Accommodating Incomplete Weak Rankings with N Ordinal Scores
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@rob I think I mostly agree with almost everything you said, except for that the examples are contrived. I tend to think that trying to including degrees of preference is usually too problematic for tactical voting and that even if “honest degrees of preference,” whatever that means, were somehow real and plotted statistically for voters with a given rank-order preference, they would sort of average out and resemble the ranking in some sense anyway, just because I think probably individual people on the whole aren’t really all that special or different from each other in terms of how they experience their preferences.
But I want to ask, putting aside the idea that the examples are contrived, let’s say that the sort of ballot activity I’m describing actually occurred in a real election. Without quoting the majority criterion or the Condorcet criterion, but just intuitively, what do you think of the election results?
Continuing on, if what you are saying about the Condorcet winner being a moderate and generally non-divisive candidate is true, then the modifications I am suggesting will almost always elect the Condorcet winner anyway. You can look at that and think, “why complicate things then?” and I understand that point of view. But again, if that’s true, then the kind of modification I am suggesting in terms of finding higher order Condorcet winners or substitutes would almost always only require a single extra check, as in one of the examples I give that you would perhaps consider to be less contrived. So it’s a question of whether it’s worth it to try to safeguard against a divisive majoritarian victory. I wager you think even the potential benefits aren’t worth the extra complication, but I personally would rather err on the side of safety and look closer to see if the benefits are significant in any way.
On another point, I would be curious to see if any examples could be contrived to illustrate why the kind of modification I am suggesting might lead to results that are not both intuitive and game-theoretically stable. What do you think of the examples I gave?
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 Accommodating Incomplete Weak Rankings with N Ordinal Scores:
I am suggesting might lead to results that are not both intuitive and game-theoretically stable.
Any instance where the Condorcet winner is not elected is exactly an instance illustrating game-theoretic instability. A relevant notion here is the core, which is exactly the Condorcet winner when one exists.
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@andy-dienes OK, perhaps, but can you please provide an example, and demonstrate what kind of strategic action would be effective to illustrate your example? That’s what I’m looking for.
I’ve given examples where the modification I am referring to is resistant to both burial and strategic nomination, and the results of the elections I’ve exemplified are pretty well intuitive to me. Are there any examples I’ve given where the result is somehow “bad” in a sense other than not satisfying the Condorcet criterion? And if so, can you please explain why it is bad, with a concrete description of how a reasonable voting tactic could alter the results significantly?
One convincing example is all I would need to see.
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60: A5, B3, C0
40: A0, B4, C5If A doesn't win then the block of 60 will vote A5, B0, C0 in the next election.
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@andy-dienes this is exactly the problem I am trying to address in this post. The examples I’m talking about having given use strict rank ordering and no degrees of preference. They can be found here: consensual Condorcet
The issue I’m trying to address is to maintain the strict order while still enabling a comparison of the ranking spectra in a reasonable way. My question is about how to accomplish that, not about how to give up trying to accomplish it.
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I think trying to enforce strict rankings as a way to patch a method is a 'code smell' if you have heard that term before. If the method cannot handle equal rankings in a relatively elegant way that should be a signal to you that there may be something more fundamental to fix rather than simply disallowing equal rankings.
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@andy-dienes it isn’t a patch, it’s a starting point. I’m trying exactly to allow equal and incomplete rankings and to still follow a reasonable analogue of the kind of procedure described. That’s the very point of this topic.
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@cfrank Any example where the Condorcet winner exists but is not elected is an example where there is some strategic instability.
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@cfrank said in Accommodating Incomplete Weak Rankings with N Ordinal Scores:
You can look at that and think, “why complicate things then?” and I understand that point of view. But again, if that’s true, then the kind of modification I am suggesting in terms of finding higher order Condorcet winners or substitutes would almost always only require a single extra check, as in one of the examples
Its less a matter of ""why complicate things" and more a matter of avoiding situations where people, following an election, regret voting as they did. When it can be shown that a positive result could have been had for some group of people if they had voted differently, that's bad news. It leads to everything from wanting to repeal the system, to parties eliminating candidates via primaries.
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@andy-dienes in this example there are more scores than there are candidates. The same problems remains though when there are only three scores for three candidates, and I can see why this is a significant issue. With the method I described, no matter what the majority does with strict rankings, the middle candidate will win, even if the ballots are
A>B>C [99%]
C>B>A [1%]Which is absurd. And without strict rankings, the majority can guarantee their top candidate’s victory by bullet voting anyway. I don’t like it but it is what it is. I think you’ve convinced me.
