I expect the big breakthrough to come when we figure out why the paradoxes in things like VNM and Arrow’s impossibility don’t in fact preclude radically better preference aggregation and thus much better coordination tech. I expect it will have turned out that those results were an artifact of the representation chosen for preferences. I expect that we will move from a bit estimate at particular times (e.g. voting) to some more fluid and continuous representation. I expect the new representations won’t just measure preferences over specific inputs and outputs (e.g. representatives and policy prescription) but something about the structures of the beliefs about how inputs map to outputs. This sounds complicated exactly because we haven’t found the nice formalism yet. It will seem elegant and obvious in hindsight.
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...
I expect the big breakthrough to come when we figure out why the paradoxes in things like VNM and Arrow’s impossibility don’t in fact preclude radically better preference aggregation and thus much better coordination tech. I expect it will have turned out that those results were an artifact of the representation chosen for preferences. I expect that we will move from a bit estimate at particular times (e.g. voting) to some more fluid and continuous representation. I expect the new representations won’t just measure preferences over specific inputs and outputs (e.g. representatives and policy prescription) but something about the structures of the beliefs about how inputs map to outputs. This sounds complicated exactly because we haven’t found the nice formalism yet. It will seem elegant and obvious in hindsight.
It is known that Arrow’s theorem is an artifact of using ordinal (ranked) systems rather than cardinal systems.
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...
The Von Neumann-Morgenstern theory is bullshit. It assumes its conclusion. See the comments by Wei Dai and gjm here.