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 <[email protected]> > 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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