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> 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.) This is fine. The

> 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.) 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!

crazygringo 4y ago
Ranked choice absolutely conveys more information than approval. It's not as much as score voting, but it's mathematically false to say it's the same amount as approval. Among five candidates, approval would be 2^5-2=30 possibilities (almost 5 bits of information, assuming you can't approve/disapprove all because that's the same as not voting), while ranked choice would be 5!=120 possibilities (almost 7 bits of information, assuming ties aren't permitted). It's only with 3 candidates that they have equal information in terms of possibilities (2^3-2=6=3!). 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.
- wnoise 4y ago
  Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)
- naniwaduni 4y ago
  > Ranked choice absolutely conveys more information than approval. It's not as much as score voting, but it's mathematically false to say it's the same amount as approval. Among five candidates, approval would be 2^5-2=30 possibilities (almost 5 bits of information, assuming you can't approve/disapprove all because that's the same as not voting), while ranked choice would be 5!=120 possibilities (almost 7 bits of information, assuming ties aren't permitted). It's only with 3 candidates that they have equal information in terms of possibilities (2^3-2=6=3!). 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.
  - crazygringo 4y ago
    > This is a common intuition trap, but it's wrong. 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.
dane-pgp 4y ago
> The probability with which a voter bullet votes vs votes three conveys the degree of preference for that candidates. 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.
- naniwaduni 4y ago
  It's not a fantastic proxy, I agree, since the aggregation rule implicitly assumes linearity and it's almost certainly not. I think it's somewhat mitigated in practice by the kind of small intersection between situations where it's strategically safe for a party to push bullet voting and where it's useful to do so being pretty constrained to elections where the top candidates are mostly acceptable to the same voters, though? I find it pretty unintuitive to construct an approval vote election scenario with a rational spoiler effect, and that's probably less big a deal than the vote weighting issues that crop up with multi-point score votes, but that's definitely something you can quibble over. 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.

crazygringo 4y ago

Ranked choice absolutely conveys more information than approval. It's not as much as score voting, but it's mathematically false to say it's the same amount as approval. Among five candidates, approval would be 2^5-2=30 possibilities (almost 5 bits of information, assuming you can't approve/disapprove all because that's the same as not voting), while ranked choice would be 5!=120 possibilities (almost 7 bits of information, assuming ties aren't permitted). It's only with 3 candidates that they have equal information in terms of possibilities (2^3-2=6=3!). 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.

wnoise 4y ago
Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)
naniwaduni 4y ago
> Ranked choice absolutely conveys more information than approval. It's not as much as score voting, but it's mathematically false to say it's the same amount as approval. Among five candidates, approval would be 2^5-2=30 possibilities (almost 5 bits of information, assuming you can't approve/disapprove all because that's the same as not voting), while ranked choice would be 5!=120 possibilities (almost 7 bits of information, assuming ties aren't permitted). It's only with 3 candidates that they have equal information in terms of possibilities (2^3-2=6=3!). 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.
- crazygringo 4y ago
  > This is a common intuition trap, but it's wrong. 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.

dane-pgp 4y ago

> The probability with which a voter bullet votes vs votes three conveys the degree of preference for that candidates. 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.

naniwaduni 4y ago
It's not a fantastic proxy, I agree, since the aggregation rule implicitly assumes linearity and it's almost certainly not. I think it's somewhat mitigated in practice by the kind of small intersection between situations where it's strategically safe for a party to push bullet voting and where it's useful to do so being pretty constrained to elections where the top candidates are mostly acceptable to the same voters, though? I find it pretty unintuitive to construct an approval vote election scenario with a rational spoiler effect, and that's probably less big a deal than the vote weighting issues that crop up with multi-point score votes, but that's definitely something you can quibble over. 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.