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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>Roger wrote:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=quotation>However, if there is the tiniest tendency toward voting one way or the other, then the probability of a close result dwindles with the turnout:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>If you are correct here, then why doesn\u2019t it upend small sample theory? Sample variance = population variance / sample size? <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nick <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal>Clark University<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Roger Critchlow<br><b>Sent:</b> Thursday, October 29, 2020 9:33 AM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> Re: [FRIAM] high turnout and tight races?<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>You're right, assuming that either vote is equally likely:<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>julia> for n in [10000, 100000, 1000000]<br> # run 1000 simulations<br> close = 0<br> for x in 1:1000<br> # collect votes<br> v = rand(Int(n))<br> n1 = count(v .< 0.5)<br> n2 = n-n1<br> if (n1-n2)/n < 0.01<br> close += 1<br> end<br> end<br> p = close/1000<br> println("pop $n has p(close) $p");<br>end<br>pop 10000 has p(close) 0.841<br>pop 100000 has p(close) 0.999<br>pop 1000000 has p(close) 1.0<o:p></o:p></p></div></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>However, if there is the tiniest tendency toward voting one way or the other, then the probability of a close result dwindles with the turnout:<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>bias = 0.51<br>for n in [10000, 100000, 1000000]<br> # run 1000 simulations<br> close = 0<br> for x in 1:1000<br> # collect votes<br> v = rand(Int(n))<br> n1 = count(v .< bias)<br> n2 = n-n1<br> if (n1-n2)/n < 0.01<br> close += 1<br> end<br> end<br> p = close/1000<br> println("pop $n has p(close) $p");<br>end<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> pop 10000 has p(close) 0.166<br>pop 100000 has p(close) 0.001<br>pop 1000000 has p(close) 0.0<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>-- rec --<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Wed, Oct 28, 2020 at 10:46 PM <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>HANG ON, Roger<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Variance decreases with N.<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Nicholas Thompson<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Emeritus Professor of Ethology and Psychology<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Clark University<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="mailto:ThompNickSon2@gmail.com" target="_blank"><span style='color:#0563C1'>ThompNickSon2@gmail.com</span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><a href="https://wordpress.clarku.edu/nthompson/" target="_blank"><span style='color:#0563C1'>https://wordpress.clarku.edu/nthompson/</span></a><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>From:</b> Friam <<a href="mailto:friam-bounces@redfish.com" target="_blank">friam-bounces@redfish.com</a>> <b>On Behalf Of </b>Roger Critchlow<br><b>Sent:</b> Wednesday, October 28, 2020 7:16 PM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <<a href="mailto:friam@redfish.com" target="_blank">friam@redfish.com</a>><br><b>Subject:</b> Re: [FRIAM] high turnout and tight races?<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I would think that the more people who vote the less likely a tie or close outcome becomes, simply by the larger number of ways you can miss with more votes in play.<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>-- rec --<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Wed, Oct 28, 2020 at 8:17 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" target="_blank">wimberly3@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>N = 3 is slightly better. But I don't have time or incentive to do a detailed statistical analysis. <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM<o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Wed, Oct 28, 2020, 6:14 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" target="_blank">wimberly3@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>In 1964 Johnson beat Goldwater by 60 to 40. The Kennedy/Nixon and Gore/Bush elections were extremely close. In all three elections the turnout was between 35 and 40 percent.<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM<o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Wed, Oct 28, 2020, 6:00 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" target="_blank">wimberly3@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'>I'm saying that in this election there will be high turnout and not a very close election.<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM<o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Wed, Oct 28, 2020, 5:59 PM u\u01ddl\u0183 \u2199\u2199\u2199 <<a href="mailto:gepropella@gmail.com" target="_blank">gepropella@gmail.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>So, what about the question I asked? You have no opinion on whether high turnout negatively or positively correlates with narrow victories?<br><br><br>On 10/28/20 4:52 PM, Frank Wimberly wrote:<br>> I predict that Biden will win by a large margin and that the outcome will be clear on election night notwithstanding any outstanding uncounted votes. Young people are voting in unprecedented numbers and are reportedly voting against Trump. Similarly the elderly, who favored Trump over Clinton by 10+ percentage points in 2016 are favoring Biden over Trump by a similar margin, according to polls.<br>> <br>> The good thing about predictions is that they can be evaluated perfectly after the events have happened.<br>> <br>> Frank<br>> <br>> ---<br>> Frank C. Wimberly<br>> 140 Calle Ojo Feliz,<br>> Santa Fe, NM 87505<br>> <br>> 505 670-9918<br>> Santa Fe, NM<br>> <br>> On Wed, Oct 28, 2020, 5:20 PM u\u01ddl\u0183 \u2199\u2199\u2199 <<a href="mailto:gepropella@gmail.com" target="_blank">gepropella@gmail.com</a> <mailto:<a href="mailto:gepropella@gmail.com" target="_blank">gepropella@gmail.com</a>>> wrote:<br>> <br>> From:<br>> <br>> <a href="https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7" target="_blank">https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7</a> <<a href="https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7" target="_blank">https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7</a>><br>> "6. High turnout makes razor-thin victories, like the ones Trump notched in Michigan, Wisconsin, and Pennsylvania in 2016, much less likely."<br>> <br>> Is that true? I've always heard that tight races lead to higher turnout, which would imply that high turnout would correlate WITH thin victories, not against them.<br><br>-- <br>\u2199\u2199\u2199 u\u01ddl\u0183<br><br>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/FRIAM-COMIC" target="_blank">http://friam.471366.n2.nabble.com/<br>FRIAM-COMIC</a> <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div></blockquote></div></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div></div></div><p class=MsoNormal>- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br>FRIAM Applied Complexity Group listserv<br>Zoom Fridays 9:30a-12p Mtn GMT-6 <a href="http://bit.ly/virtualfriam" target="_blank">bit.ly/virtualfriam</a><br>un/subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>archives: <a href="http://friam.471366.n2.nabble.com/" target="_blank">http://friam.471366.n2.nabble.com/</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a> <o:p></o:p></p></blockquote></div></div></body></html>