Does it really matter that a candidate with 52% support wins over a candidate with 51% support?
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As stated in the title, my pondering is whether or not it matters that a candidate with slightly more support wins if the election method instead chooses another candidate who also has majority support. It has been several years since the last time I read about all the different desirability criteria, so I am not sure which one such an election method would fail, but the question is more philosophical than mathematical. If there are two candidates that both have the support of the majority and have nearly the same support, does it really matter which is elected?
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@k98kurz yes, assuming we are operating in the context where the concept of such indivisible, voter-wise support makes sense, the one with more support should win. We don’t just care about the majority for the sake of majoritarianism, the ideal is a broad consensus. It depends on the procedure that is agreed upon, though, and similarly it depends on what we mean by “support.”
The simplest context for this is an approval voting ballot. Maybe I’m wrong, but I don’t think there is any method other than maximizing the approval rating of a candidate that is not either stochastic or inherently unfair to voters or candidates. The alternative also introduces non-monotonicity into the system and causes a failure of the participation criterion.
Maybe you’re considering a system where, for example, a candidate among all those who surpass a majority’s approval is elected at random? What led you to this question?
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@cfrank It was just a random philosophical musing. People are very sensitive because modern politics are very polarized, but I wonder if anyone would care if the slightly less supported consensus candidate won over the slightly more supported consensus candidate -- if the level of consensus is within a typical margin of error, then statistically we cannot say that one is a better candidate than the other with reasonable certainty. I have seen some example elections and how various tallying methods could cause the less supported consensus candidate to win, but I am not convinced that it much matters if there is a sufficiently broad consensus for both candidates.
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It matters, but only a little bit.
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There are methods where voters rank candidates and also have an approval cut-off, so the winner isn't necessarily the most approved, but is also dependent on the ranks in some way.
But one thing I would say is that with approval voting, I don't see getting over 50% as anything particularly special. If it's OK for a candidate with 51% to beat one with 52%, then it's also OK for a candidate with 49% to beat one with 51%.
Edited to put the numbers the right way round.
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@k98kurz there’s a book called Collective Decisions and Voting by Tideman you might find interesting, at least the first half of it or so. One of the key factors in collective decision making is “agreement on procedure.” If you can get people to agree on a procedure that has the kind of outcome you suggest, maybe it would be fine. But in general, I doubt such a procedure would stand up to much scrutiny.
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@toby-pereira do you mean for the percentages to be reversed? As in, a candidate with 49% support may as well beat a candidate with 51% support? I think the specialness of >50% is that the voters who support that candidate outnumber those who don’t. My opinion is it’s definitely clear that a candidate with 51% approval should beat a candidate with 49% approval.
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@cfrank said in Does it really matter that a candidate with 52% support wins over a candidate with 51% support?:
@toby-pereira do you mean for the percentages to be reversed? As in, a candidate with 49% support may as well beat a candidate with 51% support? I think the specialness of >50% is that the voters who support that candidate outnumber those who don’t. My opinion is it’s definitely clear that a candidate with 51% approval should beat a candidate with 49% approval.
Yeah, I did mean for the numbers to be reversed! I would say if it's OK for 48% to beat 49% or 51 to beat 52, then it's also OK for them to straddle the 50%.
Obviously in plain approval voting, then it's just total approvals that wins so it's not an issue. But with e.g. a ranked method that has an approval cut-off, other things are looked at. But if you have a clause that says if a candidate uniquely gets over 50% approvals then they are elected, you would end up with unsatisfactory discontinuities in the method - weird, abrupt cut-offs where the result can suddenly flip.
Edit - It would result in failures of Independence of Irrelevant Ballots as well. Just sticking in some new ballots that don't approve any of the frontrunners can shift someone below 50% and cause them to lose if they only won by the >50% clause in the first place.
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@cfrank $50+ for an ebook is excessive. Is this a college text book?