[FRIAM] high turnout and tight races?

Thu Oct 29 12:55:08 EDT 2020

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:ThompNickSon2 at gmail.com> ThompNickSon2 at gmail.com

 <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/

From: Friam <friam-bounces at redfish.com> On Behalf Of Roger Critchlow
Sent: Thursday, October 29, 2020 9:33 AM
To: The Friday Morning Applied Complexity Coffee Group <friam at redfish.com>
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 <thompnickson2 at gmail.com <mailto:thompnickson2 at gmail.com> > wrote:

HANG ON, Roger

Variance decreases with N.

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

 <mailto:ThompNickSon2 at gmail.com> ThompNickSon2 at gmail.com

 <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/

From: Friam <friam-bounces at redfish.com <mailto:friam-bounces at redfish.com> > On Behalf Of Roger Critchlow
Sent: Wednesday, October 28, 2020 7:16 PM
To: The Friday Morning Applied Complexity Coffee Group <friam at redfish.com <mailto:friam at redfish.com> >
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 <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com> > 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 <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com> > 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 <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com> > 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 ↙↙↙ <gepropella at gmail.com <mailto:gepropella at gmail.com> > 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 ↙↙↙ <gepropella at gmail.com <mailto:gepropella at gmail.com>  <mailto:gepropella at gmail.com <mailto:gepropella at gmail.com> >> 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

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