[EM] MUMA like method with MJ style ballots

Jameson Quinn jameson.quinn at gmail.com
Wed Oct 5 16:56:29 PDT 2016

One final adjustment to MAS.

Problem: in a center squeeze scenario, the squeezed center could plausibly
get less than 25% upvotes, but should still get a default of midvotes,
because they will probably get a number of explicit midvotes.


New default rule: If a candidate gets upvoted by over 25%, *or explicitly
midvoted by 50%, or any combination which yields the same score as these
two possibilities*, blank votes for them count as midvotes (1 point); if
they get *a lower score from explicit votes*, 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.

2016-10-05 13:53 GMT-04:00 Jameson Quinn <jameson.quinn at gmail.com>:

> 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
>> total.
>> 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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>>>> info
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