<div><br><br><div class="gmail_quote">2011/9/14 Toby Pereira <span dir="ltr"><<a href="mailto:tdp201b@yahoo.co.uk">tdp201b@yahoo.co.uk</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div><div style="color:#000;background-color:#fff;font-family:times new roman, new york, times, serif;font-size:12pt"><div><span>From what I understand it's independent of Smith-dominated alternatives. So ranking the Smith Set should be sufficient.<var></var><br>
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<div><br></div></div></div></blockquote>Really? Then it's computable. Warren, are you really going to say that you're objecting because of the possibility of a 50-candidate - or for that matter a 28-candidate - Smith set?<div>
<br></div><div>JQ </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div><div style="color:#000;background-color:#fff;font-family:times new roman, new york, times, serif;font-size:12pt">
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</div><b><span style="font-weight:bold">From:</span></b> Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>><br><b><span style="font-weight:bold">To:</span></b> <a href="mailto:ElectionMethods@votefair.org" target="_blank">ElectionMethods@votefair.org</a><br>
<b><span style="font-weight:bold">Cc:</span></b> <a href="mailto:election-methods@electorama.com" target="_blank">election-methods@electorama.com</a><br><b><span style="font-weight:bold">Sent:</span></b> Wednesday, 14 September 2011, 18:21<br>
<b><span style="font-weight:bold">Subject:</span></b> Re: [EM] Kemeny challenge<br></font><div><div></div><div class="h5"><br>
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<div>2011/9/14 Richard Fobes <span dir="ltr"><<a href="mailto:ElectionMethods@votefair.org" rel="nofollow" target="_blank">ElectionMethods@votefair.org</a>></span><br>
<blockquote style="border-left:#ccc 1px solid;margin:0px 0px 0px 0.8ex;padding-left:1ex">Large pairwise-count numbers do not increase the likelihood of a longer computation time. They just test the processor's integer limit, or the language-specified integer limit, or the efficiency of big-integer algorithms.<br>
<br>Based on lots and lots of calculations using lots and lots of real data, I've learned that just a few ballots (which corresponds to small pairwise-count numbers) are more likely to increase the computation time. This makes sense when you stop and think about it.<br>
<br>If you come up with a ballot-based version of this challenge (rather than this pairwise-count version), I'd like to try it out.<br><br>Regardless of the results, remember that real elections only require identifying the winner, whereas here we are discussing the computation time for producing a full ranking.<br>
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<div>Is there any way to prove that X is the winner, if they aren't the CW and you don't have the full ranking?</div>
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<div>JQ </div>
<blockquote style="border-left:#ccc 1px solid;margin:0px 0px 0px 0.8ex;padding-left:1ex"><br>Richard Fobes
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<div><br><br><br>On 9/12/2011 12:00 PM, Warren Smith wrote:<br>
<blockquote style="border-left:#ccc 1px solid;margin:0px 0px 0px 0.8ex;padding-left:1ex">KEMENY CHALLENGE<br>=================<br><br>Here is an attempt by me to intentionally create small elections for<br>which it is difficult to determine the Kemeny winner.<br>
<br>Consider this pairwise matrix:<br> <a href="http://www.rangevoting.org/Tourn27.html" rel="nofollow" target="_blank">http://www.RangeVoting.org/<u></u>Tourn27.html</a><br>and replace all the +1s by random numbers in the interval<br>
[A, B]<br>and all the -1s by ditto but negated, to get the pairwise margins matrix<br>for a 27-candidate election.<br>Here B>A>0 are two parameters chosen by the Devil to try to cause<br>these problems to be hardest [I'd originally suggested A=9million<br>
B=10million, but maybe some other choice like A=0 and B=10billion<br>would tend to make it harder]. Also of course randomly permute the
27<br>candidate-names in a way unknown to the solver, before giving the<br>problem to the solver [equivalently permute both the rows and columns<br>of the 27x27 matrix by one random permutation].<br><br>THE CHALLENGE: Find the Kemeny winner or order... can anybody do<br>
either reliably for 27-candidate elections of this class, or is this<br>usually beyond humankind's abilities?<br><br><br><br></blockquote><br><br></div></div>----<br>Election-Methods mailing list - see <a href="http://electorama.com/em" rel="nofollow" target="_blank">http://electorama.com/em</a> for list info<br>
</blockquote></div><br></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></div></div></div></blockquote>
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