People often have strong feelings about their top preference, and approval rating destroys that.
And then in my example, the voter is tempted to approve just 1 in order to give them a better chance of winning. (Known as bullet voting.)
It's much more intuitive and less cognitive load to rank options by preference than to decide on an arbitrary threshold of approval. You already know your ranking; you have to strategically decide on an approval cutoff.
(Also, between the candidates you disapprove of, you still often think some would be better/worse than others, and want that to count too.)
All voting systems have drawbacks, but I think approval is best relative to effort and impact.
This is fine. The probability with which a voter bullet votes vs votes three conveys the degree of preference for that candidates. This is not as informative as score voting on a wider range (because okay, degree of preference doesn't map perfectly linearly with probability of vote), but it's an perfectly adequate proxy.
By comparison, ranked choice, despite feeling like it gives you the ability to choose relative ranks, doesn't actually convey more information because it says nothing about your degree of preference! "Candidate A is perfect in every way > Candidate B agrees with me on all policy decisions but is my ex > Candidate C literally wants to murder me" looks exactly the same on a ranked choice ballot as "Candidate A is perfect in every way > Candidate B literally wants to murder me > Candidate C literally wants to murder me and also kicked my dog".
> It's much more intuitive and less cognitive load to rank options by preference than to decide on an arbitrary threshold of approval. You already know your ranking; you have to strategically decide on an approval cutoff.
Spoken like someone who doesn't have intransitive preferences!
And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
Yes score voting would be ideal if it were easy to convert preferences strength into numbers, but one person's 7 can be another person's 3. There's no objective way to do it. The same as approval voting isn't objective, because there's no objective threshold. Whereas ranked voting is purely objective, a person can always express an ordered preference in a consistent, repeatable way.
Very well then I contradict myself,
(I am large, I contain multitudes.)
This is a common intuition trap, but it's wrong. Consider the difference between score voting on a 16-point scale vs a million-point scale vs arbitrary-precision score voting. A ballot for the first conveys 4 bits per candidate; the second, about 20 bits per candidate; the last conveys infinite bits of information. You ... probably don't expect a substantial difference between election results with each option.
The trick is that the aggregation rule destroys information, which is kind of the point of aggregation. Different aggregation rules destroy different information. The difference between aggregated approval voting and aggregated arbitrary-precision score voting eats LSBs, sure, but the obvious probabilistic constructions for extracting approval votes from arbitrary precision score votes actually approximate the arbitrary-precision votes quite well, which is not what your intuition predicts, because it turns out LSBs are, well, less significant.
Also, the flat fact is that most single-victor elections in practice don't have more than three "top" candidates that you're practically interested in extracting information about.
> And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
That's one hell of a bad assumption.
I respectfully disagree. Yes it's true that jumping to lots of information with score voting doesn't produce an equivalent increase of meaningful information and that information is eaten by the aggregation technique, but I would argue that's not the case with ranked voting.
In the larger practical sense, yes there is a good argument to be made for approval voting if everybody voted honestly and gradations in preference strength were truly "dithered" relatively accurately among the population in a way that approval voting could "recover" the actual score-like preferences in aggregate. But the reality is that approval voting is easily subject to bullet voting manipulation, which destroys all of the information that it would otherwise contain in theory.
So in the real world, I submit that ranked voting ends up conveying more information that actually gets used, because there's more incentive to vote honestly.
> > And individuals don't have intransitive preferences, only populations can. (Assuming mental competence.)
> That's one hell of a bad assumption.
I assume you're just joking. Because yes while we can joke "hur hur people are dumb", if you're not taking people's votes seriously then what are we even doing? Every mathematical model must assume that individual's preferences are transitive, or we'd go mad.
You would be largely wrong for single-victor elections, and even trivially so for those without more than three major candidates in the race (to wit: most of them). So you're going to have to make that argument.
> But the reality is that approval voting is easily subject to bullet voting manipulation, which destroys all of the information that it would otherwise contain in theory.
No, this is not the reality. At an individual level, bullet voting is part of your strategic frontier of (all sincere!) votes, but the only strategic bullet vote is for your sincere favorite who is also a likely candidate to win. It is possible to get your most preferred candidate elected over a more widely approved candidate, but this still requires a plurality of second-candidate approvers to prefer your most preferred candidate (and enough to bullet vote them!), which is, like, not the worst outcome in the world, realistically speaking.
Meanwhile, at a campaign level, it only makes sense to push bullet voting to (a) people who most prefer your candidate, whose only viable competition is a more widely preferred candidate who shares largely the same voter base, which in context is basically betting on your targeting specificity, and (b) people who are going to vote for multiple candidates, none of which are yours, who you're convincing to vote against their own interests.
Also, you don't have a 100% success rate on convincing people to bullet vote, so your ability to convince people to bullet vote your candidate is still a proxy for strength of preference. You're making it a lossier proxy, but since you're destroying information from people who you were able to convince to follow your suggested voting strategy, this is not really a winning strategy unless you're already winning.
All in all, bullet voting simply is not remotely as much of a bogeyman to approval voting as it is to some ranked voting systems. There is some degree of strategic influence available, but it certainly happens less easily than in a ranked vote and is weaker in approval voting than in pretty much any other voting system under discussion—I challenge you to find a bullet voting "manipulation" that manages to make approval voting contain less information after aggregation than your favorite ranked choice model.
> Every mathematical model must assume that individual's preferences are transitive, or we'd go mad.
It's okay to accept some error. People genuinely have non-transitive preferences. This only has to drive you mad if you insist on generating a total ordering.
I can see why that would be a useful assumption, but is there really empirical evidence to confirm that?
A much bigger factor in determining what the voter does, I would guess, is whether they hear activists for their party telling them (perhaps disingenuously) that their candidate won't win if you "betray" them by approving your second or third preference.
So there will be probability distributions of parties that try spreading such a message, and people who hear such a message, and voters who are loyal enough or risk averse enough to follow the advice, but I don't think the combined distribution matches closely enough to the genuine "degree of preference".
As a result, some candidates will get a tactical boost at the expense of their rivals, and eventually all voters will start to question whether they should have voted differently.
The wider point imo is that compared to all forms of ranked choice voting, arbitrary-precision score voting is pretty obviously night-and-day superior (information-content-wise, at least), to which approval voting is a "close enough", at worst moderately inferior but at least theoretically equivalent, trade-off in favor of implementability.
I've been very encouraged by the results in Alaska after the special election that just happened there in August. 85% found it simple. 73% ranked multiple candidates. And the election workers implementing it had a flawless go of it.
Some data from one of the groups that helped educate voters: https://alaskansforbetterelections.com/polling-shows-alaskan...
But what's conspicuously absent from these statistics is how happy the voters are with the outcome (compared to a counterfactual world where the election had been carried out under FPTP and a potentially different candidate won).
Sadly it was an outcome which allowed Sen. Tom Cotton (R-Ark.) to make the argument[0] that:
> 60% of Alaska voters voted for a Republican, but thanks to a convoluted process and ballot exhaustion — which disenfranchises voters — a Democrat ‘won.’
This is exactly the sort of well-poisoning that supporters of other voting reforms are afraid of.
[0] https://www.independentsentinel.com/60-of-voters-cast-ballot...
I'm waiting to see RCV pushed by someone's who ideology doesn't exactly benefit from it in their area. It's not a second place always wins, but I have seen a lot of examples of "My party will not win in my area, but it's kinda close, and RCV gives me a higher statistical probability of "my side" getting in".
Maybe approval voting is better, I'm not sure how likely it is for unpopular candidates to win in close areas. If it suffers from the same issues as ranked choice or not.
I'm tired of it all being game.
The two-party system is so dominant in the US because of the first-past-the-post voting system. With such an election (even disregarding the financial power of the parties, or the role of the electoral college) third-party candidates never have a shot, because any intelligent voter knows that a vote for them is a spoiler for their second-favorite candidate.
Multi-choice voting systems generally reduce or eliminate spoiler effects, which both allows a third party to build support, and reduces the chance that an election will go to a candidate with lower support simply because the other side had their vote split.
Even when we're not talking about the two-party system, multi-vote systems better reflect the will of the people. My city has a ranked choice, multi-seat election for city council. All councilors are at-large, meaning you're voting a group of about ten of them in, and selecting from a pool of about 20 candidates. There's almost no other system that could accurately capture the majority of the people's positions.
So the strength of RCV would then be more built in tie-breaking.
To put it another way: given a (sufficiently large) set of [0,1] score votes, you can generate a set of approval votes that give a very good estimate for the score voting results by mapping each score vote to an approval vote by randomly picking a number in [0,1) for each vote and marking options scored above that threshold. Handwaving a bit, this implies that at scale approval voting and arbitrary-precision score voting give the same results with pretty good probability.
Now, score voting with arbitrary precision pretty clearly conveys more information than ranked choice! You can extract an RCV from a score vote directly, but this loses substantial information about how far apart the options were rated. Conversely, if you extract a score vote from an RCV, you ... well, you can get something like Borda count. For other RCV aggregation algorithms a score vote extraction is not quite as clean, but it's substantially less clear whether the information "lost" is real or an accidental artifact of the RCV itself. Certainly you can argue all day over the merits of Borda count and variants vs other IRV aggregation algorithms, but then score voting with arbitrary precision not only strictly dominates Borda count, but also is clearly conveying additional information about degree of preference on top of that which is obviously useful and not encoded in ranked choice votes at all!
Bonus: a surprisingly large number of decisions are dominated by no more than three viable choices that are clearly preferred over all others. When selecting for among three options, there are seven unique approval votes (the all marked/unmarked votes, expressing no preference, are equivalent), and only six ranked unique choice votes. It should be pretty clear that RCV and approval don't convey equivalent information in this case!
Which is emblematic of the biggest problem with RCV, which is that the aggregation algorithms are too opaque to realize at a glance that the results they give are ... not as good as doing a straightforward thing.
No, they're both six. There are 8 unique approval votes (2^3) but two are thrown out -- the all-marked and all-unmarked, so you're left with 6, same as ranked. RCV and approval absolutely do convey equivalent information in the case of three candidates.
I don't know where you're getting seven from.
For instance suppose you encode the position of missile strikes on some land area in a 16x16 grid, meaning 8 bits of information.
Another person uses only six bits of information, encoding the missile strike position as degrees and distance from the center point of the grid.
Then it turns out the latter method is more accurate because the missiles tend to always strike pretty close to the center of the grid.
The specific patterns of voter preference that emerge in a realistic scenario are counterintuitive and can end up being more accurately measured by the kind of expression approval voting allows. You can get people who have radically different intensity of preference but the same order of preference so that they look identical to a ranked voting method but appear different to approval voting based on their thresholds.
In addition, you have tactical behavior, as well as the efficiency of how the voting method uses the information on the ballots. When you combine all of these factors together, approval voting tends to perform better than ranked voting methods.
https://www.electionscience.org/library/expressiveness-in-ap...
In a nutshell, the reason this works is because the people who approve only X or Y have a pretty similar X versus Y opinion as the whole electorate, just based on random chance. It's just statistical sampling principles.
https://www.electionscience.org/library/expressiveness-in-ap...
https://fairvote.org/the_troubling_record_of_approval_voting...
https://www.rangevoting.org/BulletBugaboo.html
(b) Approval voting only incentivizes bullet voting when that is very close to actually capturing the voter's intent. The strategic thing to do is vote approve on all those you like better than whoever you think the most likely candidate to win is.