I’m not sure how familiar with voting theory (or cake cutting theory) the average LessWrong reader is, so I may be preaching to the choir. But Arrow’s theorem (You can wiki it, I can’t give a precise mathematical definition off the top of my head.) pretty much states that having a decent voting system is impossible. Of course, we use the worst one possible (plurality) so anything would be an improvement. But mathematically, any solution proposed here will not be perfect, or perhaps even any good.
That’s interesting. Thanks for linking to that. As I said in my other comment though, there are still significant problems with that voting system—even if it does technically meet all of Arrow’s criterion. It encourages strategic voting to a tremendous degree, as you have no incentive to give any points to a candidate that you don’t want to see win. In that sense, it would likely result in an election almost identical to approval voting—which doesn’t fit Arrow’s criteria.
If you could trust voters to actually rank their preferences, then almost any voting system would work well—it’s just a question of opinion on which you think is “fairest”. I’m a IRV person, myself. Or a slight modification thereof. But I digress.
When it comes to large scale voting systems, I actually think that because of the Public Good nature of intelligent voting, voters are likely to vote with prosocial intent but also irrationally (they want the government to be good for people in general, but they favor stupid methods for doing that; see this). Thus the major problem large scale voting systems have is not the design of the voting system but with poor decision making on the part of voters. I actually have a proposal for taking advantage of prosocial voting but encouraging more intelligent voting decisions (link). I do not claim it is likely to ever get enacted.
I don’t have an opinion on whether the particular mechanism McCabe gives is a good one or not.
However, the point that Arrow’s theorem does not prove what many people say it proves is solid. Arrow’s theorem does strongly suggest that multi-agent decision mechanism design is difficult, but it does not prove that ‘good’ decision mechanisms are impossible.
However, the point that Arrow’s theorem does not prove what many people say it proves is solid.
No it is not. The argument was that Arrow’s theorem applies to voting systems in which voters state their preference rankings for the options, but what about voting systems in which voters give different information? This is a map-territory error. Whether or not the voting system is directly told about the voters’ preference rankings, it cannot in all cases yield a decision satisfying the desired criteria. Arrow’s theorem holds.
I did not intend to disagree with this. The lessons I have drawn from that post (and other related material) is that lots of people over interpret Arrow’s theorem thinking it proves something like RobertLumley statement “pretty much states that having a decent voting system is impossible.” even though there are things which you might want to call ‘voting systems’ which (but violate the conditions of Arrow’s theorem) and have nice properties. In other words, lots of people think Arrow’s theorem proves you can’t have good collective decision making algorithms, but it only applies to a certain subset of algorithms, so other kinds of algorithms may be ‘good’. I do agree that Arrow’s theorem suggests “designing a good collective decision system is hard”.
In case it’s still relevant, I don’t see how that is a map-territory error.
That comment is a misinterpretation of the mathematical definition of IIA—but it does raise a good point. The proposed system would, in actuality, be rather poor, it would encourage strategic voting to a tremendous degree, which would make it almost exactly like approval voting—which doesn’t fit all criteria.
My recollection from the class was that cake cutting was impossible to be done fairly as well, but we only briefly discussed it for about 30 minutes. In reading Wikipedia, it seems I’m wrong—it just takes many, many cuts. Thanks for correcting me.
If I had taught that class I would have emphasized that Arrow’s theorem involves discrete choices. There are many ways around it using continuous choices. Thus, cake cutting should not be surprised.
Also, I would have emphasized n=2. Arrow’s theorem is obvious in that case. And everyone knows how to cut cake into two pieces.
Yeah, it seems as though that would have been a better approach. I never got that.
But the class was almost three years ago and it was just a one credit hour Credit/No Credit “freshman honors symposium”. It wasn’t exactly the most rigorous of introductions.
But Arrow’s theorem (You can wiki it, I can’t give a precise mathematical definition off the top of my head.) pretty much states that having a decent voting system is impossible.
In that case, we should reinstate the monarchy right now, since no system of voting is worthwhile.
I’m not sure how familiar with voting theory (or cake cutting theory) the average LessWrong reader is, so I may be preaching to the choir. But Arrow’s theorem (You can wiki it, I can’t give a precise mathematical definition off the top of my head.) pretty much states that having a decent voting system is impossible. Of course, we use the worst one possible (plurality) so anything would be an improvement. But mathematically, any solution proposed here will not be perfect, or perhaps even any good.
Arrow’s Theorem is a lie. Not really, but it is widely misinterpreted.
That’s interesting. Thanks for linking to that. As I said in my other comment though, there are still significant problems with that voting system—even if it does technically meet all of Arrow’s criterion. It encourages strategic voting to a tremendous degree, as you have no incentive to give any points to a candidate that you don’t want to see win. In that sense, it would likely result in an election almost identical to approval voting—which doesn’t fit Arrow’s criteria.
If you could trust voters to actually rank their preferences, then almost any voting system would work well—it’s just a question of opinion on which you think is “fairest”. I’m a IRV person, myself. Or a slight modification thereof. But I digress.
When it comes to large scale voting systems, I actually think that because of the Public Good nature of intelligent voting, voters are likely to vote with prosocial intent but also irrationally (they want the government to be good for people in general, but they favor stupid methods for doing that; see this). Thus the major problem large scale voting systems have is not the design of the voting system but with poor decision making on the part of voters. I actually have a proposal for taking advantage of prosocial voting but encouraging more intelligent voting decisions (link). I do not claim it is likely to ever get enacted.
The article you cite is incorrect. The proposed ranged voting counterexample does not satisfy Independence of irrelevant alternatives.
I don’t have an opinion on whether the particular mechanism McCabe gives is a good one or not.
However, the point that Arrow’s theorem does not prove what many people say it proves is solid. Arrow’s theorem does strongly suggest that multi-agent decision mechanism design is difficult, but it does not prove that ‘good’ decision mechanisms are impossible.
No it is not. The argument was that Arrow’s theorem applies to voting systems in which voters state their preference rankings for the options, but what about voting systems in which voters give different information? This is a map-territory error. Whether or not the voting system is directly told about the voters’ preference rankings, it cannot in all cases yield a decision satisfying the desired criteria. Arrow’s theorem holds.
I did not intend to disagree with this. The lessons I have drawn from that post (and other related material) is that lots of people over interpret Arrow’s theorem thinking it proves something like RobertLumley statement “pretty much states that having a decent voting system is impossible.” even though there are things which you might want to call ‘voting systems’ which (but violate the conditions of Arrow’s theorem) and have nice properties. In other words, lots of people think Arrow’s theorem proves you can’t have good collective decision making algorithms, but it only applies to a certain subset of algorithms, so other kinds of algorithms may be ‘good’. I do agree that Arrow’s theorem suggests “designing a good collective decision system is hard”.
In case it’s still relevant, I don’t see how that is a map-territory error.
That comment is a misinterpretation of the mathematical definition of IIA—but it does raise a good point. The proposed system would, in actuality, be rather poor, it would encourage strategic voting to a tremendous degree, which would make it almost exactly like approval voting—which doesn’t fit all criteria.
Odd that you should mention cake-cutting theory, because it says the opposite of Arrow’s theorem.
My recollection from the class was that cake cutting was impossible to be done fairly as well, but we only briefly discussed it for about 30 minutes. In reading Wikipedia, it seems I’m wrong—it just takes many, many cuts. Thanks for correcting me.
If I had taught that class I would have emphasized that Arrow’s theorem involves discrete choices. There are many ways around it using continuous choices. Thus, cake cutting should not be surprised.
Also, I would have emphasized n=2. Arrow’s theorem is obvious in that case. And everyone knows how to cut cake into two pieces.
Yeah, it seems as though that would have been a better approach. I never got that.
But the class was almost three years ago and it was just a one credit hour Credit/No Credit “freshman honors symposium”. It wasn’t exactly the most rigorous of introductions.
In that case, we should reinstate the monarchy right now, since no system of voting is worthwhile.