[EL] McDonald study, birthdate distribution in real voter list

[Justin Levitt]

Last point (from me) on this: the easiest approach is actually the 
inverse of the question Adam has raised.  To get the total frequency of 
duplications, you need not the odds of _a_ pair of people, but the odds 
of _any_ pair of people.  And the easiest way to come at the problem is 
-- as we did in the article -- to ask what the odds are that NO pair of 
people in the pool duplicates both a birthdate and a name.

And yes, as you can see in the charts in our article, the expected 
number of matches rises exponentially with the size of the relevant pool.


On 9/11/2011 11:51 AM, Adam Morse wrote:
> Isn't the question actually "given a distribution of names and a 
> distribution of birthdates, what are the odds of a pair of people 
> duplicating both a birthdate and a name?"  We don't care in advance 
> whether it's Robert Smith that has a false duplicate or Jane Smith, 
> but we care what the total frequency of duplications of both name and 
> birthdate is across all names.  That's not quite the same as the way 
> you're phrasing it.
>
> Also, intuitively this will be sensitive to the total size of the pool 
> and to the distribution of names within the pool, and the distribution 
> of names over time, which also won't be the same--Aedan is a much more 
> common name now than it was 20 years ago, when it was much more common 
> than 40 years ago.  Changing ethnic distributions will produce similar 
> effects among surnames.  But leaving aside the change over time, I 
> wonder how much of the difference between what Bev is seeing and what 
> Michael and Justin calculated depends on the size of the pool--when 
> you care about the total number of multiple chance hits, the 
> difference between 600,000 voters and 2.5 million voters is vastly 
> more than the simple ratio of 4:1.
>
> --Adam Morse
>
> On Sun, Sep 11, 2011 at 2:39 PM, Bev Harris <bev at blackboxvoting.org 
> <mailto:bev at blackboxvoting.org>> wrote:
>
>     Forgive me if I'm wrong, but isn't the question whether a specific
>     person,
>     Robert Smith, has the same birthdate as a different Robert Smith?
>     The question
>     is not whether any two people in a pool share a birthday.
>
>     The number of shared birthdays among all people on the list works
>     out to about
>     1:10,000 (in a large list), which can readily be seen just by
>     counting the
>     shared birthdates on the list. (On a small list, the presence of
>     twins will
>     provide an extra sprinkle of same birthdates)
>
>     The chances that one specific individual shares the same birthdate
>     as another
>     specific individual is the question. The rest of the people in the
>     room really
>     don't matter.
>
>     > Put differently, the question isn't whether two people on a list
>     share a
>     > single date of birth, but whether _no_ two people in a large
>     pool share
>     > a birthday.
>
>
>     Bev Harris
>     Founder - Black Box Voting
>     http://www.blackboxvoting.org
>
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-- 
Justin Levitt
Associate Professor of Law
Loyola Law School | Los Angeles
919 Albany St.
Los Angeles, CA  90015
213-736-7417
justin.levitt at lls.edu
ssrn.com/author=698321

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