Not really? I mean, it says that there will always be someone who can benefit from dishonestly representing their beliefs, which is unfortunate, but it is a looser restriction, and in practice, the distortions that this introduces into approval voting or score voting are minimal, and they achieve much better results than plurality voting or IRV obtain.
Do you know whether there are other extensions of Arrow’s theorem to single-winner elections? Having a voting method return a full ranking of alternatives does not appear to be super important in practice...
Doesn’t Gibbard’s theorem retain most of Arrow’s bite?
Not really? I mean, it says that there will always be someone who can benefit from dishonestly representing their beliefs, which is unfortunate, but it is a looser restriction, and in practice, the distortions that this introduces into approval voting or score voting are minimal, and they achieve much better results than plurality voting or IRV obtain.
Oh, right; I seemed to have confused Gibbard-Satterthwaite with Arrow.
Do you know whether there are other extensions of Arrow’s theorem to single-winner elections? Having a voting method return a full ranking of alternatives does not appear to be super important in practice...