<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Sun, Dec 15, 2013 at 5:55 AM, Jameson Quinn <span dir="ltr"><<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div dir="ltr">Just eyeballing the pictures, it seems that the radii are very conservative. If you doubled them, it would be 4 times as fast.</div>
</blockquote><div><br></div><span style="font-family:arial,sans-serif;font-size:13.333333969116211px">Yes, that makes sense.</span><br style="font-family:arial,sans-serif;font-size:13.333333969116211px"><span style="font-family:arial,sans-serif;font-size:13.333333969116211px"> </span><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div dir="ltr"> I realize you want to stay on solid ground mathematically, but given how conservative things look, I think you probably could. Can you build the Hessian matrix of the tightest decisive vote margin? If so, would taking things to second order allow a less-conservative first-order approximation? (Just wild ideas, I'm not sure what I'm saying even makes sense.)</div>
</blockquote><div><br></div><div style="font-family:arial,sans-serif;font-size:13.333333969116211px">I don't know what that means, but I'm pretty rusty on my maths. However I do agree that there probably is some reasonably efficient way to loosen the (very conservative) radius bound, as it's not taking into account the information about which way voters are shifting, and whether or not its relevant to the front runner. But it's probably not worth expending a great deal of computational power eking out every last bit of radius, if a good conservative approximation is much faster.</div>
<div style="font-family:arial,sans-serif;font-size:13.333333969116211px"><br></div><div style="font-family:arial,sans-serif;font-size:13.333333969116211px">I should mention that this solution really was all Claude, I posed a problem, we discussed it, and he ran with it and 5-ish hours later had this, and then he explained what he'd done. (Nerd sniping for the win? Although his technique did inspire another alternative algorithm I'd like to play with myself... one that more easily generalizes from plurality voting to any ranked voting method.)</div>
<div style="font-family:arial,sans-serif;font-size:13.333333969116211px"><br></div><div style="font-family:arial,sans-serif;font-size:13.333333969116211px">Really it doesn't seem to be that much faster than what already exists, but there should be plenty of room for improvement (on both the naive and this more sophisticated approach.) However this does seem create much higher-resolution images (while still being accurate) with a similar amount of computing resources.</div>
<div style="font-family:arial,sans-serif;font-size:13.333333969116211px"><br></div><div style="font-family:arial,sans-serif;font-size:13.333333969116211px">Best,<br></div><div><span style="font-family:arial,sans-serif;font-size:13.333333969116211px">Leon</span></div>
<div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_extra"><br><div class="gmail_quote">
2013/12/11 Leon Smith <span dir="ltr"><<a href="mailto:leon.p.smith@gmail.com" target="_blank">leon.p.smith@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
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<div dir="ltr">Here's the result of a conversation I had with <span style="white-space:pre-wrap">Claude Heiland-Allen today about faster algorithms for generating Yee Diagrams.</span><div><br></div><div>
<a href="http://mathr.co.uk/blog/2013-12-11_distance_estimation_for_voting_simulation_visualisation.html" target="_blank">http://mathr.co.uk/blog/2013-12-11_distance_estimation_for_voting_simulation_visualisation.html</a><br>
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</div><div>I haven't run any timing tests yet, so it's not clear if this is faster as-is or not. And there is probably substantial room for further improvement... e.g. in selecting starting points more intelligently.</div>
<div><br></div><div>Also, the obvious generalization of this algorithm to ranked methods would also slow it down a bit. But I thought it might be of interest to some people here on this list.<br><br>Best,</div><div>Leon</div>
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