Quantile-Normalized Score
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@jack-waugh yes, you’re right, if ballots are directly elements in a vector space (or maybe more generally an Abelian group), and the first operation of the voting system is to compute the sum of the elements directly and have no future reference to the original ballot set, there are definitely appealing consequences. And score ballots after quantile normalization almost surely fail to have inverse elements, which is the issue under consideration.
I think I’m coming around to your point of view, I just want to understand it as transparently as I can. My concern is that it seems to impose very rigid restrictions on the kinds of transformations or normalizations we should be able to do to ballots, for example it seems to restrict to linear projections or group homomorphisms, and then aggregation, which would have the same effect as if aggregation were performed before the transformations. Maybe that’s just the way it is.
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@cfrank Well, maybe some of that is more restrictive than necessary.
The ballots can be referred to again for rounds of tallying (maybe impractical for public office because of integrity issues, but applicable in organizations that trust their IT departments) but again treated additively, just in the context of some candidates already having been eliminated from consideration by prior rounds. I included this in a recent proposal here.
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@jack-waugh yes, so that is in one sense multiple voting systems passing information in series to perform projections, such as eliminating certain candidates based on the result of a preceding system. That does add complexity, it’s essentially a hierarchical model of additive systems, and kind of like a one-pass neural network.
One of my concerns is that the end result seems heavily utilitarian, and that borders on majoritarianism to me, the issue is complicated. I’ll check out your proposal!
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@jack-waugh another point about “cancellation,” is whether it is actually necessary in practice. I think it’s arguable that effective or practical cancellation is just as good as perfect theoretical cancellation in almost all instances. For example, while a subset of N voters may not be able to perfectly cancel each other out, they can still on aggregate amount to little more than noise, which is a form of practical cancellation. I think there’s an argument to be made that sacrificing perfect cancellation for practical cancellation is justified to obtain other desirable properties. Playing devil’s advocate, one could even say that noise is a positive thing, since it’s a robust way to decide effective ties, which is more or less what would have occurred in your 3,000,002 voter illustration.
In practice, small margins victory lead to recounts anyway, which has its own practical noisiness.
And here is an adjustment to quantile normalized scoring inspired by your proposal: we could force the final quantile values to be symmetrical. I think that preserves the structure of an abelian group.
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@cfrank said in Quantile-Normalized Score:
@toby-pereira the problem is bullet voting and a synthesis of rank and score systems, this is one way to address it. Also, many very difficult problems in the real world are solved by "solutions in search for a problem," including most of the most impactful drug treatments.
I'm not aware score has a problem with bullet voting. And while drugs are often found by some sort of trial and error, they have to be tested. So I suppose I can be patient and wait to see what this method offers!
Edit - I see there's a new version now so I'll have a look.
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@jack-waugh said in Quantile-Normalized Score:
Which voters are going to have their votes diluted by such a procedure?
In reply to this, you might be interested to note that, based at least on my own observations of the symmetrized version, it is the bullet-voters and min-maxers who will have the advantages of their tactical behavior reduced in favor of a broader consensus, in a fashion very similar to what would be expected in a Condorcet method. However, the method is not Condorcet compliant, I found a counter-example.