<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>On Aug 24, 2011, at 8:16 PM, Jameson Quinn wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="word-wrap:break-word"><div><div class="h5"><div><blockquote type="cite"><div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word"><div><div><div><blockquote type="cite"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>:<br>
<br>
>> Lundell:<br>
>> 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.<br>
>><br>
>> 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.<br>
><br>
> --(1) using, not range voting, but DOUBLE RANGE VOTING,<br>
> described here:<br>
> <a href="http://rangevoting.org/PuzzRevealU2.html" target="_blank">http://rangevoting.org/PuzzRevealU2.html</a><br>
> the ballot scores ARE utilities for a strategic-honest voter. Any<br>
> voter who foolishly<br>
> uses non-utilities as her scores on her ballot, will get a worse<br>
> election result in expectation. This was not an "unwarranted leap,"<br>
> this was a "new advance"<br>
> because the Simmons/Smith double-range-voting system is the first<br>
> voting system which (a) is good and which (b) incentivizes honest<br>
> utility-revelation (and only honest) by voters.<br>
<br>
</div>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?<br>
<br>
Let me put the question another way. Suppose I'd rank three candidates A > B > C.<br>
<br>
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?<br>
<div><br></div></blockquote><div>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.</div></div></blockquote><br></div></div></div><div>
And if the polls suggest that A & B are strong favorites and C is doing poorly, how should I vote to maximize my utility?</div><div><br></div></div></blockquote></div>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.</blockquote>
<br></div></div></div><div>How does it keep me honest in that scenario? Presumably I'd vote 1-0-0; what's my motivation to do otherwise?</div><div><br></div><div><br></div></div></blockquote><div>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.</div>
<div><br></div><div>JQ</div></div>
</blockquote></div><br><div>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.</div><div><br></div><div>This is true, of course, of any manipulable voting rule.</div><div><br></div></body></html>