[EM] More on MAS (version 3.0)

[Jameson Quinn]

I've been refining a 3-slot system for several weeks now. Let me be clear
that I'm only working on one system, even though I've gone through various
names as I refine it. The current name is MAS, Majority Acceptable Score.
Here's my latest definition. Note that I've tweaked the default rule so
that it can be said in one sentence. Mathematically it's trickier, but I
think it makes some intuitive sense, as explained in the last sentence.

*Here’s how MAS works: you can give each candidate 0, 1, or 2. Any
candidate that gets a majority of 0’s is eliminated, unless that would
eliminate everyone. Of the remaining candidates, highest score wins. *

*Blank votes for a candidate are read as 0’s or 1’s; the proportion that
count as 0’s is equal to the proportion between the voters that didn't give
the candidate in question a 2, and those that gave a 2 to a candidate with
a higher explicit score. Basically, that rule assumes that a voter would
want to give 0s to they left blank if those candidates were weaker than
their favorite, but 1s if those candidates were stronger.*

Here's a scenario to illustrate:

Candidate

2 votes

1 votes

0 votes

Blank votes

Explicit score

A

30

0

0

70

60

B

25

25

0

50

75

C

42

0

55

3

84

D

8

42

0

50

58

(Note: I think that a scenario like the above, where one candidate got many
more explicit 1-votes, would only happen in cases of center squeeze; that
is, B's 1-votes probably come primarily from C voters. Thus, B is
almost-certainly, but not quite provably, the CW here.)

Candidate A has 70 blank votes, and 70 voters who didn't give them a 2. 67
voters gave 2 to a candidate with a higher explicit score (C or B). 67 of
A's blank votes count as 0s, leaving 3 1's. A gets a total score of 63, and
is eliminated for a majority of 0's.

B has 50 blank votes, and 75 voters who didn't give them a 2. 42 voters
gave 2 to a candidate with a higher explicit score (C). So 28 of the blank
votes count as 0, 22 count as 1; B gets a score of 97.

C is eliminated by explicit 0s. D has all their blank votes count as 0
since the number of 2-votes for explicitly stronger candidates is greater
than the number who didn't vote for them. They are not quite eliminated.

So B wins this scenario. If B had gotten 9 or fewer explicit 1-votes, A
would have had a higher explicit score, and after assigning blank votes, A
would have won.

This default rule does cause the system to technically fail FBC, because
giving extra 2-votes to eliminated candidates can change how blank votes
are assigned for uneliminated candidates. However, constructing an
FBC-violating scenario would be nontrivial; I don't think it would ever
happen in practice.
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