[EM] MAS: latest wiki page

[Jameson Quinn]

Here's the latest version of the electowiki page on MAS. It includes a
Bucklin-friendly description; discussion of two-round MAS and NOTA; and the
Wikipedia "Tennessee" voting example with MAS.
Majority Acceptable Score voting
<http://wiki.electorama.com/wiki/Majority_Acceptable_Score_voting#mw-head>
<http://wiki.electorama.com/wiki/Majority_Acceptable_Score_voting#p-search>

Majority Acceptable Score voting works as described below. Technically
speaking, it's the graded Bucklin
<http://wiki.electorama.com/wiki/Graded_Bucklin> method which uses 3 grade
levels <http://wiki.electorama.com/wiki/3_grade_levels> and breaks median
ties using Score voting <http://wiki.electorama.com/wiki/Score_voting>.

   - Voters can give each candidate 0, 1, or 2 points.
   - If there are any candidates given *above* 0 by a majority, then
   eliminate all who aren't (that is, those with half or more *at* 0).
      - (Do the same for 1. This probably doesn't matter, because any
      majority-2 candidate that exists would almost certainly win in the next
      step anyway. But this step is part of Bucklin voting, which was used in
      over a dozen US cities during the Progressive era, and thus it gives this
      method a stronger pedigree, and makes it easier to model mathematically.)
   - The remaining candidate with the highest points wins.

Blank votes are counted as 1 or 0 points in proportion to the fraction of
all voters who gave the candidate a 2. For example, a candidate could not
win with more than 71% blank votes, because even if the other 29% are all
2-ratings, that would leave 71%*71%=50.41% 0-votes, enough to eliminate.

Here's a google spreadsheet to calculate results: [1]
<https://docs.google.com/spreadsheets/d/1siFG6XmOZokygY-86EhAKgv8YwzKtTET6AJopyXRqu0/edit#gid=0>.
On page 1, it has some examples of how different combinations of ratings
would come out, suggesting that it could work well in both chicken dilemma
<http://wiki.electorama.com/wiki/Chicken_dilemma> and center squeeze
<http://wiki.electorama.com/wiki/Center_squeeze> scenarios. On page 2, it
has some hypothetical results for the Egypt 2012 election, showing that
this system could have elected a reformer over Morsi, despite
vote-splitting among the various reformers. IRV could have elected Morsi.
As the first round of a two-round system ("MAS with runoff")[edit
<http://wiki.electorama.com/w/index.php?title=Majority_Acceptable_Score_voting&action=edit&section=1>
]

If this system is used as the first round of a two-round runoff, then you
want to use it to elect at two finalists in the first round. Thus, run the
system twice. The first time, instead of eliminating any candidates with a
majority below a threshold (as long as there are any with a majority above
the threshold), eliminate only those with over 2/3 below the threshold (as
long as there are any with 1/3 above).

Then, to find the second winner, if the first-time winner got 1/3 or more
of 2's, first downweight those ballots as if you'd eliminated enough of
them to make up 1/3 of the electorate. Otherwise, discard all of the
ballots which gave the first-time winner a 2. After downweighting or
discarding, run MAS normally.

If all the candidates in the first round got a majority of 0's, then you
can still find two finalists as explained above. But the voters have sent a
message that none of the candidates are good, so one way to deal with the
situation would be to have a rule to allow candidates to transfer their
2-votes to new candidates who were not running in the first round, and if
those transfers would have made the new candidates finalists, then add them
to the second round along with the two finalists who did best in the first
round. In that case, since there would be more than 2 candidates in the
second round, it would be important to use MAS for the second round too.
Relationship to NOTA[edit
<http://wiki.electorama.com/w/index.php?title=Majority_Acceptable_Score_voting&action=edit&section=2>
]

As discussed in the above section, if all the candidates in the first round
got a majority of 0's, then the voters have sent a message that none of the
candidates are good, akin to a result of "none of the above
<http://wiki.electorama.com/wiki/None_of_the_above>" (NOTA). MAS still
gives a winner, but it might be good to have a rule that such a winner
could only serve one term, or perhaps a softer rule that if they run for
the same office again, the information of what percent of voters gave them
a 0 should be next to their name on the ballot
An example[edit
<http://wiki.electorama.com/w/index.php?title=Majority_Acceptable_Score_voting&action=edit&section=3>
]Imagine that Tennessee is having an election on the location of its
capital. The population of Tennessee is concentrated around its four major
cities, which are spread throughout the state. For this example, suppose
that the entire electorate <http://wiki.electorama.com/wiki/Electorate>lives
in these four cities, and that everyone wants to live as near the capital
as possible.

The candidates for the capital are:

   - Memphis <http://en.wikipedia.org/wiki/Memphis> on Wikipedia, the
   state's largest city, with 42% of the voters, but located far from the
   other cities
   - Nashville <http://en.wikipedia.org/wiki/Nashville> on Wikipedia, with
   26% of the voters, near the center of Tennessee
   - Knoxville <http://en.wikipedia.org/wiki/Knoxville> on Wikipedia, with
   17% of the voters
   - Chattanooga <http://en.wikipedia.org/wiki/Chattanooga> on Wikipedia,
   with 15% of the voters

The preferences of the voters would be divided like this:
42% of voters
(close to Memphis)26% of voters
(close to Nashville)15% of voters
(close to Chattanooga)17% of voters
(close to Knoxville)

   1. *Memphis*
   2. Nashville
   3. Chattanooga
   4. Knoxville


   1. *Nashville*
   2. Chattanooga
   3. Knoxville
   4. Memphis


   1. *Chattanooga*
   2. Knoxville
   3. Nashville
   4. Memphis


   1. *Knoxville*
   2. Chattanooga
   3. Nashville
   4. Memphis

Assume voters in each city give their own city 2; any city within 100
miles, 1; any city that is over 200 miles away or is the farthest city, 0;
and the rest (those between 100 and 200 miles), get 1 or blank with 50/50
chance. (These assumptions can be varied substantially without changing the
result, but they seem reasonable to start with.)
City2'sexplicit 1'sexplicit 0'sblankstotal 0'sscore
Memphis 42 0 58 0 58 (84)
Nashville 26 37 0 37 27.4 98.6
Chattanooga 15 30 21 42 49.9 65.1
Knoxville 17 28 42 13 52.8 (64.2)

Memphis and Knoxville are both given 0 by a majority, so they are
eliminated. Of the remaining two, Nashville has a higher score and wins.

If Memphis voters tried to strategize by rating Nashville and Chattanooga
at 0 in the above scenario, it would take a bit over half of them to
successfully execute the strategy. Even if all the Memphis voters
strategized, Chattanooga and Knoxville voters could protect Nashville
against this strategy as long as under half of those who had given
Nashville a blank above switched to giving it a 1 (or a 2). Note that the
offensive strategy involves moving a natural 1 down to the extreme value of
0, but the defensive strategy only means changing a lazy blank to a natural
1 (not to the extreme value of 2).
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