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 ---- Election-Methods mailing list - see http://electorama.com/em for list info
