One other bad mistake I noticed on <a href="http://scorevoting.net/MedianVrange.html">http://scorevoting.net/MedianVrange.html</a>: <div>"<span class="Apple-style-span" style="font-family: Arial, sans-serif; font-size: medium; ">Suppose this <b>"unhappy with all choices" scenario</b> happens. When it does, every candidate's median score will be exactly zero. (In contrast: Their <i>average</i> scores will generally be distinct nonzero values, and everything will be fine.) Hence Balinski & Laraki's tiebreaking procedure will be invoked. It will elect the candidate with the fewest 0s, which is exactly <a href="http://scorevoting.net/Glossary.html#antipl">antiPlurality</a> voting."</span></div>
<div><font class="Apple-style-span" face="Arial, sans-serif" size="3"><br></font></div><div><font class="Apple-style-span" face="Arial, sans-serif" size="3">This is not antiplurality voting, it's just approval voting, with any non-zero value representing approval, and the additional assumption that no candidate has a majority of approval. It's a bad situation, with voters who overall dislike all candidates, but it's not the worst voting system to handle the situation.</font></div>
<div><font class="Apple-style-span" face="Arial, sans-serif" size="3"><br></font></div><div><font class="Apple-style-span" face="Arial, sans-serif" size="3">JQ</font></div><div><div><br><div class="gmail_quote">2011/10/12 Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</a>></span><br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><br><br><div class="gmail_quote"><div class="im">2011/10/12 Clay Shentrup <span dir="ltr"><<a href="mailto:clay@electology.org" target="_blank">clay@electology.org</a>></span><br>
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<div>On Wednesday, October 12, 2011 11:16:52 AM UTC-7, Jameson Quinn wrote:<blockquote class="gmail_quote" style="margin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="gmail_quote">
<div>Warren and I had a long technical discussion about strategy incentive in MJ versus range. He did some clever calculations, and I picked holes in them, and we repeated it for several rounds. At the end we hadn't quite completely converged on a consensus, but we both agreed that Range had a greater strategy incentive than MJ. That result seems more robust than a bald assertion from you.</div>
</div></blockquote><div><br></div></div><div>I <i>think</i> you're confused. I presume that what you were talking about was how often strategy makes a difference, or how much of a difference it makes on average. I <i>don't</i> believe this changes the ideal strategy one iota. You give any candidate you like better than the expected value a max score, and others a min score.</div>
<div><br></div><div>This should be <i>reeeally</i> obvious. If you think X=7, Y=3, and the scores are X={9, 7, 0}, Y={8, 8, 3}, then you vote X=10, Y=0. Now the scores are X={10, 9, 0}, Y={8, 8, 0}. X wins. I.e. you just polarize, so that you may get lucky enough to have your otherwise median score move the median up or down.</div>
</blockquote><div><br></div></div><div>This is true. But as the argued below, you can be essentially arbitrarily certain of getting the same result, if you vote outside a certain band. For instance, X=9, Y=1 would get you 99% certainty, and X=8, Y=2 would get you 90% certainty, and your honest X=7 Y=3 would get you 70% certainty. (These are arbitrary numbers; in real life, they'd be based on historical scores of the top two candidates) </div>
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<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div> </div><blockquote class="gmail_quote" style="margin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>The point is, even with zero information on a particular candidate, you have a pretty good historical benchmark for the median scores of the first and second place candidates. Outside of that range, you have a safe leeway to be honest.</div>
</div></blockquote><div><br></div></div><div>This is a flawed argument. You're saying it's very improbable that the scores will exceed those historical norms, so you should take the tiny risk of casting a weak vote, for the sake of honesty/expressiveness. But with ordinary Score Voting, there's an incredibly tiny probability that your vote will make a difference, so you might as well be honest. This is statistically equivalent.</div>
</blockquote><div><br></div></div><div>Not comparable at all. In any voting system at all, your chances of being decisive are epsilon. In this case, your chances of even having any impact at all on the margin of victory are epsilon. The chance of that impact then being decisive are epsilon squared. Separate issues.</div>
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<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div> </div><blockquote class="gmail_quote" style="margin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div>And it seems that MJ reacts much worse to such plausible behaviors.<br></div></blockquote>
<div><br></div><div>??? What are you even talking about? If everyone exaggerates, MJ and range are identical; they're both approval. And if a fixed X% of voters exaggerate, it has a bigger effect on Range than MJ; that's an implication Warren's result that I mentioned above. So you're 180 degrees wrong here.</div>
</div></blockquote><div><br></div></div><div>If most (but not all) exaggerate, then you can get very weird results like Warren describes here.</div><div><a href="http://scorevoting.net/MedianVrange.html" target="_blank">http://scorevoting.net/MedianVrange.html</a></div>
</blockquote><div><br></div></div><div>Are you talking about the bimodal distribution stuff at the bottom? That's an issue when one candidate is exaggerated but others aren't. But if some voters exaggerate across the board, it is at worst as bad as approval. It degrades to approval less smoothly than range - that is, the effect of exaggeration is smaller if few people exaggerate, and larger if many people exaggerate. I believe that that's superior, because it makes all-honest-voting into a more stable state (actually an equilibrium under certain plausible assumptions, but even if not an equilibrium, still more stable than Range).</div>
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<div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><br></div><div><br></div><div>I speculate that you may be misunderstanding Warren's result. But it would be nice to see Warren's result instead of speculating. Could someone post it here or add it to the page?</div>
</blockquote><div><br></div></div><div><a href="http://scorevoting.net/MedianAvg1side.html" target="_blank">http://scorevoting.net/MedianAvg1side.html</a> </div><div class="im"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><br></div><div>Oh, and aside from calculations of how often strategies work and such, did Warren ever get actual BR figures for MJ?</div></blockquote><div><br></div></div><div>I don't know.</div><div><br></div><font color="#888888"><div>
JQ </div>
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