On Wed, 25 Jul 2001 09:33:41 -0400, Sanford Lefkowitz
<[EMAIL PROTECTED]> wrote:
> In a certain process, there are millions of people voting for thousands
> of candidates. The top N will be declared "winners". But the counting
> process is flawed and with probability 'p', a vote will be miscounted.
> (it might be counted for the wrong candidate or it might be counted for
> a non-existent candidate.)
For clarification: I assume you are talking about votes and winners
in the thoroughly abstract, hypothetical, imaginary instance - where
(for example) votes are miscounted TOTALLY AT RANDOM, and
not because of ballot-flaws relating to position on a ballot; etc.
>
> What is the probability that the counted top N will correspond to the
> real top N?
> (there are actually two cases here: 1 where I want the order of the top
> N to be in the correct order and the other where I don't care if the
> order is correct)
We could say, you are referring to "errors in counting" that are
entirely uncorrelated with each other, or with anything.
I can offer: You will need to parameterize the cases according
to the spread in vote. And use some model. Is this, 20% of the
candidates get 80% of the vote? or 10% get 90%? or 1%, 99%?
(There is some name for those curves - Pareto?)
AND - what is your question, to be quantified? I can be
sure without doing anything, that for large N and smooth
distributions, the top N counts will not fall in perfect order.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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