Condorcet with Borda Runoff
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@rob Here is a further modification, which you may dislike perhaps, but I think it produces a candidate that is very broadly consensual. One can continue defining tertiary and quaternary and Nth-order Condorcet winners, etc. Rather than having a Borda difference runoff or something of that nature, one can try to find the first N such that the Nth order Condorcet winner positionally dominates the (N+1)st order Condorcet winner, and by that criterion try to elect the Nth order Condorcet winner.
For example, if the ballots are
C>B>D>A [38%]
A>B>C>D [30%]
A>C>D>B [22%]
B>D>A>C [10%]Then the primary, secondary, tertiary and quaternary Condorcet winners are A, C, B and D in that order. B is the lowest-order Condorcet winner who positionally dominates the (N+1)st Condorcet winner, and is in some ways a potentially better candidate than C. If you look at the ballots, B is in the top two positions for 78% of the electorate (although the remaining 22% scored them minimally). That's just a different method but I think it could be interesting to look into.
This method conforms to the results of the first example given as well, since in that case B is the lowest-order Condorcet winner who positionally dominates their successor. One issue is that it's possible that none of the Nth-order Condorcet winners positionally dominate their successor.
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@cfrank This is quite similar to the construction here, where generalized Condorcet winners are defined by positional dominance over progressively larger subsets of candidates. I think you would enjoy that paper.
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@andy-dienes I think you may have sent this or a similar paper before, and I did enjoy it and would definitely like to read about this concept again, I think something like it is a good idea.
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This idea is quite similar to MARS. And in the examples you list, MARS would yield the same results each time (assuming a range 0-3). The main difference is that it seems you imply strict rankings. This creates a teaming effect. The A voters fail to win strategically, because of the number of candidates supported by the other group, not because of a resistance to polarization inherent in the method. When you think about it, it's quite odd if a majority has no way to vote that ensures them winning (majority criterion).
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@casimir I don't think avoiding the majority criterion is odd if it means that the slim majority is required in some way to make concessions to the minority and thereby somehow build a broad supermajority consensus. Unfortunately you are correct that this method is vulnerable to strategic nomination and trying to address that while preserving "minority consent" gets complicated. Sometimes I think that single-winner systems are not ideal at all, and it would just be better to have proportional representation and some kind of sortition system.
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@cfrank said in Condorcet with Borda Runoff:
I don't think avoiding the majority criterion is odd if it means that the slim majority is required in some way to make concessions to the minority and thereby somehow build a broad supermajority consensus.
Let's say the electorate is split into polarized groups of 52% and 48%, each of which is thoroughly unwilling to compromise with the other. Do you agree that the larger group should get to choose the winner? Supermajorities just aren't possible all the time, and it still doesn't make sense to try to force the issue in a single-winner method.
it would just be better to have proportional representation and some kind of sortition system.
yes yes yes. this is precisely what I mean by suggesting the philosophy guide the design at a higher level than actual algorithm mechanics.
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@andy-dienes oh absolutely, when there is no hope of compromise the majority should win out, there isn't a better option. In my opinion that's the worst-case scenario. Ideally there would be some mechanism of finding some level of supermajority consensus if one exists. I think the path of least resistance for the majority to take control should be for them to make reasonable concessions to the minority whenever possible. They could in principle take control by force, but hopefully they won't be motivated enough to do that.
I was trying to think of finding the primary Condorcet winner A, and then ignoring the ballots that rank A as highly as appears and finding the "minority" Condorcet winner B, then doing some kind of comparison of the rankings between the voters who marked A as highly as appears and the voters who marked B as highly as appears. But that's probably getting too complicated.
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@cfrank said in Condorcet with Borda Runoff:
I was trying to think of finding the primary Condorcet winner A, and then ignoring the ballots that rank A first and finding the "minority" Condorcet winner B, then doing some kind of comparison of the rankings between the voters who marked A first and the voters who marked B first. But that's getting too complicated.
I mean, this is basically what IRV does though
lol (and as it happens, IRV has one of the strongest 'veto powers' aka minority protection of any voting method) -
@andy-dienes that is sort of what IRV does, but I think it's a bit different from what I'm considering since IRV doesn't operate on Condorcet winners but rather on elimination by anti-pluralities. For example, if the "majority" and "minority" Condorcet winners were identical, the election could end.
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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@cfrank said in Condorcet with Borda Runoff:
IRV doesn't operate on Condorcet winners but rather on elimination by anti-pluralities.
A better IRV could work by elimination of candidates remaining after eliminating pluralities. Or by elimination of candidates remaining after eliminating candidates remaining after eliminating anti-pluralities.
(I'm saying that converges quickly on Condorcet winner if they exist, if they don't exist, it converges on the Condorcet-iest candidate)
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@andy-dienes said in Condorcet with Borda Runoff:
Supermajorities just aren't possible all the time, and it still doesn't make sense to try to force the issue in a single-winner method.
I’m not sure I understand the manner in which it doesn’t make sense. Can you explain why it doesn’t make sense to try to elect a candidate that is not highly divisive whenever possible?
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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@cfrank said in Condorcet with Borda Runoff:
Can you explain why it doesn’t make sense to try to elect a candidate that is not highly divisive whenever possible?
I personally think a method should indeed do that, but trying to label that a "supermajority" might be misleading or at best, vaguely defined. Supermajority what? Supermajority might indicate something like 70%, but the other variable is "degree of approval." So does it mean something like, over 70% thinks they are pretty good, as opposed to a simple majority where over 50% thinks they are awesome? If so, I would describe that as the system "favoring moderate candidates."
Regardless, I still suspect that a Condorcet compliant method will accomplish such a goal (favoring moderate candidates) better than any given method that isn't Condorcet compliant -- at least if you also want to avoid strategic manipulation and all that ugliness.
Notice that FairVote's primary complaint about Condorcet systems seems to be almost the exact opposite of yours. They think that Condorcet systems favor moderate candidates too much. (Then again, maybe you consider "moderate" to be significantly different from "supermajority support". I am considering them roughly the same, if I properly understand what you mean by "supermajority.")
