From: Edward Cherlin <edward_dot_cherlin_at_etssg_dot_com>

Date: Tue Aug 26 2003 - 16:50:55 CDT

Date: Tue Aug 26 2003 - 16:50:55 CDT

The calculation described below is an APL one-liner. The binomial

function is an APL primitive, represented by "!". Thus

0 ! 5

1

1 ! 5

5

2 ! 5

10

0 1 2 3 4 5 ! 5

1 5 10 10 5 1

There is no need for a trial and error method of finding the

right sample size, either in Excel (which has goal-seeking) or

in APL, which has an equivalent repeat-until operator. Actually,

there is a closed-form solution, but I haven't looked at your

calculation yet to determine exattly what you need. Python is

based in part on APL, so it should also handle these

calculations with ease.

On Sunday 27 July 2003 04:47 pm, Alan Dechert wrote:

*> From: "Douglas W. Jones" <jones@cs.uiowa.edu>
*

*>
*

*> > Indeed, your system, and for that matter, the Populex system
*

*> We can use binomial distribution to do the calculations. I
*

*> have a calculator that a fellow by the name of Bill Buck
*

*> helped me with. It's in Excel and uses the BINOMDIST function
*

*> in Excel. I am trying to get someone else to write a
*

*> standalone calculator. Anyway, if you have Excel you can try
*

*> it out here:
*

*>
*

*> http://home.earthlink.net/~adechert/LOTAcceptanceCalculator.xl
*

*>s
*

*>
*

*> In this case, the sample is accepted if no defects are found
*

*> -- rejected if one is found. So, the "defects found in
*

*> sample" will have to be zero.
*

*>
*

*> For example, suppose in a two way race candidate A got 505,000
*

*> votes and candidate B got 495,000 according to the electronic
*

*> record. Let's say, for now, that if we compute a 99.999
*

*> percent confidence level, we can safely announce candidate A
*

*> as the winner (with 99.999, we'll be wrong once in 100,000
*

*> contests). The outcome could only be wrong if 5,000 votes
*

*> turn out to be taken away from A or added to B. This is a
*

*> fraction of .005 of the million votes cast. If we enter .005
*

*> in the LOT FRACTION DEFECTIVE cell along with 1,000,000 in the
*

*> "Election Size" field and play with the required sample size,
*

*> we can find a number that will give us the 99.999 Confidence
*

*> Level we want. A few tries and I get .99999 with 2,300
*

*> samples. So with this in mind, we know if we can collect a
*

*> random sample of 2,300 ballots and check them against the
*

*> electronic record (and the match), we are 99.999 percent
*

*> certain that Candidate A won. This sample could be obtained
*

*> pretty quickly. A fuller audit can be performed later. In
*

*> practice, samples will usually be much smaller since races are
*

*> usually won or lost by several percent -- not so close as this
*

*> example. For example, you only need a sample of 550 ballots
*

*> where a 2.5 percent swing could change the outcome.
*

*>
*

*> If everyone follows procedures, there should not be any
*

*> mismatches. Even if a defect is found (for example, a paper
*

*> ballot that has no corresponding record in the electronic
*

*> table of ballot images), it won't necessarily disturb the
*

*> outcome -- it will just take a little longer. You just take a
*

*> larger sample until you reach the desired confidence level.
*

*> If more than a few defects are showing up, we may have to scan
*

*> all the ballots. Again, this might delay the result slightly
*

*> but still should be done fairly quickly. We can then also do
*

*> hand sampling of the scanned result for further verification.
*

*>
*

*> It may be that all the ballots will be scanned as the election
*

*> is audited in the days after Election Day.
*

*> ******
*

*> more on this later.
*

*>
*

*> Alan
*

-- Edward Cherlin, Simputer Evangelist Encore Technologies (S) Pte. Ltd. Computers for all of us http://www.simputerland.com, http://cherlin.blogspot.com ================================================================== = The content of this message, with the exception of any external = quotations under fair use, are released to the Public Domain ==================================================================Received on Sun Aug 31 23:17:16 2003

*
This archive was generated by hypermail 2.1.8
: Sun Aug 31 2003 - 23:17:18 CDT
*