Yes, Arrow's Theorem does assume ordinal ranking, since the whole goal of the decision process was to find a community-wide decision about how options should be placed in an order from favorite to least favorite (rather than just find a winner), and he expressly dismissed cardinal scores as meaningful input. He actually discusses the concept of range voting (not by that name) but asserts "It is hard not to see that the suggested assignment of utilities is extremely unsatisfactory." Obviously Range Voting advocates disagree with his assessment.
Terry Bouricius ----- Original Message ----- From: "Jonathan Lundell" <[email protected]> To: "Andrew Myers" <[email protected]> Cc: "Election Methods Mailing List" <[email protected]> Sent: Monday, November 16, 2009 4:44 PM Subject: Re: [EM] Anyone got a good analysis on limitations of approvalandrange voting? On Nov 16, 2009, at 2:15 PM, Andrew Myers wrote: > Jonathan Lundell wrote: >> This is in part Arrow's justification for dealing only with ordinal (vs >> cardinal) preferences in the Possibility Theorem. Add may label it >> preposterous, but it's the widely accepted view. Mine as well. > Arrow's Theorem seems like a red herring in the context of the cardinal > vs. ordinal debate. IIA makes just as much sense when applied to range > voting as it does to ranked voting. Arrow was just making a simplifying > assumption and I don't see that it makes his results lose generality. I don't have his proof in front of me (I'm on the road), but I'm pretty sure that it assumes ordinal ranking. ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
