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

From: Ron Crane <voting_at_lastland_dot_net>
Date: Sun May 22 2005 - 13:28:08 CDT

On May 22, 2005, at 1:45 AM, Edward Cherlin wrote:

> On Tuesday 17 May 2005 21:27, Ron Crane wrote:
>> ...
>> The idea is carefully to specify the process for generating
>> the random result, not leaving anything to the imagination,
>> and keeping everything open to observation. Something like
>> this is a start:
>
> Even if you knew how to specify a random process, which you
> evidently haven't the first idea of, the witnesses will at best
> be able to follow the procedure without being able to verify for
> themselves that it is random.
>
>> 1. Each witness volunteers a coin.
>
> Forget it. We use tested devices or there is no point in
> bothering.
>
>> 2. Each witness inspects the others' coins. Only coins that
>> pass all volunteers' scrutiny are used for the next steps.
>
> How many witnesses will know how to test for a rigged coin? How
> many can do it without equipment by visual inspection?
>
>> 3. The volunteers elect a coin tosser.
>
> Oh, come now. If you're going to have a random process, you can
> at least pick the coin tosser's name out of a hat. However,
> having a single coin tosser is a security hole in itself.
>
>> 4. Using each coin in round-robin sequence,
>
> A predetermined, non-random sequence is another weakness....

Putting aside your tone, the process certainly has some weaknesses,
which is why I labelled it "a start". The purpose, of course, is to
create a process that is at once fully transparent to the general
public and adequately random. Full transparency rules out devices that
the general public cannot understand -- even if such devices, like a
Geiger-based one, actually would (if fairly implemented) produce more
random (less predictable) results than the transparent process does.

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.

This is transparent and practical. What are its weaknesses?

-R

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Received on Tue May 31 23:17:45 2005

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