# Re: Scanner, write-ins, printer (was Re: Barcode -- printed ballot)

Date: Mon Oct 20 2003 - 11:19:27 CDT

Jan,
>
> Ahem, I seem to have pressed the wrong button on my calculator...
> The number of valid votes is about 2.7*10^14, but that is still
> only about 3*10^-21 of the total combinations. So it is of course
> still a very good way to check.
>
Rather, it seems your calculator is broken.

My calculator says there are 87,967,386,295,948,799 possible ways the ballot
could be voted (excluding all contests blank, which I consider not valid).

Cat Catcher is the only contest that's a bit tricky to figure the
combinations. For this, there are basically four possibilities. Vote for
3, Vote for 2, Vote for 1, and Vote for none.

The unordered combinations of n things taken k at a time is given by

n!/(k! * (n-k)!)

So you can choose three of ten 120 different ways, two of ten 15 ways, one
of ten, 10 ways, and none of 10 one way. So that's 120 + 15 + 10 + 1 = 146
ways the cat catcher race could be voted.

For the county commissioner race, each contestant could have one of 9
different scores (8 possible rankings plus blank). So, there are
9*9*9*9*9*9*9*9 = 43,046,721 ways this contest could be voted (allowing the
same rank for multiple candidates).

The basic conclusion is still fine, however.

87,967,386,295,948,799

is a small number compared with

83,076,749,736,557,242,056,487,941,267,521,535
(the number of possible strings of zeros and ones 116 chars long, excluding
all zeros).

I have changed the code (I will post the update shortly) in the bva
application so that it checks for a valid ballot -- no more than one
selection in contests 1 - 11; no more than three cat catchers; no more than
one ranking for each county commissioner.

Coupled with the check sum error checking already built in, this means it's
just about impossible for the Cue Cat to misread the barcode and still wind
up with a valid ballot.

If you take the barcoded 40-digit number from the ballot and change one
digit, bva will find the ballot invalid. About the only exception you can
find would be to change the right-most digit -- it's possible to still have
a valid ballot after changing that one. With our barcode system, though,
it's not possible (or maybe very very unlikely) to change just one digit
since character set C has digit pairs. So if one pair is wrong, another
pair would also have to be wrong to pass the check sum test. So it looks
like 2 pairs of digits would have to be changed -- the odds of a misread
still resulting in a valid ballot must be astronomical.

Alan D.
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Received on Fri Oct 31 23:17:02 2003

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