<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">For an ordinary sum of values, as described by the central limit theorem with finite variance, variance increases linearly with N.<div class=""><br class=""></div><div class="">It is relative variance \u2014 variance normalized by the square of the mean \u2014 that decreases with N as 1/N.</div><div class=""><br class=""></div><div class="">Eric</div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Oct 28, 2020, at 10:46 PM, <<a href="mailto:thompnickson2@gmail.com" class="">thompnickson2@gmail.com</a>> <<a href="mailto:thompnickson2@gmail.com" class="">thompnickson2@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">HANG ON, Roger<o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Variance decreases with N.<o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Nicholas Thompson<o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Emeritus Professor of Ethology and Psychology<o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Clark University<o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><a href="mailto:ThompNickSon2@gmail.com" style="color: blue; text-decoration: underline;" class=""><span style="color: rgb(5, 99, 193);" class="">ThompNickSon2@gmail.com</span></a><o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f&c=E,1,JpIZN4i-yJIZ3nSFKQVodYv2Ly1HWZoKAqszi3I-n6LurxDMqTHolpMDI76QMgxqfRW4JWJNyrNPap9LQzH1zbNsfyYEnHD3o3kqMNyV5ClOewKj&typo=1" style="color: blue; text-decoration: underline;" class=""><span style="color: rgb(5, 99, 193);" class="">https://wordpress.clarku.edu/nthompson/</span></a><o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""></o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(225, 225, 225); padding: 3pt 0in 0in;" class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class="">From:</b><span class="Apple-converted-space"> </span>Friam <<a href="mailto:friam-bounces@redfish.com" style="color: blue; text-decoration: underline;" class="">friam-bounces@redfish.com</a>><span class="Apple-converted-space"> </span><b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Roger Critchlow<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Wednesday, October 28, 2020 7:16 PM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>The Friday Morning Applied Complexity Coffee Group <<a href="mailto:friam@redfish.com" style="color: blue; text-decoration: underline;" class="">friam@redfish.com</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [FRIAM] high turnout and tight races?<o:p class=""></o:p></div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">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 class=""></o:p></div><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">-- rec --<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On Wed, Oct 28, 2020 at 8:17 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" style="color: blue; text-decoration: underline;" class="">wimberly3@gmail.com</a>> wrote:<o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0in 0in 0in 6pt; margin-left: 4.8pt; margin-right: 0in;" class="" type="cite"><div class=""><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 11pt; font-family: Calibri, sans-serif;">N = 3 is slightly better. But I don't have time or incentive to do a detailed statistical analysis. <o:p class=""></o:p></p><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">---<br class="">Frank C. Wimberly<br class="">140 Calle Ojo Feliz,<span class="Apple-converted-space"> </span><br class="">Santa Fe, NM 87505<br class=""><br class="">505 670-9918<br class="">Santa Fe, NM<o:p class=""></o:p></div></div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On Wed, Oct 28, 2020, 6:14 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" target="_blank" style="color: blue; text-decoration: underline;" class="">wimberly3@gmail.com</a>> wrote:<o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0in 0in 0in 6pt; margin-left: 4.8pt; margin-right: 0in;" class="" type="cite"><div class=""><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 11pt; font-family: Calibri, sans-serif;">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 class=""></o:p></p><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">---<br class="">Frank C. Wimberly<br class="">140 Calle Ojo Feliz,<span class="Apple-converted-space"> </span><br class="">Santa Fe, NM 87505<br class=""><br class="">505 670-9918<br class="">Santa Fe, NM<o:p class=""></o:p></div></div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On Wed, Oct 28, 2020, 6:00 PM Frank Wimberly <<a href="mailto:wimberly3@gmail.com" target="_blank" style="color: blue; text-decoration: underline;" class="">wimberly3@gmail.com</a>> wrote:<o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0in 0in 0in 6pt; margin-left: 4.8pt; margin-right: 0in;" class="" type="cite"><div class=""><p class="MsoNormal" style="margin: 0in 0in 12pt; font-size: 11pt; font-family: Calibri, sans-serif;">I'm saying that in this election there will be high turnout and not a very close election.<o:p class=""></o:p></p><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">---<br class="">Frank C. Wimberly<br class="">140 Calle Ojo Feliz,<span class="Apple-converted-space"> </span><br class="">Santa Fe, NM 87505<br class=""><br class="">505 670-9918<br class="">Santa Fe, NM<o:p class=""></o:p></div></div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div class=""><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On Wed, Oct 28, 2020, 5:59 PM u\u01ddl\u0183 \u2199\u2199\u2199 <<a href="mailto:gepropella@gmail.com" target="_blank" style="color: blue; text-decoration: underline;" class="">gepropella@gmail.com</a>> wrote:<o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-width: 1pt; border-left-color: rgb(204, 204, 204); padding: 0in 0in 0in 6pt; margin-left: 4.8pt; margin-right: 0in;" class="" type="cite"><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">So, what about the question I asked? You have no opinion on whether high turnout negatively or positively correlates with narrow victories?<br class=""><br class=""><br class="">On 10/28/20 4:52 PM, Frank Wimberly wrote:<br class="">> 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 class="">><span class="Apple-converted-space"> </span><br class="">> The good thing about predictions is that they can be evaluated perfectly after the events have happened.<br class="">><span class="Apple-converted-space"> </span><br class="">> Frank<br class="">><span class="Apple-converted-space"> </span><br class="">> ---<br class="">> Frank C. Wimberly<br class="">> 140 Calle Ojo Feliz,<br class="">> Santa Fe, NM 87505<br class="">><span class="Apple-converted-space"> </span><br class="">> 505 670-9918<br class="">> Santa Fe, NM<br class="">><span class="Apple-converted-space"> </span><br class="">> On Wed, Oct 28, 2020, 5:20 PM u\u01ddl\u0183 \u2199\u2199\u2199 <<a href="mailto:gepropella@gmail.com" target="_blank" style="color: blue; text-decoration: underline;" class="">gepropella@gmail.com</a><span class="Apple-converted-space"> </span><mailto:<a href="mailto:gepropella@gmail.com" target="_blank" style="color: blue; text-decoration: underline;" class="">gepropella@gmail.com</a>>> wrote:<br class="">><span class="Apple-converted-space"> </span><br class="">> From:<br class="">><span class="Apple-converted-space"> </span><br class="">> <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.electoral-vote.com%2fevp2020%2fPres%2fMaps%2fOct28.html%23item-7&c=E,1,3R5-SLwhyeJQbthWDBlxAt16YrH15rD0P_-VBW59uGNp9HZJJE3AT5JAzdreT8oFrKqT1lWi-JNLZ-doFp0UZ0KNVVTZ_7gV8hSceUx81MbMtuDvaYx4pjLsGQ,,&typo=1" target="_blank" style="color: blue; text-decoration: underline;" class="">https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7</a><span class="Apple-converted-space"> </span><<a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.electoral-vote.com%2fevp2020%2fPres%2fMaps%2fOct28.html%23item-7&c=E,1,bXYSsq70zdX7RpHGBMmz8GczNqObKoxd3aoM-giya3dZ_Qbzmb5ka_WQ0is5kHTuA76TFPDK_jWeVMoFv0zCGre-WYf2dJ2nmd1rQtPMdK7mzaLLCfcwpEHzGxOb&typo=1" target="_blank" style="color: blue; text-decoration: underline;" class="">https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7</a>><br class="">> "6. High turnout makes razor-thin victories, like the ones Trump notched in Michigan, Wisconsin, and Pennsylvania in 2016, much less likely."<br class="">><span class="Apple-converted-space"> </span><br class="">> 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 class=""><br class="">--<span class="Apple-converted-space"> </span><br class="">\u2199\u2199\u2199 u\u01ddl\u0183<br class=""><br class="">- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .<br class="">FRIAM Applied Complexity Group listserv<br class="">Zoom Fridays 9:30a-12p Mtn GMT-6 <span class="Apple-converted-space"> </span><a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,Wxafx_7WIJ4cbe6kG4vPFgG-t2jmxEB6dHPaV6Pvm3U_JgbnIKM24dWPGFstj7TkhMYdO29j5_xX1TYa1ep-2h9RXJt1vuY0d38oW7ODl-ZzzYXvOMQhUdk12JUv&typo=1" target="_blank" style="color: blue; text-decoration: underline;" class="">bit.ly/virtualfriam</a><br class="">un/subscribe<span class="Apple-converted-space"> </span><a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,Z9AfwH6YQqwwbAdgX4_VgANFcMou21nCiq71srt6HjYuND_0R5QEzcsxOjc6kxJnjEo5ymGhj81VL60H7Mrj15ukEAxrfZVA-VnYAzOw6LBr8ps9j32qpWY,&typo=1" target="_blank" style="color: blue; 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