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

[Andy Jennings]

Jameson,

I really like these MCA-Asset methods.  If the public thinks asset voting is
too strange, maybe it is more palatable as a fallback method.  It does seem
to be a good fit with MCA.

Are all candidates eligible to win in the fallback asset election, or only
the ones who were tied for the highest median grade in the MCA election?

Andy Jennings


On Sat, Feb 26, 2011 at 2:47 AM, Jameson Quinn <jameson.quinn at gmail.com>wrote:

> Just a note about non-monotonicity in MCA-Asset: the actual result of the
> scenario I talked about would be that C voters would defensively approve B,
> and so B (the PC / CW) would win.
>
> 2011/2/26 Jameson Quinn <jameson.quinn at gmail.com>
>
> 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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