[EM] MAV on electowiki

Wed Jun 19 05:48:42 PDT 2013

Here's the current version of the article. Note the new paragraph on
strategy at the bottom.

---------

Majority Approval Voting (MAV) is a modern,
evaluative<http://wiki.electorama.com/wiki/Evaluative> version
of Bucklin voting <http://wiki.electorama.com/wiki/Bucklin_voting>. Voters
rate each candidate into one of a predefined set of ratings or grades, such
as the letter grades "A", "B", "C", "D", and "F". As with any Bucklin
system, first the top-grade ("A") votes for each candidate are counted as
approvals. If one or more candidate has a majority, then the highest
majority wins. If not, votes at next grade down ("B") are added to each
candidate's approval scores. If there are one or more candidates with a
majority, the winner is whichever of those had more votes at higher grades
(the previous stage). If there were no majorities, then the next grade down
("C") is added and the process repeats; and so on.

Note that if this process continues without a majority until the last grade
("F") is added, no new rules are needed. Since by that point all grades
will have been counted, all candidate tallies will reach 100%. The process
above then naturally elects the candidate with the most approvals at the
higher grades (D or above); that is, whichever has the fewest F's. This is
the best way to resolve such an election using only the information on the
given ballots. However, in this and other cases of multiple majorities, a
runoff, if feasible, would be a better way to ensure a clean majority win.

This system was promoted and named due to the confusing array of Bucklin
and Median proposals. It is intended to be a relatively generic, simple
Bucklin option with good resistance to the chicken
dilemma<http://wiki.electorama.com/wiki/Chicken_dilemma>.
It was named by a
poll<http://lists.electorama.com/pipermail/election-methods-electorama.com/2013-June/031938.html>
on
the electorama mailing list in June 2013.

The grades or ranks for this system could be numbers instead of letter
grades. Terms such as "graded MAV" or "rated MAV" can be used to
distinguish these possibilities if necessary. In either case, descriptive
labels for the ratings or grades are recommended. For instance, for the
letter grades:

   - A: Unconditional support
   - B: Support if there are no other majorities above "C"
   - C: Support if there are no other majorities above "D"
   - D: Oppose unless there are no other majorities at all.
   - F: Unconditional opposition.

As the above labels indicate, support at the middle grades or ratings is
not partial, as in Score voting<http://wiki.electorama.com/wiki/Score_voting>,
but conditional. That is, the typical ballot will still count fully for or
against a given candidate. The different grade levels are a way to help the
voting system figure out how far to extend that support so that some
candidate gets a majority.

For a strategic voter, the most important ratings are the top ("A"),
second-to-bottom ("D"), and bottom ("F"). A typical zero-knowledge strategy
would be to give the best 30% of candidates an "A", the next 25% a "D", and
the bottom 45% an "F". If the typical "honest" voter roughly calibrates
their grades to an academic curve, with a median vote at "B" or "C", then
strategic and honest votes will mesh well. For instance, if candidates can
differ on two dimensions, ideology and quality, and voters are normally
distributed along the one dimension of ideology (with all voters preferring
highest quality), then this system will tend to elect the candidate
preferred by the median voter, that is, the one with the smallest sum of
quality deficit plus ideological skew; and this tendency will hold for any
unbiased combination of "honest" and "strategic" voters as defined above.

---------

The assertions in the strategic paragraph are based on some
back-of-the-envelope diagrams; that is, I consider them likely to be true,
but I have not run simulations to prove them. I think it would be
interesting to do so. Would others be as interested as I would in such
results; that is,

1. Finding an equilibrium zero-knowledge strategy (percentile-grade
correspondence) in impartial culture. (I think this would be an exciting
new direction for simulation research.)

2. Finding how broad the strategic conditions are (testing different
"honest" grade distributions, unbiased strat/hon mixes, and strategic
biases) in which MAV elects the median voter's favorite in the 2D/1D model
sketched above? If my intuition is right, this model (unlike sparse or
impartial models as criticized by Regenwetter) will allow good systems to
show near-optimal BR; so MAV and Score will be have nearly the same (and
nearly 0) honest BR, and the differences will be in that BR's robustness to
different strategic profiles.

Jameson

2013/6/18 Jameson Quinn <jameson.quinn at gmail.com>

> I've reworked the description. See what you think.
>
>
> 2013/6/18 Abd ul-Rahman Lomax <abd at lomaxdesign.com>
>
>> At 04:25 PM 6/18/2013, Juho Laatu wrote:
>>
>>> I quickly read the article. Here are some observations.
>>>
>>> - Term "Bucklin system" has not been defined. I can guess that it
>>> probably refers to Bucklin style stepwise addition of new approvals, but
>>> that may not be as obvious to all readers. If there is no definition of
>>> "Bucklin system", maybe one could say "As in Bucklin" instead of "As with
>>> any Bucklin system".
>>>
>>
>> There is a link to Bucklin voting in the article.
>>
>>
>>  - Sentence "if there are more than one with a majority, the "B" votes
>>> are removed and the highest sub-majority wins" is ambigious in the sense
>>> that it is not clear if "highest sub-majority" refers to all candidates or
>>> to candidates that had majority after adding the "B" votes.
>>>
>>
>> It's poorly worded, all right. Minor point: "There are more than one"
>> grates. (I find the use of the singular or plural with "more" to be
>> ambiguous. I'd avoid it.)
>>
>> An example is given when the principle has not been stated.
>>
>> The method does not make sense as stated. The "back-up" is a tie-breaker,
>> considering multiple majorities as if they were ties. They *are* ties in
>> median vote. The tie-breaker only selects a member of the tied set.
>>
>> Something went south. What was proposed was a Bucklin system. Bucklin
>> does use, I've suggested, a range ballot, but the way that it does this is
>> with a ranked structure. I ran into this when trying to design a set of
>> votes to show a problem that I have not seen examined.
>>
>> The description on the wiki page makes the system seem more complex than
>> it is.
>>
>> It's been designed to be five-rank, with explicit F. That's a fish
>> bicycle. "No support" means merely "no support." No vote. Introducing the D
>> vote is a later possible reform, it is an unapproved category. It makes the
>> ballot considerably more complex, and the explanation is more complex.
>>
>>  *D: Oppose unless there are no other majorities at all.
>>>
>>
>> Is that clear? I don't think so. Bucklin as Approval Voting doesn't have
>> a "disapproved rank." All blanks are disapproved.
>>
>>
>>  - It is not quite clear what happens and if it is possible that there is
>>> no majority after the "F" votes have been counted.
>>>
>>
>> The F votes are never counted, first of all. Listing them is a mistake.
>> (If the F votes continued the amalgamation, then someone would be voting
>> *for* a candidate rated F. That was the intention for the D rating.
>>
>> It is far better, however, to introduce a D rating in combination with a
>> runoff system, where the D rating could improve runoff candidate selection.
>>
>> When a voter rates a candidate as "D", they are opposing the election of
>> that candidate.
>>
>> The Bucklin system required amalgamating three ranks. It's looking like
>> MAV requires five, but that could be reduced to four, but the whole idea
>> here was to have a *simple* next step beyond basic Approval Voting, and, as
>> well, a clear similar method for use in a runoff system.
>>
>> (We basically need a step up from approval as a plurality method, and
>> from approval as a primary method in a runoff system.)
>>
>>
>>  - The grades could be letters or numbers, but they could also be e.g.
>>> columns without any letter or number. This part of text discusses what the
>>> ballots might look like. I'm not sure if ballot different ballot formats
>>> should be seen as an essential part of the method definition, or if the
>>> method should be defined abstractly without referring to what the actual
>>> ballots might look like. I tend to define the methods abstractly without
>>> assuming anything on the ballots, and then discuss possible ballot formats
>>> as a separate topic, but I'm not saying that's the only and best approach.
>>> The current text is thus ok. I just first read the grades of the definition
>>> as abstract grades, not as definitions on what would be written in the
>>> ballots.
>>>
>>
>> *Something* should be on the ballot that expresses the *function* of a
>> vote. Jameson took this concept from me. A voter should be able to see the
>> ballot and have a reasonably clear idea, just from it, what the vote
>> *means* ... and the meaning is the *effect* that the vote causes.
>>
>> The original Bucklin ballot, however, simply instructed voters to mark
>> "1st choice," "2nd choice," or '3rd choice." The googlebooks copy is
>> unclear, http://books.google.com/books?**id=QcIqAAAAYAAJ&pg=RA1-PA757&**
>> dq=The+Grand+Junction+plan+of+**city+government+and+its+**
>> results&hl=en&ei=**uOTdS7aFKMKclgfq9739Cg&sa=X&**
>> oi=book_result&ct=result&**resnum=3&ved=0CDsQ6AEwAg#v=**
>> onepage&q=The%20Grand%**20Junction%20plan%20of%20city%**
>> 20government%20and%20its%**20results&f=false<http://books.google.com/books?id=QcIqAAAAYAAJ&pg=RA1-PA757&dq=The+Grand+Junction+plan+of+city+government+and+its+results&hl=en&ei=uOTdS7aFKMKclgfq9739Cg&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDsQ6AEwAg#v=onepage&q=The%20Grand%20Junction%20plan%20of%20city%20government%20and%20its%20results&f=false>
>>
>> Page 95. It looks like they actually instructed people to vote for all
>> but one. But that part is quite unclear. In the first set of instructions,
>> at the top of the ballot, they did suggest not voting for one candidate.
>> There may be another copy of this ballot somewhere. Bucklin was widely
>> covered.
>>
>> MAV *assumes that voters err if they approve two candidates by a
>> majority.* That's why it backs up. But what, indeed, if it backs up and the
>> multiple majority candidates are not the plurality winner in the previous
>> round? What if there are *no* votes for those candidates in that round, or
>> the vote is small.
>>
>>
>> It said: "
>>
>>
>>  - The linked definition of "evaluatve" says that ranked systems can not
>>> give same ratings to two candidates. I think that's confusing and wrong.
>>>
>>> Juho
>>>
>>
>> Well, that's a common assumption of "ranked systems." It's essentially a
>> definition, which is why we have said that Bucklin is *not* a ranked
>> system. But, really, it's a ranked system that allows equal ranking.
>> (Original Bucklin allowed equal ranking in the third rank only. We have
>> simple expanded the approval principle to all ranks. *That is a convenience
>> to voters.*)
>>
>>
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>
>
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