On Aug 24, 2011, at 8:16 PM, Jameson Quinn 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? >>> >>> In double-range, you'd say that if you felt that B was clearly better than >>> a 50/50 chance of A or C, but as good as a 70/30 chance. >> >> And if the polls suggest that A & B are strong favorites and C is doing >> poorly, how should I vote to maximize my utility? >> >> The point of double-range is that it introduces a small random factor to >> keep you honest. Thus, I don't think most societies would accept it as a >> serious system, but it does demonstrate that cardinal ballots can have a >> "meaning" beyond rankings. > > How does it keep me honest in that scenario? Presumably I'd vote 1-0-0; > what's my motivation to do otherwise? > > > Because there's a small chance that your (first "honest" range) vote actually > will decide between a lottery of some chance of A or C and a certainty of B. > If you haven't voted honestly, then that could make the wrong decision. And > such decisions are all your "honest" ballot is ever used for, so there is no > motivation to strategize with it. > > JQ
That's always the case with strategic voting when we don't have perfect knowledge of the other votes. There's a larger chance (in this example) that a sincere vote will cause B to defeat A. The more I know about the state of other voters, the more motivation I have to vote insincerely. This is true, of course, of any manipulable voting rule.
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