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

[Michael McDonald]

This is the surprising counter-intuitive result the Birthday Problem
reveals. You have to test each Robert Smith against all other Robert Smiths
to properly calculate the probabilities. Once you have one Robert Smith
without a match, his birth date is taken up, so you have to remove that
birth date from the matching search for the remaining Robert Smiths.
Iteratively applying this insight leads to the counter-intuitive result that
you only need 23 people to have a 50% probability of sharing a birthday, or
for our application, 180 Robert Smiths on a voter file to have a 50%
probability that two share the exact same birth date. Also note that while
the probabilities are of course much lower for single pairs of unusual
names, the sheer volume of these pairs leads to at least a few expected
matches.

============
Dr. Michael P. McDonald
Associate Professor, George Mason University
Non-Resident Senior Fellow, Brookings Institution

                             Mailing address:
(o) 703-993-4191             George Mason University
(f) 703-993-1399             Dept. of Public and International Affairs
mmcdon at gmu.edu               4400 University Drive - 3F4
http://elections.gmu.edu     Fairfax, VA 22030-4444


-----Original Message-----
From: law-election-bounces at department-lists.uci.edu
[mailto:law-election-bounces at department-lists.uci.edu] On Behalf Of Bev
Harris
Sent: Sunday, September 11, 2011 2:40 PM
To: law-election at department-lists.uci.edu
Subject: Re: [EL] McDonald study, birthdate distribution in real voter list

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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