Re: Random choice (was Re: exit polls vs. election results)

From: Edward Cherlin <cherlin_at_pacbell_dot_net>
Date: Mon May 23 2005 - 05:09:21 CDT

On Sunday 22 May 2005 11:28, Ron Crane wrote:
> So let's take another swing at a transparent process that has
> fewer weaknesses.
>
> One of the original procedure's weaknesses is the single
> tosser. So let's replace her with a empty box into which the
> participants deposit a single coin, then close the cover. Then
> each participant shakes the box to her satisfaction. When all
> are done, they open the box and read the value.
>
> Another weakness is that a biased coin biases fixed bits of
> the output. Thus, officials could, for example, cheat in
> odd-numbered precincts, then use a coin fixed to come up tails
> (= 0) more often than heads, and somehow try to ensure that
> that coin always formed the LSB of the output precinct
> numbers. This'd be hard to do, but possible. So let's make any
> one-sided bias counteract itself by repeatedly tossing the
> coin twice until we get either a TH (=1) or an HT (=0)
> sequence. Since p(TH) = p(HT) = p(H)p(T) no matter what p(T)
> and p(H) are, this is guaranteed to be fair as long as the
> probabilities don't change between the tosses. It'd be
> possible to concoct a radio-controlled coin that would allow a
> cheater to change the probabilities between the tosses, but
> it's pretty darn unlikely.

Vastly improved, but not anywhere near good enough.

> This is transparent and practical. What are its weaknesses?
>
> -R

Legion, Ron. I don't have time to list all the ones I know, and
the pros know many more. Let's see...For ordinary coin tosses:

o Easy: Swap the coins between tosses using sleight of hand. Make
sure to swap your biased coin in for the LSB (or whatever chosen
bit).
o Easy, but also relatively easy to detect: Throw the coin so
that it spins rather than tumbling.
o Moderately difficult: Practice until you can toss a coin with
exactly three and a half turns every time, or even just most of
the time.

Then for the box. I don't know the methods for coins, but surely
you have seen magicians put a card into an envelope, and then
have it turn out to be the same as the card you pick after the
envelope is sealed? It isn't the same trick, but the principle
applies.

People do cheat at coin tossing games and every other form of
gambling. Any stage magician or casino security expert would
laugh loud and long at your assertion of transparency and
practicality. (It might be worthwhile to see if we can recruit
The Amazing Randi to the cause. He enjoys debunking those
without professional training who claim that they can prevent
cheating.) Casinos use physical layouts for dice tables to make
cheating much harder, requiring throws to go end-to-end, and
then employ eagle-eyed croupiers who know how to recognize all
of the known dice cheats. Spinning rather than tumbling the dice
is one of the easier methods, but is also one of the easier ones
to detect. Please read some of "Scarne on Dice" or a book on
coin tricks before you try to propose a secure randomizer using
physical objects.

A genuinely random process is practical and we should use one,
but it will not be transparent in the way you would like.

-- 
Edward Cherlin
Generalist & activist--Linux, languages, literacy and more
"A knot! Oh, do let me help to undo it!"
--Alice in Wonderland
http://cherlin.blogspot.com
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Received on Tue May 31 23:17:45 2005

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