Arrow’s theorem is correct, but it only applies to voting methods in which voter-assigned votes are distributed among the choices. VoteFair ranking does not use such an approach. Instead, VoteFair ranking calculates a score for every possible outcome and regards the outcome with the highest core as the best match. For more information, look at the entry for VoteFair ranking (aka “Kemeny-Young”) in Wikipedia.

I’m curious if anyone has analyzed which of the 3 Arrow criteria Australia’s Prime Minister voting system lacks.

It’s the people in the institutions, and the culture within which they work, which produce good collective decision making. My guess is that it’s a mistake to not think of people.

If you’re talking about policy making, then my suggestion is that the people in the institution should be open to different ideas, perhaps even ones that they have previously or instinctively rejected, and that they be guided by data, evidence and reasoning.

Bryan Eastin and I talk about this all the time. We think it’s very analogous to the theory of fault-tolerance. We want the institution to be robust to some (possibly large) fraction of “bad” voters. Unfortunately, I think the reason this field is still in it’s infancy is that it’s so darn hard to find solutions that don’t just have good theoretical properties once implemented, but that might actually be possible to attain starting from our current institutions. If we’re at a “stable fixed point” in “institution space”, it will be very hard to leave, even if we find good alternatives.

Alejandro: Votes are numbers, so it’s the same as the usual order on numbers (except reversed).