[EM] MUMA like method with MJ style ballots

Jameson Quinn jameson.quinn at gmail.com
Wed Oct 5 08:17:19 PDT 2016

Inspired by Forest's proposal, I did think of a way to simplify MUMA still
further. I call it NUMA, Net Upvotes Majority Approval.

Ballot has 3 levels: upvote/preferred, neutral, or downvote/unacceptable.
Default is neutral for candidates with over 25% upvotes, and downvote
otherwise. Anyone with majority downvotes is eliminated. Of the remaining
candidates (or, if none remain, of all of them), the winner is the one with
the highest "net score" (upvotes minus downvotes).

In practice, the winning score could easily be negative, even for a
reasonably good candidate, in a chicken dilemma scenario. For example,
imagine Clinton/Obama/McCain; Obama had a historically high median
temperature in polls, but if he lost upvotes to Clinton, he could still end
up with a negative score. That's OK.

This is slightly worse than MUMA on chicken dilemma, but slightly better on
center squeeze. I think most real-world chicken dilemma scenarios will have
at least a dash of center-squeeze dynamics; that is, the Condorcet-losing
plurality will have a weak net preference for one of the subfactions of the
majority. If that's true, then NUMA is better than MUMA.

It's more of a stretch to claim that NUMA is a variant of Bucklin, though.
It's more like a Bucklin/Score hybrid; or, if you want to speak of only
systems with a longer pedigree, a Bucklin/Borda hybrid.

I think that NUMA is easier to explain than MUMA.


If you want a runoff version: If any candidate has a majority upvotes, or
if only one candidate has a majority non-downvotes and at least 25%
upvotes, then they win in the first round. If more than one candidate has a
majority non-downvotes and at least 25% upvotes, then the two of those with
the highest net score go to a runoff. Otherwise, the runoff includes the
two candidates with the fewest downvotes and at least 25% upvotes, and the
two candidates with the highest net scores; this could be 2-4 candidates in

A new candidate may be added to the runoff if they have support from
first-round candidates whose pooled upvotes and max explicit downvotes
would have given them a net score high enough to be in the runoff. Such
support may only be given once and any candidate giving such support must
withdraw from the runoff if they themselves would be eligible. Such support
must be announced within a reasonably short time frame (say, 1 week) of the
initial election.

So if the first round was:

Total votes: 100
A: +30 -60; net -30
B: +26 -55; net -29
C: +20 -40 (-5); net -25
D: +20 -60 (-20); net -60
E: +15 -15 (-70); net -70

Type II runoff. A and B qualify by fewest downvotes and 25% upvotes; B and
C qualify by highest net; and D and E combined have 35 upvotes and 60 max
explicit downvotes, or enough for an net of -25, so if they both support a
new candidate F, the runoff would be between A, B, C, and F.

2016-10-05 7:35 GMT-04:00 Jameson Quinn <jameson.quinn at gmail.com>:

> I think Forest's proposed method is quite a good one in practice. But as
> soon as you bring pairwise into the picture, you fall into a trilemma:
> 1. If you do pairwise between more than two candidates, you need a
> Condorcet tiebreaker, and so complexity explodes.
> 2. If you do pairwise between two candidates selected by different ballot
> thresholds, then only one of the chicken-dilemma allies will make it; this
> means that the chicken problem will be as bad as in approval.
> 3. If you do pairwise between the top two candidates at one ballot
> threshold (ie, above-bottom), then you encourage cloning.
> Forest's proposal falls into 2. Personally, I think 3 is the best of those
> options. For instance, I'd like a 3-slot "pairwise winner of the most
> acceptable" (PWMA) method: 3-slot ballots, elects pairwise winner between
> the two with fewest explicit bottom-ranks.
> Or, for a system that falls into 1, "pairwise MUMA": eliminate as in MUMA,
> choose the CW if one exists, otherwise fall back to MUMA (most upvotes).
> I think any system falling into 1 or 3 will in practice get results as
> good as MUMA. In fact, slightly better: it helps deal with center squeeze.
> I have my doubts about 2; it could spoil over chicken strategy.
> Also, a minor point: any method that brings a pairwise race into account
> is n²-summable, not n-summable. This has implications for ballot-counting
> machines.
> All in all, though, I still favor MUMA as the simplest robust system that
> beats approval.
> 2016-10-04 20:52 GMT-04:00 Forest Simmons <fsimmons at pcc.edu>:
>> How about Grade style ballots as in Majority Judgment, but simple MUMA
>> style counting:
>> Each voter assigns grades A, B, C, D, or F to each of the candidates.  A
>> blank counts as an E, between D and F.
>> Elect the pairwise winner between the candidate with the greatest number
>> of votes above C (pretty good), and the greatest number of votes above D
>> (not too bad)
>> It seems to me that this simple method would be even more apt than MJ to
>> elicit sincere ballots.  In fact, if the pretty good (PG) and not too bad
>> (NTB) marks were not strictly required to be consistent with the grade
>> marks, then there would be no incentive to vote insincere grades or to
>> collapse preferences beyond the built in resolution constraint
>> corresponding to only six levels.
>> It would be fun to see if voters did vote their grades consistent with
>> their PG and NTB marks when not required to.
>> For more resolution in the pairwise comparison allow grades with plus (+)
>> or minus (-) attached.
>> And while we're proposing simple methods, don't forget basic single
>> winner asset voting as first advocated by Charles Dodgson (aka Lewis
>> Carroll).
>> Forest
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