Even without the 1-seat minimum,. Bias-Free, in the census apportionments, still nearly always does worse than Webster when the two dilffer.
There are two possible explanations: 1. Maybe, though I've believed that the frequency distribution causes large-bias, I was mistaken and it actually instead causes small-bias. In that case, Webster may have just enough intrinsic large-bias to nearly cancel the distribution's small-bias. Bias-Free, with no intrinsic bias wouldn't do as well. (It goes without saying that Cycle-Webster and Adjusted-Rounding would still do better than any other methods, since their unbias is unconditional). 2. Maybe the use of correlation between _states'_ q and s/q instead of _cycles'_ q and s/q gives sufficiently different results as to give the result shown. Maybe, in large simulations, the s/q disparities caused by 2 states being in different parts of their cycles would cancel out, and then the two correlations, the state correlation and the cycle correlation would give the same result. Probably the 2 kinds of correlation don't give very different results, and that that canceling tendency is present even in a few census apportionmentss. So I rather suspect that explanation #1 is the correct one. Note that someone could fix the correlation, reduce it, by tweaking roundoff points up or down. They coudl even tweak a fixed rounding point in that way, a rounding point that is at the same part of each cycle. That would make the correlation come out lower, but would it actually eliminate bias, as I've defined it, and as we mean it? Mike Ossipoff ---- election-methods mailing list - see http://electorama.com/em for list info
