Condorcet with Borda Runoff
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@cfrank All good and likewise.
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@rob you are probably right to be careful about stability, I’m trying to stay very near to Condorcet. I think this system may still be vulnerable to burial but my guess is that it’s still highly resistant to tactics in general. I could be wrong, I’m going to code it up and see what happens.
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@rob said in Condorcet with Borda Difference Runoff:
I believe an election that elects the Condorcet winner tends to be a Nash equilibrium when everyone votes sincerely
Is that because it is too hard to figure out the better voting decision procedure?
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh said in Condorcet with Borda Difference Runoff:
Is that because it is too hard to figure out the better voting decision procedure?
I don't understand your question.
It is a Nash equilibrium when everyone votes sincerely (*), because it is specifically designed to be.
If you are wondering why I think that is a good thing, ask.... although I think it should be fairly obvious to most people, and I think I just explained it in another thread.
* not 100% perfect, but close enough
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@rob Well, let's suppose everyone knows a more effective strategy for serving that person's values. Then voting "sincerely" is not a Nash equilibrium, because once everyone does it and the outcome is observed, some voters will regret that they gave up power, so next time around, they will change to insincerity.
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh Then it isn't a Nash equilibrium. A Nash equilibrium is when no one can get better results by changing their behavior, without anyone else changing their behavior. (*) The scenario you described is the opposite of that.
/* note that "better results" is rather tricky with voting, since no individual voter will tend to change the outcome. So there are reasonable ways of defining "better results," that is a discussion of its own.
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@rob said in Condorcet with Borda Difference Runoff:
Then it isn't a Nash equilibrium.
Exactly. So I want to deny that sincere voting can be a Nash equilibrium. There exists a better way to vote, per Gibbard. All the voters have to do is find it.
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh This is one of the strongest selling points of Approval actually. Given complete information, the election of a Condorcet winner (when one exists) is a Nash equilibrium in Approval voting.
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@andy-dienes said in Condorcet with Borda Difference Runoff:
Given complete information,
That's the tricky part, though, isn't it?
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@jack-waugh said in Condorcet with Borda Difference Runoff:
So I want to deny that sincere voting can be a Nash equilibrium.
You are mixing issues. Gibbard is one thing, that applies to discrete candidates, and is a tiny corner case of imperfection, rather than a thing that generalizes to all cases.
This is why I go back to voting for a number and choosing a median, because you can speak of all this stuff about Nash equilibria and strategic voting and such without being thrown off by Gibbard or Arrow or what have you.
If you wish to deny that for any given election method, sincere voting and strategic voting are not 100.00000% identical, fine. For temperature voting as I described, I will argue, no, they actually are identical, you gain exactly zero value by voting with anything other than your preferred temperature. (*) It is indeed a case of "everyone voting sincerely is a Nash equilibrium."
For good Condorcet methods, this is so close to being true that I think it is good enough, but if you want to spin on Gibbard, knock yourself out. I don't think it is a productive use of time, though. It is black and white thinking, basically like "even the safest airplanes crash some percentage of the time, therefore I might as well fly in this thing"
For Score, Approval, and choose-one, it is obviously not close to true that sincere voting is a Nash equilibrium.
/* please don't try to find contrived counterexamples such as people who like both 68 and 72 better than 70.
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@rob said in Condorcet with Borda Difference Runoff:
For temperature voting as I described, I will argue, no, they actually are identical, you gain exactly zero value by voting with anything other than your preferred temperature.
"Temperature" voting is usually referred to in academic literature as the "single-peaked preference model" and in fact median is strategyproof! (as is approval, and Condorcet methods)***
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.***pretty sure this is true at least. been a while since I read the relevant papers.
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@rob said in Condorcet with Borda Difference Runoff:
You are mixing issues. Gibbard is one thing, that applies to discrete candidates,
How are human candidates for political office not discrete?
and is a tiny corner case of imperfection, rather than a thing that generalizes to all cases.
What does it take to bring about the tiny corner case?
Approval-ordered Llull (letter grades) [10], Score // Llull [9], Score, STAR, Approval, other rated Condorcet [8]; equal-ranked Condorcet [4]; strictly-ranked Condorcet [3]; everything else [0].
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@jack-waugh said in Condorcet with Borda Difference Runoff:
How are human candidates for political office not discrete?
They are discrete, I was contrasting them with the opposite extreme, which is where they lie along a continuum.
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@andy-dienes said in Condorcet with Borda Difference Runoff:
"single-peaked preference model" and in fact median is strategyproof!
Awesome. I've never seen any discussion of it elsewhere, it's good to know that others have used it as an example.
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@rob yep, in particular this is the Median Voter Theorem
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@andy-dienes right, I'm familiar with that one, I took it a bit further by having, rather that discrete choices along a spectrum, an infinite number of potential choices along the same spectrum. Works well for temperature, club dues, etc, and the extreme simplicity of the voting and tabulating serves the example well.
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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).
