[EM] MUMA like method with MJ style ballots
jameson.quinn at gmail.com
Wed Oct 5 10:53:47 PDT 2016
I'm renaming NUMA to MAS, Majority Acceptable Score. (In Spanish, Mayoría
Aceptable Sopeso.) Here's the new, equivalent, definition:
You should explicitly give 0, 1, or 2 points to each candidate; call these
actions "downvoting", "midvoting", and "upvoting". Eliminate all candidates
who were downvoted by a majority. Then, take the highest remaining point
score, or if no candidates remain, the highest score overall.
Default rule: If a candidate gets upvoted by over 25%, blank votes for them
count as midvotes (1 point); if they get upvoted by less, blank votes for
them count as downvotes (0 points). A voter who leaves all candidates in a
race blank is not counted as having voted in that race at all.
Obviously, this could in principle be simplified yet further, with
essentially no strategic consequences in the abstract, by simply having
blank votes always count as downvotes. However, I think that would be bad
in a chicken dilemma situation, where most voters will tend to do what they
thing most other voters will tend to do. Thus, it should be clear that the
default in a chicken dilemma is to midvote, while the default for a dark
horse candidate is to downvote.
By redefining it to scores of 0/1/2 instead of -1/0/1, I remove the
possibility of negative scores, which simplifies things for those not
comfortable with math.
2016-10-05 11:17 GMT-04:00 Jameson Quinn <jameson.quinn at gmail.com>:
> 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
>> 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
>> 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
>>> Election-Methods mailing list - see http://electorama.com/em for list
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