If voters are strategic then in a two-candidate election Score is the same as Plurality/what we have right now. This is already sort of an improvement over most methods because they're the same as Plurality even if voters aren't strategic. If there are more candidates then it can be strategic to give multiple candidates points. Technically with perfectly strategic Score (with perfect information) decays into (Strategic) Approval, only giving the minimum and maximum score, though not necessarily just one maximum. In practice with less information it can be strategic to hedge your bets by giving some partial scores.

@@MustSeto you are correct, I even forgot I made this comment! hahahah I kept reading the other day about this topic and indeed, Score voting would degenerate into Approval voting in that perfect-information strategic scenario. Now I like Approval more than Plurality. But I also like Approval more than Score voting, because it's more simple and easier to understand. To make it even more simple, my fav option would be Approval voting with the choice of choosing 3 candidates max. This would make everything even easier to understand by citizens, and would still avoid favorite betrayal🥰

@@trincotrunco8932 Cool! Yeah voting methods is a real rabbit hole. It just keeps going... I largely agree about Approval being simpler than Score, and I also think that having larger and larger score ranges gives diminishing returns pretty quickly, even in theory. That said it seems like a lot of people _really_ hate being limited to just two options, and having to chose between putting compromises with either favorites or their hated, so I've wondered if 3 (e.g. for/neutral/against) would be more popular while still being simple. Maybe increase that to 4 if having an exact middle causes issues... I think there's been research on ratings scales like this (usually for surveys and things) that suggests people are unreasonably drawn towards middle scores, and you get better data on average if there's no true middle. Not sure how we'll that'd apply to this, or if voter frustration would outweigh the benefits, though. What do you mean about choosing 3 candidates max? You mean only 3 candidates can run, or each voter can only approve 3? I don't think I'd do either. I could see having a "unified primary" election to narrow the field a bit before having a "final" election being useful to let voters focus research on a more manageable number of candidates, though I don't know if I'd limit that to 3. Maybe 5, or maybe the top 20%, or something. A big draw of alternative methods and avoiding the spoiler effect is moving away from duopoly and towards more varied and nuanced races with multiple candidates. And I don't see the point of limiting a voter to just 3 approvals, especially if we do start getting a good spread of candidates.

Like in Plurality? Plurality votes can be losslessly encoded as ranks, and fails IIA. You could score them instead though. Scores can't be losslessly encoded as ranks, so Arrow's theorem doesn't apply.

@@MustSeto Just see who ever has the most votes, IDK.

@@Auroral_Anomaly That's a great method, if you allow voters to vote for more than one candidate (Approval). Otherwise, if you only let them vote for one candidate, it's terrible (Plurality).

@@MustSeto Ok, ig.

I don't think the main issue with favorite betrayal is whether it's "unfair" or "a legitimate choice" with respect to any particular voting method, the bigger issue is with what higher-order effects it has, such as center-squeeze, and artificially encouraging duopoly. In Arrow's theorem, the dictator must be a consistent voter across elections. If you hold a new election using the same method, then the same voter must be a dictator again and the results will be a copy of their new ballot, no mater how anyone else votes. This does mean that Dictatorships must violate Anonymity.

@@MustSeto It is impossible for anyone know the other voters vote so no one can PLAN to be the dictator, besides it is an edge case that only happens in very balanced elections so one vote can make this. It is unreal as an Adam with a bellybutton.

@@agranero6 > It is impossible for anyone know the other voters vote so no one can PLAN to be the dictator Why would it matter if no one knows how any one else will vote? The identity of the dictator does not depend on anyone's votes, so the dictator could easily know that they're the dictator ahead of time.

@@MustSeto How if everyone votes at the same time? It is only possible if excluding the dictator there is a tie. Explain how he could know he is the dictator? Dictator is a misnomer: dictators can impose their will no matter what the case. The pivot, the deciding vote is a legitimate as any other.

@@agranero6 Arrow's theorem is agnostic to how such a method could come to be used. But in real life, I suppose they (or their regime) would have to enact and enforce the usage of the method themselves. And the method would have to have fail Anonymity -- it'd need some way of identifying which ballot is the dictator's. Or on a smaller scale, the dictator could just be tricky. Create a method with them as the dictator, but disguise how the method works and convince some electorate/organization to use it. Something like that.

Every system can be affected by strategic voting, it's mostly a matter of how much it helps/harms the outcome, and I think saying Score is "broken" because of this is a bit too strong. It would effectively make it equivalent to (strategic) Approval Voting, which is generally still considered a very good system by many (if anything I'd say it's more popular than Score/Range at the moment). > And the more 5 stars you give the more voting power you have. I don't think this is true at all. For example, if you give everyone 5 stars, then your vote isn't a net help or harm to any candidate; it's basically the same as not showing up. If you do that for everyone except your least favorite... well, if your least favorite was a no-hoper regardless, then again it's basically useless. Generally, compared to just giving points to a few favorites, giving out more points to compromises decreases the chances of a favorite winning, but also decreases the chances that a least favorite wins. As-is, this system basically tries to pick the candidate with the highest average rating. If instead you divided up people's power based on how many candidates they support then it'd really be vulnerable to bullet-voting, basically turning it into (strategic) Plurality.

@@MustSeto You give stars to every minor candidate you like too. Ofc not the ones you oppose, just everyone who's for ex conservative if you are and just give 5 stars to 10 of them including really small ones why not. It becomes a competition for what side will vote for the most candidate's.

@@darklazerx7913 Yes, strategically you can safely and arguably should give minor candidates you like above some threshold the max score as well. But artificially running extra candidates doesn't really help your side any. Range/Score is proven to be "cloneproof". You're just independently assessing each candidate. Adding an extra candidate doesn't change the existing candidate's scores. So it doesn't help your major candidate. It also doesn't help any other extra candidates from your side. To have a chance at changing the winner, it'd have to independently be scored higher than its own major candidate, which they'd have to reach more voters than the other to do (like genuinely having better support from the opposition without losing your side's support), which doesn't sound so bad. So the only way this'd benefit your side is if many of the candidates are genuinely distinct and your side is hoping one of them is genuinely superior for the electorate, and you don't have a way to tell ahead of time, so you throw extra dice. But (1) that still implies this results in genuinely better candidates being elected, and (2) in reality even if you technically field a bunch of candidates, probably people won't be able to investigate all of them and will coalesce around a few anyways, or you won't be able to financially support all of them with good campaigns, etc

That's not really what this is saying. The proof shows that a pivot must exist, but doesn't say where they are. For the sake of example they picked a position near the middle, but they could have been first. But regardless of where they are, the final results will be a copy of their ballot. And it's not just some kind of cancellation effect either, where in a different election it might be someone else; it's always the same voter for as long as the same method is used. Of course real methods that are actually used in the real world fail IIA, so this doesn't apply to them.

Every (sane) method has strategic considerations, the ultimate question I'm concerned with is about how good the final results tend to be with realistic voter behavior. Honenstly I consider most debates around strategy to be a bit of a red herring, at least for most seriously proposed methods. Unless you count Borda. Strategy destroys Borda. Don't use Borda. For example, if under one method usually few voters have an opportunity to be strategic but the few who do can change the results a lot, while under another method almost everyone can be a bit strategic but it can't effect the final results hardly at all, then which is more "vulnerable" to strategy? Or more generally, if one method is virtually immune to strategy but gives consistently poor results, while another method is in profoundly effected by strategy in whatever sense you prefer, but even so it's worse-case is generally fairly decent, which of the two would you prefer? Could there be a method that benefits from strategic voting? I think Plurality at least might count. If a method is basically defined as being an "automatically strategic" version of another method, can any vote ever be considered honest? Maybe some other external consideration is more important, like whether or not it encourages duopoly? Most methods behave the same as Plurality when there are only two strong options. So if a method "technically" works well in some sense with many parties, but somehow encourages duopoly anyways, then it kind of might not matter. This kind of gets to the "true" meaning of scores in Range/Score. Strategic voting can involve giving bad compromises fewer points than you might have if you thought everyone was equally likely to win, but it can also involve giving extra points to better compromises. At the extreme, it becomes (strategic) Approval Voting, which is still usually considered very good (and seems to be explicitly preferred by quite a few). In general, compared to giving points only to fewer favorites, giving more points to compromises decreases the chances that one of the favorites will win, but also decreases the chances that a _least_ favorite will win. You're more likely to at least get a compromise. IMO being "slightly" strategic is possible for almost everyone, but I don't expect it to have a huge negative effect on the overall quality of the final winner. This style of strategic voting might not even be harmful. If Alice and Bob have the "same preferences" in some naive sense, but Alice decides to be strategic while Bob doesn't, maybe that indicates something more subtle but valuable after all, like Alice believes she has more at steak, maybe enough to risk settling for a compromise as long as someone worse is kept away, while Bob decides he might as well focus on getting his favorite. Condorcet/top-cycle methods might be good too though. I'd be a little worried about the dark horse + 3 pathology, but Condorcet should at least resist it better than Borda, and I hear some Condorcet methods are immune to it, so maybe it's fine if we use one of those. I think minimax with equal ranks is supposed to be immune? Unfortunately, IIRC Shulze's Beatpath method and Tideman's Ranked Pairs methods aren't immune, though.

The method is just a function that can take any possible collection of ballots, so it's not like we're assuming someone sees the other ballots and carefully crafts their own to get what they want. We can always consider a collection of ballots which is exactly the same except that this someone submits any other ballot. The theorem doesn't start out assuming whether or not the method is anonymous. "Anonymity" is another criteria a method can pass or fail, it's basically saying that if you reorder ballots then the result will always be the same. But it turns out that's incompatible with Unanimity + IIA. Because a Dictator is not just a "tipping point", they're in full control of the every election no mater how anyone else votes for as long as that method is used. So dictatorships cannot be anonymous. You're right of course that that's not how any real voting method works. Because every real voting method fails IIA.

By IIA, B > S. Also by IIA, C > B. But Rankings are transitive, so since C > B and B > S, C > S as well. The problem is that it passes IIA. Which together with Unanimity means the method has a dictator. It's not that the magnitude of relative ranking isn't being respected, it's that only one voter is considered at all, no mater how anyone else votes.

The pivot is only defined by one change in a specific scenario. Once we've found that we don't immediately assume they are the pivot for another even slightly different scenario (though we eventually derive it). Instead we just use Unanimity and IIA. To try to define the pivot another way, this time using the specific scenario in the video, they're the first voter such that if everyone before them votes C>S>B and everyone after them says B>C>S, their switching between B>C>S and C>B>S switches the results between B>C>S and C>B>S. (We don't then assume they'll remain "pivotal" in the same way if the ballots were tweaked slightly _pre se._ We just immediately, blindly start applying IIA, only using the pivot scenarios as a starting point. We don't assume the pivot is preserved after we start doing that.) Proving that such a pivotal situation must exist at all in this concrete scenario is mostly what the first part of the proof was doing, but the positions of Bulbasaur and Charmander were only _relative,_ and they kept the _relative_ position of Squirtle in the votes and results abstract/unknown. But eventually they strategically assume Squirtle was in positions such that unanimity ensured they would finish last anyways, letting us use a more concrete example where everyone's rankings in the votes and results are absolute.

"Range" used to be the more common name. From the upload time I think this video was made around the time the transition was happening (around the same time I was getting interested, now that I think about it).

Eh, IIRC that's theoretically the optimal strategy if you have good enough information, but with more uncertainty in the details of how other people will vote I think it starts to make sense to give some partial scores. Anyways I'm not sure this would harm the method's overall performance much, Approval Voting is supposed to be pretty good as well. Plus, there's a method actually _named_ "STAR" (Score Then Automatic Runoff) which modifies plain Score slightly to try to encourage differentiating compromises a bit. First there's a plain Score step to find the top _two_ (instead of just electing first place), then whoever between those two is scored higher on the most ballots wins, even if they were 2nd place. This is using the same ballots as before; there's no separate round where you show up again or anything. So whether you say A=5, B=4 (difference of 1 point) or A=4, B=0 (difference of 4 points) that's one point to A in the 2nd round. But if you say A=5, B=5 then neither gets anything. So if A and B are competitive you're better off docking B at least one point, unless you're truly very indifferent between the two. It doesn't hurt B much against other candidates in the first part, but if it comes down to it, it helps A a lot in the end.

Why shouldn't they be first? I mean, we never assumed the method _didn't_ have a dictator. And if F is a dictator for the method, then obviously the method would put Charmander first there. The application of Unanimity and IIA just helps us find who they might be. The process described in this video can be thought of as the process of diagnosing an unknown method to find who any dictator might be.