On Aug 24, 2011, at 7:33 AM, Warren Smith wrote: >> Lundell: >> Arrow would not, I think, quarrel with the claim that a cardinal ballot has >> a pragmatic/operational "meaning" as a function of its use in determining a >> winner. >> >> But but it's an unwarranted leap from that claim to use the ballot scores as >> a measure of utility. Arrows objection to cardinal scores, or one of them, >> is that they are not and cannot be commensurable across voters. > > --(1) using, not range voting, but DOUBLE RANGE VOTING, > described here: > http://rangevoting.org/PuzzRevealU2.html > the ballot scores ARE utilities for a strategic-honest voter. Any > voter who foolishly > uses non-utilities as her scores on her ballot, will get a worse > election result in expectation. This was not an "unwarranted leap," > this was a "new advance" > because the Simmons/Smith double-range-voting system is the first > voting system which (a) is good and which (b) incentivizes honest > utility-revelation (and only honest) by voters.
It still seems to me that you're arguing in a circle. A utility score needs to have meaning logically prior to a voting system in order for a voter to vote in the first place. What is utility, from the point of view of a voter? Let me put the question another way. Suppose I'd rank three candidates A > B > C. On what grounds do I decide that (say) A=1.0 B=0.5 C=0.0 is honest, but A=1.0 B=0.7 C=0.0 is dishonest? > --(2) I agree that it is difficult to measure utilities commensurably > across voters. > However, range voting and double range voting do not do so, and do not > claim to do so. What IS commensurable across voters, are the scores > voters give to candidates (since those by the rules of the voting system > lie within fixed bounds). Double range voting will extract honest > utilities from > each voter, but not commensurably, i.e. with different and not-known scaling > factors for each voter. > > As a result, neither range voting, nor double range voting, are > "perfect" regret-free voting systems, and they were never claimed to > be. What I am claiming, > is that a double range voting ballot (honest part) has a MEANING. It > has a very definite, very unique, very clear, meaning, which due to > the Gibbard-Satterthwaite theorem is clearer than the meaning of > ballots in any (rank-order, deterministic) voting system Arrow ever > considered in his life. NO such rank-order system exists or ever can > exist, in which meaning is as clear as in double range voting. > > Therefore, Arrow's "meaning"-based argument against score-type and in > favor of rank-order-type ballots, is busted and has no validity. ---- Election-Methods mailing list - see http://electorama.com/em for list info