[EM] Truncation-resistant MCA method: MCA-Asset

[Jameson Quinn]

Clearly, "MCA-Asset" as I originally stated it is too complex. So here's a
simpler revision. From here on, "MCA-Asset" will refer to the following
system:

As before, it's an MCA variant, so the basic MCA rules are the same. Voters
rate candidates into N categories, including the default bottom-rating
category. (I suggest that 3<=N<=5 is plenty for expressing the basics,
without opening up too much room for strategic second-guessing or pointless
hairsplitting.)

1. (MCA base) Any candidate who is the only one with a majority at or above
a given rank wins.

2. If there are multiple or failed majorities, any candidate may "give their
votes" to any other candidate who has more first-choice votes than them. If
A "gives votes" to B, all ballots are considered to have voted A at least as
high as B. (For example, a B>A>C vote is changed to A=B>...>C, but an A>B>C
vote is unchanged).

3. Repeat step 1.

4. If there's still multiple or failed majorities, the winner is the one
with the most top-rated votes (original or gifted).

Here's the advantages. I think this is a great method; along with Approval
and MCA-Range, it is currently one of the 3 favorites I'd advocate for real
world democracies.
A1. Condorcet - If there's a step-1 winner and a pairwise champion (PC /
CW), they will be the same candidate. If there's a majority PC / CW, then
they will win in round 1 in a Nash equilibrium. I think that covers most
real-world cases, and the system seems to give reasonable results even if
these conditions don't hold.

A2. Semi-honest. Except for the (to me implausible) scenario I discuss below
under "(Non)monotonicity", there is no reason to ever reverse your honest
preferences between two candidates.

A3. No serious problems with strategies. In particular, this handles
vote-splitting / "intraparty truncation arms race" well. Although there are
many rated systems, including Range and most MCA systems, which share the
other advantages, this is the only such system I know which doesn't tend to
elect C, the condorcet loser, with the following honest preferences:
30: A>B>C
25: B>A>C
45: C>A=B (or C>...)
As in most other rated systems, the A and B voters are tempted to truncate,
bullet-voting to ensure their candidate wins. But in MCA-Asset, B can then
give his votes to A and elect her. Thus, MCA-Asset carries off the "miracle"
of seeing that A is the PC/CW, when only given a pile of bullet votes,
without needing a second balloting round.

A4. One balloting round, at most two summable counting rounds.

A5. Good balance of expressivity and balloting simplicity. It's rare that
you're strategically forced to give up expressivity; in most cases, the
"most expressive" ballot is also the "most strategic" one. (In contrast,
Approval is less expressive, ranked methods are cognitively harder to vote,
and Range forces one to choose between expresivity and strategy).

Here's the disadvantages:
D1: Less simple to describe than Approval.

D2: The vote-transfer portion could be criticized as undemocratic "back room
deals", although personally I believe it would happen rarely and
even-more-rarely give any result that wasn't obvious from before the
election.

D3: (Non)Monotonicity
The restriction that a candidate may only give to another who has more
first-choice votes than them is to avoid the "no, YOU give me YOUR votes"
problem. However, like the bottom-up elimination in IRV, it does technically
make the method nonmonotonic. Say there's 1-dimensional ideology, the
candidates are placed
A---B--C--
with each dash or letter representing an equal number of voters at that
ideology. If all voters bullet-vote, then C has the lead, but A transfers
their votes to B and B wins. But C voters, if they're very careful, can give
A enough first-choice votes to prevent A from transferring votes to B. Then,
B is the kingmaker between C and A; but since C is closer to B
ideologically, B may let C win instead of passing votes to A.
I don't think that nonmonotonicity would be a real-world issue, though. I
can't find any cases where it comes up naturally, without strategy. And as a
strategy, it is a very dangerous, and thus unattractive, for three reasons.
First, if enough B voters put A above bottom instead of bullet voting, this
strategy becomes impossible, because it would elect A. Second, even with all
bullet voters, it is easy for C voters to overshoot and elect A by mistake.
And third, this strategy depends on candidate B not passing votes to A,
which B could do either on a whim, or to punish the sneaky C voters.

Jameson
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