<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto"><SPAN style="RIGHT: auto">I wouldn't say that this method makes Joe's utilities measurable. It puts him in a position where it's in his best interests to consider the utilities and come up with the best approximation he can. But it doesn't mean he'll get it right. But by getting people to think in terms of B being equal to a coin toss between A and C when the average utility of A and C is equal to the utility of B then this could help people's thinking (maybe).</SPAN></div>
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<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Also, when it comes to the meaning of a normal range ballot, then it still makes sense to talk about utility in these terms - the relative scores you give to candidates. But not everyone would give 0 to their least candidate and the top score to their favourite. If there are two candidates in a range voting election, and someone gives scores of 10 out of 10 and 8 out of 10, what would you say this means? I'm not sure that 0 and 10 or any absolute score can be said to have a set definition when not everyone uses the full range.<VAR id=yui-ie-cursor></VAR></SPAN></div>
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<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt"><FONT size=2 face=Arial>
<DIV style="BORDER-BOTTOM: #ccc 1px solid; BORDER-LEFT: #ccc 1px solid; PADDING-BOTTOM: 0px; LINE-HEIGHT: 0; MARGIN: 5px 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; HEIGHT: 0px; FONT-SIZE: 0px; BORDER-TOP: #ccc 1px solid; BORDER-RIGHT: #ccc 1px solid; PADDING-TOP: 0px" class=hr readonly="true" contenteditable="false"></DIV><B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Jameson Quinn <jameson.quinn@gmail.com><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> electionscience@googlegroups.com<BR><B><SPAN style="FONT-WEIGHT: bold">Cc:</SPAN></B> election-methods <election-methods@electorama.com><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Friday, 9 September 2011, 21:12<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re: [EM] [CES #3586] How to measure somebody's utilities<BR></FONT><BR>
<DIV id=yiv1790164601>The problem is, what if Joe doesn't understand?
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<DIV>In a separate thread, Dodeca proposes a definition of utility that is intuitively easy. The problem is, it's probably not the perfect definition of "utility" for range voting... especially when you consider that you'd have to rescale strategically to vote in range.</DIV>
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<DIV>That's one of the reasons why I like MJ. As long as the voters agree on what the numbers/grades mean, it works, even if nobody is rescaling and the scale isn't even linear.</DIV>
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<DIV>JQ<BR><BR>
<DIV class=yiv1790164601gmail_quote>2011/9/9 Warren Smith <SPAN dir=ltr><<A href="mailto:warren.wds@gmail.com" rel=nofollow target=_blank ymailto="mailto:warren.wds@gmail.com">warren.wds@gmail.com</A>></SPAN><BR>
<BLOCKQUOTE style="BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex; PADDING-LEFT: 1ex" class=yiv1790164601gmail_quote>It is often erroneously claimed that utilities are "unmeasurable."<BR><BR>Here is a way to do it. This kind of idea was one ingredient in F.W.Simmons's<BR>invention of various honesty-inducing voting methods,<BR>such as "double range voting," but it is worth isolating this ingredient since<BR>it is of interest by itself.<BR><BR>We suppose there are N items, alternatives, events, candidates, or<BR>whatever you want to call them.<BR>We want to know Joe's N utilities for those N events.<BR>We make a machine to carry out the following<BR><BR>UTILITY-REVELATION ALGORITHM:<BR>STEP 1. Machine tells Joe:<BR>"Please tell me your utility values (real numbers U_1, U_2, ..., U_N)<BR>for the N events,."<BR><BR>STEP 2. [Joe tells.]<BR><BR>STEP 3. Machine chooses 3 events A,B,C at random from the N<BR>with (say) U_A <= U_B <=
U_C<BR><BR>STEP 4. Machine now chooses a random real p with 0<=p<=1.<BR><BR>STEP 5. Machine now GIVES to Joe, either B, or {A with probability p<BR>and C with probability 1-p},<BR>whichever of these two has greater utility according to the U-values<BR>Joe had told us in step 2.<BR>The utility of the former is U_B and of the latter is p*U_A + (1-p)*U_C.<BR><BR>The end.<BR><BR>THEOREM:<BR>No matter what the random processes are in steps 3 and 4 (provided they<BR>cause positive probability for each triple {A,B,C}, and no subsegment of the<BR>real p-interval [0,1] has probability=0, and the randomness is not<BR>predictable by Joe),<BR>Joe's uniquely best (expected-utility-maximizing) strategy is<BR>to give honest (perhaps rescaled) utility values in step 2.<BR><BR>(Certain weaker conditions on the triples also would be acceptable.)<BR><FONT color=#888888><BR><BR>--<BR>Warren D. Smith<BR><A href="http://rangevoting.org/" rel=nofollow
target=_blank>http://RangeVoting.org</A> <-- add your endorsement (by clicking<BR>"endorse" as 1st step)<BR></FONT></BLOCKQUOTE></DIV><BR></DIV></DIV><BR>----<BR>Election-Methods mailing list - see <A href="http://electorama.com/em" target=_blank>http://electorama.com/em</A> for list info<BR><BR><BR></DIV></DIV></div></body></html>