<table cellspacing="0" cellpadding="0" border="0" ><tr><td valign="top" style="font: inherit;"><DIV>Hi Jameson,<BR><BR>--- En date de : <B>Lun 21.3.11, Jameson Quinn <I><jameson.quinn@gmail.com></I></B> a écrit :<BR></DIV>
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<DIV class=yiv1215623519gmail_quote>2011/3/19 Kevin Venzke <SPAN dir=ltr><<A href="http://fr.mc296.mail.yahoo.com/mc/compose?to=stepjak@yahoo.fr" target=_blank rel=nofollow ymailto="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</A>></SPAN><BR>
<BLOCKQUOTE class=yiv1215623519gmail_quote style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Hi,<BR><BR>Jameson, I did most of what I looked into.</BLOCKQUOTE>
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<DIV>Wow, thanks.</DIV></DIV></BLOCKQUOTE>
<DIV>No problem, I'm glad to look into areas of interest.</DIV>
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<DIV class=yiv1215623519gmail_quote> </DIV>
<BLOCKQUOTE class=yiv1215623519gmail_quote style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">I didn't complete the Asset<BR>methods though. I did come up with a good universal way to estimate the<BR>candidates' utilities for each other though: Have the candidates read the<BR>minds of the voters (the base quantities of each bloc), and multiply each<BR>opinion by their opinion of the candidate asking the question. (I'm<BR>assuming utilities range from 0 to 1.) So, a candidate will like the same<BR>candidates you like, if you like that candidate. This way, B will like<BR>C not because of the spectrum, but because most of his "goodwill" comes<BR>from the C voters.<BR></BLOCKQUOTE>
<DIV class=yiv1215623519gmail_quote><BR></DIV>
<DIV class=yiv1215623519gmail_quote>I think my trick is somewhat better: only have them look into the minds of voters which top-rate them specifically. My rationale is that with your method, I believe it would be impossible to have a Condorcet cycle among the candidates, since A feels about B exactly as B feels about A. With my method, a Condorcet cycle would be possible, which is good - a real-life robust Condorcet cycle would probably be some variant of three candidates, three single-issue voting blocs, and appropriate strength for each bloc. In that circumstance, I'd expect candidates to transfer to the other one who is middling where they are strong, not to the one who is strong where they are middling.</DIV></BLOCKQUOTE>
<DIV class=yiv1215623519gmail_quote>Hmm, I think you're right about the cycles. I'm not sure it's less accurate to do it</DIV>
<DIV class=yiv1215623519gmail_quote>my way though. We're sort of finding a correlation between candidates' high rankings,</DIV>
<DIV class=yiv1215623519gmail_quote>so I'm not sure why we would expect to find cycles. Not sure there is more information</DIV>
<DIV class=yiv1215623519gmail_quote>there to be found.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
<DIV class=yiv1215623519gmail_quote>If we do it your way, B will do the bidding of the middle bloc, which prefers A to C.</DIV>
<DIV class=yiv1215623519gmail_quote>If that's how B "feels" it's odd that C voters like him so much.</DIV>
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<DIV class=yiv1215623519gmail_quote><BR>Anyway, the Asset methods stumped me somewhat because I couldn't come<BR>up with a deterministic way to solve the method that doesn't seem to<BR>be contrived. For instance, it's possible that two of the three candidates<BR>are able to transfer. Who has initiative? How do they even know if they<BR>would like to have initiative? Maybe they'd rather do nothing. So, I<BR>didn't attempt to write a method that might not be faithful to the idea.<BR></DIV>
<DIV class=yiv1215623519gmail_quote><BR></DIV>
<DIV class=yiv1215623519gmail_quote>All "transfers" are simultaneous and represent "copies" rather than bowing out. Since the "can I transfer to you" criterion is the same as the "will you beat me without transfers" criterion, at least in the 3-candidate case there are no issues of initiative or transfer strategy. The pre-transfer 2nd place has no motivation whatsoever to transfer to the pre-transfer 1st place, and no ability to transfer to the 3rd place. So, if transfers are happening at all, it's just that 3rd place is acting as a kingmaker (pseudo-IRV style); that's simple.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV></BLOCKQUOTE>
<DIV class=yiv1215623519gmail_quote>Aha. I'll think about it again.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
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<DIV class=yiv1215623519gmail_quote>"MCARA" 96 87<BR>BBB-MMM 99 100 86<BR>TTTT--- 75 100 90<BR>TTTTM-- 46 100 86<BR>TTTTMM- 44 100 85<BR>BBT-MMM 41 100 86<BR>TBB-MMM 35 100 88<BR>TTTT--M 31 100 89<BR>TTTTMMM 29 100 84<BR>BTB-MMM 28 100 85<BR>BBB-CCC 28 93 94<BR>***MCCC 26 94 93<BR>TTTT-MM 26 100 87 ...<BR><BR>You were right that this would do pretty well by SCWE, but your guess<BR>for strategy was ---TTTT (which is actually a quite rare outcome under<BR>any method).<BR><BR>"MCARP"
97 87<BR>TTTTMM- 71 100 84<BR>BBB-MMM 70 100 87<BR>***MCCC 62 94 95 (*=M+P+B, i.e. "A=C>B")<BR>TTTTM-M 48 100 89<BR>TTTTMMM 32 100 88<BR>TTB-MMM 32 100 88<BR>BBT-MMM 30 100 87<BR>TTTT-MM 29 100 85<BR>BTB-MMM 28 100 87<BR>TBB-MMM 24 100 87 ...<BR><BR>This was a little higher by SCWE but your MMMTTTT guess never occurred<BR>once in any (recorded) result for any method!<BR></DIV>
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<DIV class=yiv1215623519gmail_quote>After some thought, I understand why my guesses were wrong. I was thinking that truncation was a strategy for near-clones, emphasis on near, whereas actually it's a strategy for competitive near-clones, emphasis on competitive. So even though A and B are farther apart than B and C, the voters are treating A and B as the "competitive near clones" because C is an also-ran with the methods I care about.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV></BLOCKQUOTE>
<DIV class=yiv1215623519gmail_quote>Interesting description.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
<DIV class=yiv1215623519gmail_quote>I also ran some sets of non-spectrum-based scenarios with different numbers of blocs.</DIV>
<DIV class=yiv1215623519gmail_quote>MCARA and MCARP rank consistently very notably with high sincere Condorcet </DIV>
<DIV class=yiv1215623519gmail_quote>efficiency (both were always top 4), high rate of compression (usually top two, but</DIV>
<DIV class=yiv1215623519gmail_quote>Approval grabbed #2 with 8 blocs), and relatively very high rate of "pushover."</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
<DIV class=yiv1215623519gmail_quote>On the latter point, nothing can touch Antiplurality (13-17%). MCARA and MCARP</DIV>
<DIV class=yiv1215623519gmail_quote>were between 4-6% of voters. Several methods hit 1-2% at least once, including</DIV>
<DIV class=yiv1215623519gmail_quote>ER-IRV(whole). And there is no contest between ER-IRV(whole) and ER-IRV(fractional).</DIV>
<DIV class=yiv1215623519gmail_quote>So maybe there is something to Chris' pushover warning.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
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<DIV class=yiv1215623519gmail_quote><BR>So, ER didn't make IRV any better but it did reduce the amount of<BR>compromise. Chris had an idea, I believe, that ER-IRV(whole) was<BR>susceptible to a straightforward push-over strategy, but I'm not sure<BR>I see that here unless some Ms or Cs are playing that role. Since the<BR>C voters are very frequently using that strategy (in many methods) I'm<BR>doubtful...<BR><BR>Also, you can note here that the IRV methods did better wrt utility<BR>maximizers than the other methods in this post. You can see (by scanning<BR>for high values) that this is expected when C is losing his win odds<BR>due to the voting patterns, and B is winning when sincere Condorcet says<BR>it should be C.<BR></DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
<DIV class=yiv1215623519gmail_quote dir=ltr>In other words, what's happening is that voters are pre-emptively compromising for "insurance" against an unreliable system, and that ends up electing a centrist, utility-maximizing candidate even when it turns out that the compromisers' sincere favorite could have been the CW.</DIV>
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<DIV class=yiv1215623519gmail_quote>That description is accurate for a lot of situations. But I want to note that I had to</DIV>
<DIV class=yiv1215623519gmail_quote>take back this observation for this instance due to my (subsequent) post on utility</DIV>
<DIV class=yiv1215623519gmail_quote>normalization. I think it was counter-intuitive and not informative to normalize sincere</DIV>
<DIV class=yiv1215623519gmail_quote>utilities when the scenario is based on a spectrum. I'm not actually sure what the</DIV>
<DIV class=yiv1215623519gmail_quote>utility situation is for each candidate, but it doesn't particularly favor or disfavor the</DIV>
<DIV class=yiv1215623519gmail_quote>IRV outcome, relative to MCA for instance.</DIV>
<DIV class=yiv1215623519gmail_quote> </DIV>
<DIV class=yiv1215623519gmail_quote>Kevin</DIV></td></tr></table><br>