Roger wrote:
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: If you are correct here, then why doesn’t it upend small sample theory? Sample variance = population variance / sample size? Nick Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University <mailto:[email protected]> [email protected] <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: Friam <[email protected]> On Behalf Of Roger Critchlow Sent: Thursday, October 29, 2020 9:33 AM To: The Friday Morning Applied Complexity Coffee Group <[email protected]> Subject: Re: [FRIAM] high turnout and tight races? You're right, assuming that either vote is equally likely: julia> for n in [10000, 100000, 1000000] # run 1000 simulations close = 0 for x in 1:1000 # collect votes v = rand(Int(n)) n1 = count(v .< 0.5) n2 = n-n1 if (n1-n2)/n < 0.01 close += 1 end end p = close/1000 println("pop $n has p(close) $p"); end pop 10000 has p(close) 0.841 pop 100000 has p(close) 0.999 pop 1000000 has p(close) 1.0 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: bias = 0.51 for n in [10000, 100000, 1000000] # run 1000 simulations close = 0 for x in 1:1000 # collect votes v = rand(Int(n)) n1 = count(v .< bias) n2 = n-n1 if (n1-n2)/n < 0.01 close += 1 end end p = close/1000 println("pop $n has p(close) $p"); end pop 10000 has p(close) 0.166 pop 100000 has p(close) 0.001 pop 1000000 has p(close) 0.0 -- rec -- On Wed, Oct 28, 2020 at 10:46 PM <[email protected] <mailto:[email protected]> > wrote: HANG ON, Roger Variance decreases with N. Nicholas Thompson Emeritus Professor of Ethology and Psychology Clark University <mailto:[email protected]> [email protected] <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: Friam <[email protected] <mailto:[email protected]> > On Behalf Of Roger Critchlow Sent: Wednesday, October 28, 2020 7:16 PM To: The Friday Morning Applied Complexity Coffee Group <[email protected] <mailto:[email protected]> > Subject: Re: [FRIAM] high turnout and tight races? 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. -- rec -- On Wed, Oct 28, 2020 at 8:17 PM Frank Wimberly <[email protected] <mailto:[email protected]> > wrote: N = 3 is slightly better. But I don't have time or incentive to do a detailed statistical analysis. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Wed, Oct 28, 2020, 6:14 PM Frank Wimberly <[email protected] <mailto:[email protected]> > wrote: 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. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Wed, Oct 28, 2020, 6:00 PM Frank Wimberly <[email protected] <mailto:[email protected]> > wrote: I'm saying that in this election there will be high turnout and not a very close election. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Wed, Oct 28, 2020, 5:59 PM uǝlƃ ↙↙↙ <[email protected] <mailto:[email protected]> > wrote: So, what about the question I asked? You have no opinion on whether high turnout negatively or positively correlates with narrow victories? On 10/28/20 4:52 PM, Frank Wimberly wrote: > 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. > > The good thing about predictions is that they can be evaluated perfectly > after the events have happened. > > Frank > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Wed, Oct 28, 2020, 5:20 PM uǝlƃ ↙↙↙ <[email protected] > <mailto:[email protected]> <mailto:[email protected] > <mailto:[email protected]> >> wrote: > > From: > > https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7 > <https://www.electoral-vote.com/evp2020/Pres/Maps/Oct28.html#item-7> > "6. High turnout makes razor-thin victories, like the ones Trump notched > in Michigan, Wisconsin, and Pennsylvania in 2016, much less likely." > > 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. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam <http://bit.ly/virtualfriam> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ <http://friam.471366.n2.nabble.com/FRIAM-COMIC> FRIAM-COMIC http://friam-comic.blogspot.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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