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

[Jameson Quinn]

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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