Mathematical Paradigm of Electoral Consent
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@brozai I also wanted to address your point about majority rule. If you are referring to May's Theorem, I think it's important to consider the scope of the proof. The theorem is proved assuming that voters can indicate one of only three options, -1, 0, or +1. The formal properties don't fully make sense beyond that scope.
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@cfrank well, this is true, but I think the monotonicity condition means that, with strategic agents, it has a natural extension to score ballots
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@brozai I would need to see it formally. I can see what you mean about strategic agents, but I don’t see any extensions mentioned on Wikipedia but a similar statement (whatever that means) for approval voting (fully strategic score voting), and then some for other first-preference aggregators which would have us using plurality voting. I personally doubt a useful extension to generic score voting exists, because of the nature of the preferential ambiguity between a strong majoritarian assertion and a weaker but broader consensus.
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@cfrank A function monotonic on [0,1]^n --> {0,1} must also be monotonic on {0,1}^n --> {0,1}
Strategic agents will only submit values in {0,1} since by monotonicity any other value makes the chance of electing their favorite strictly lower.
Therefore the method must coincide with majority on {0,1}^n ballots, which is the entire domain of ballots from strategic agents
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@brozai this reasoning implies that a voter only considers the outcomes “my favorite wins” and “my favorite does not win.” A voter can also consider outcomes like “my favorite doesn’t win, but my second favorite does,” or “my favorite doesn’t win, but neither does my least favorite.”
Bullet voting is maybe a good strategy for an econ voter who is not at all risk averse and are all-or-nothing for their top choice, but real people are risk averse with stratified preferences and will try to establish at least a Plan B in case Plan A doesn’t work out.
Increasing the probability that one’s favorite wins as much as possible locally does not necessarily increase the probability of a more global “acceptable outcome” as much as possible, which is what many real people try to accomplish, depending on their definition of what constitutes an acceptable outcome.
This does somewhat seem to lead to approval voting, which I don’t think is a bad system actually. I’d have to learn more about it. Obviously it has its own problems, but at least burial is quite minor..
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@cfrank I am specifically referring to the case of 2 candidates! In this case, bullet voting will always be optimal
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@brozai I see! Yes that makes more sense. I still am not sure, because there may be a minority with a strong preference against the weakly held majority preference, and this just isn't taken into account. Obviously that is the whole issue with majoritarianism. The more I consider it the more and more keen I am on multi-winner proportional representation. In that case I feel like something like quadratic voting might potentially do a very good job identifying candidates with interests that represent those of the electorate.
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@cfrank If you are interested in proportional representation I would read the following paper which gives a good overview of PR schemes for approval ballots: https://arxiv.org/pdf/2007.01795.pdf
Quadratic voting is a somewhat poor quality method (imo) unfortunately.
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@brozai Oh really, why is QV poor quality? I'm sure there are superior more sophisticated methods.
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@cfrank Afaik, it does not have very good proportionality guarantees. It's probably better suited for something like participatory budgeting than it is for elections.
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@brozai I see, yes according to what I've learned about it QV tends to incorporate the strengths of interests and not just the proportion of people with those interests. Depending on what is desired that may be a good thing or a bad thing. There has also been research on its resistance to collusion and it seems to hold up very well, which is a property that I definitely like.
I found this presentation very interesting:
One point brought up by an audience member during the Q&A was that QV seems to illuminate the relative preferences of the electorate, which show up in the presenter's data as approximate Gaussian distributions and the grouping together of different strata of right-wing and left-wing groups, which does not occur without the quadratic cost.