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.
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.