From: Jerry Lobdill <lobdillj_at_charter_dot_net>

Date: Sun Jul 09 2006 - 09:56:51 CDT

Date: Sun Jul 09 2006 - 09:56:51 CDT

From the FederalVVPAT@yahoogroups.com discussion list:

Stephanie,

Thanks for broaching this subject. Your story and your concerns are

an illustration of why a law should be careful not to use such

language as "chosen at random". Some of the worst "deciders" about

randomness are lawyers and election administration officials. :-)

As a scientist who designed or analyzed simulators that required the

generation of time series with specified statistical characteristics

that simulate data series originating in natural processes and being

processed through various signal processing systems, I have spent

many an hour studying and arguing the merits of various simulation

schemes. Even experts in the business of building such equipment

frequently make mistakes or become deluded and go down a primrose path.

The term, "uniformly distributed", as you know, is a mathematical

term that refers to the probability density function that describes a

population of samples of a given process. The probability density

function (a plot of "value" of a sample vs the frequency of

occurrence of that value in the population) is flat; i.e., the

frequency of occurrence is constant regardless of the value.

For example, suppose that we have a box of marbles of identical size.

There are, say, five colors of marbles, and 50 of each color. For

this simple case there is a total population of 250 marbles, and the

frequency of occurrence of each color is 1/5. The population is

uniformly distributed. Suppose I put these marbles into a bingo drum

that outputs one marble "at random" with every rotation. Is this

really an effective randomizer? We can test that hypothesis to any

desired confidence level by conducting a "sampling with replacement"

experiment.

But the question is, does this model apply to the problem of

detecting corrupted precincts in an election? What if the probability

of corruption is not constant over all precincts? Then no matter what

method we devise to ensure that our selection process doesn't favor

any precinct or group of precincts, we are assuming a characteristic

of the population of precincts that doesn't exist in our situation.

That is, we are assuming that no precinct is more likely to be

corrupted than any other. This assumption may ignore advance

knowledge that we might have about an election and the county whose

precincts comprise our population.

What is our goal? Is it to be "fair", or is it to detect compromise?

Jerry

Stephanie wrote:

*>
*

*>What does "random" mean???
*

*>
*

*>
*

*>
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*>
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*>
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*>Posted by: "Stephanie Frank Singer"
*

*><mailto:music@symmetrysinger.com?Subject=Re:
*

*>What%20does%20%22random%22%20mean%3F%3F%3F>music@symmetrysinger.com
*

*> <http://profiles.yahoo.com/sleepy_sfs>sleepy_sfs
*

*>
*

*>
*

*>
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*>
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*>
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*>Sun Jul 9, 2006 5:56 am (PST)
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*>
*

*>
*

*>Here's a concern I have and don't know what to do with:
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*>How do governing bodies implement "randomness"? We talk of "routine
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*>random audit", but how, in fact, would the precincts be chosen? My
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*>tentative answer (please send more ideas!) is that the precincts
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*>should be selected by the same physical mechanism used to select
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*>lottery winners.
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*>We need to protect against enforcers who would protect misdeeds by
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*>making sure that suspect precincts are *not* chosen for audit.
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*>This is not a merely theoretical concern. I went with the Committee
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*>of Seventy (a local election watchdog organization) to test
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*>Philadelphia election machines before the 2005 primary. Because the
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*>city has about 2000 machines, and there were maybe 10 of us on the
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*>team, we couldn't hope to test all of them. The person in charge of
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*>the Committee of Seventy effort, a lawyer, had chosen the machines to
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*>test in what he considered a random fashion. However, his method was
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*>flawed. So flawed, in fact, that there were over 1000 of the 2000
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*>machines that were guaranteed not to be on his list!!!
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*>((OK, here are the details: Philly is divided into 66 "wards", each
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*>of which has between 20 and 30 precincts. Each precinct has (at
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*>least) two voting machines. This fellow had a list of wards (Ward 1
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*>through Ward 66) and had written opposite each ward a number between
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*>1 and 20. So he had chosen one precinct in each ward. He sent this
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*>list of precincts to someone in charge of the voting machine
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*>warehouse. When we got to the warehouse, the technicians had open
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*>one machine from each of these precincts. But remember, each
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*>precincts has at least two machines! So the technicians got to
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*>choose which machine to open. Ask Marian Vos Savant if you don't
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*>believe me: this really screws up the works. Plus, the technicians
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*>had advance knowledge of which machines would be inspected, so any
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*>nefarious ones among them would have a chance to cover any exposed
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*>tracks.))
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*>By the way, the word "random" has two related but different
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*>meanings. One is the definition you would find in, say, a graduate
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*>mathematics text book. The other is a collective general public
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*>understanding that corresponds to what mathematicians would call
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*>"random, and uniformly distributed." Here's an example. Suppose I
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*>have a trick coin, weighted so that, on average, it will land on its
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*>head 99 times out of 100. Can I use that coin to choose between two
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*>precincts under the law? According to the standard mathematical
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*>definition, the results of that coin toss are in fact "random", since
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*>there is no way to predict when the unlikely event of "tails" will
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*>occur. However, surely we don't want that kind of mechanism for
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*>precinct selection -- if we had two precincts to choose from, we
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*>would want to use a fair coin. (Of course, we're talking about
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*>picking, say, 200 out of 10,000 precincts, not one out of two. But I
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*>wanted to distill the idea into its simplest form.)
*

*>Cheers from one of your resident mathematicians,
*

*>Stephanie
*

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Received on Mon Jul 31 23:17:03 2006

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