without majority
downvotes and with more than half the upvotes of the most-upvoted), then
they should win, with no runoff.
-If neither of the above holds, and there is more than one
majority-acceptable (minority-downvoted) candidate, then the two
least-downvoted should go into a "pairwise" runoff.
-If no candidates are majority acceptable, then there should be a
"multi-way" MUMA runoff. (This should be decisive; no second runoff.)
Candidates in the runoff should include:

1)The two least-downvoted candidates from the first round

2)The one most-upvoted candidate from the first round (may be the same as
one of the above)

3)Any new candidate(s) who individually gets "nominated" by first-round
candidates totalling as many upvotes as the most-upvoted candidate [from 2)
above]. The candidates above from 1) or 2) may not nominate a new candidate
unless they themselves withdraw from the runoff. Each first-round candidate
can nominate only one new candidate.

Note that in many cases this "multi-way" runoff could have as few as 2
candidates, if 1) and 2) overlap and there is not enough agreement from
other candidates to put forward any 3).

In a center-squeeze scenario, using naive honest first-round ballots, this
runoff system would elect the CW in a pairwise runoff. Unlike one-round
MUMA, this happens without the centrist supporters being sophisticated
enough to use truncation strategy.

In a NOTA-type situation, on the other hand, you'd get a "multi-way"
runoff, with a possibility of new candidates. There are many ways for the
second round not to be another NOTA result, though of course it cannot be
entirely ruled out without foregoing a rated system for the second round.
In the most bitterly-divided electorates, the "multi-way" runoff would
actually be likely to have only two candidates, essentially guaranteeing
that one would get a nominal majority in the second round.

I still think that MUMA without runoffs should be the primary proposal.
MUMA with runoffs is only intended for cases where runoffs are already part
of the voting system, and where voters care about the extra robustness they
can give.
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