[EM] Kristofer: Small correction
Michael Ossipoff
email9648742 at gmail.com
Thu Jul 12 06:53:39 PDT 2012
When you said that the optimal value for the "p" in Warren's formula
could be found by trial and error, using an empirical bias measure
(such as correlation between q and s/q), I said that it isn't
necessary to do it by trial and error, because, since a certain kind
of probability distribution function is assumed (exponential), to get
the conclusion that p is a constant, and because, in any case, there
are ways to estimate a good approximation to that distribution
function.
But of course, it could still be worthwhile checking the correlation
between q and s/q, for various p values, because of course, as I've
said, the approximating function is only a guess or an assumption. So
yes, the trial and error optimization of p makes sense, if p really is
constant with an exponential distribution function, and if that's a
good estimate for the distribution function.
But that trial and error optimization of p would only be valid over
many allocations, because Weighted-Webster most definitely does not
claim to minimize, for each allocation, the correlation between q and
s/q. So really, it might be better to just try to make a good estimate
of the best function to approximate the distribution function.
Suggestions:
1. Interpolation in small regions, using several
cumulative-seat-number(population) data points in and near each N to
N+1 interval
2. Least squares, using more data points
3. Least squares using data points over the entire range of state populations
4. Warren's suggestion to find an exponential approximating function
based on the total number of states and the total number of seats.
Mike Ossipoff
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