[EM] A little simplification of bias-test

Michael Ossipoff mikeo2106 at msn.com
Thu Jan 25 06:40:13 PST 2007

Because one can increase the number of apportionments that are done and 
averaged, there’s no need to have  the additional option of increasing the 
number of states and the House-size. So I’m dropping the option of 
increasing the number of states and the House-size.

Since, as described in one of the last paragraphs of the posting about the 
bias-test, a method is unbiased if an unbias-measure can be made arbitrarily 
good by doing and averaging sufficiently many apportionments, and that’s 
part of the test, there’s no need to speak of two parties with opposing 
goals who have the option to increase the number of apportionments to 
achieve their goals. So I’m dropping mention of the two parties.

I started with the two parties because that approach  was useful when 
talking about what it means to meet or fail a single-winner criterion, when 
I spoke of the “failure-example-writer”.

In the fine-version (the other version will be called “the coarse version), 
I’m keeping the specification of correlation between the q and s/q of 
_cycles_  (as opposed to individual states). But, with sufficiently many 
apportionments done and averaged, it probably won’t make any difference 
whether cycle correlation or state correlation is used, because the local 
bias that affects state correlation (when s/q differs between states because 
they’re in different parts of their cycles) will probably tend to cancel 
itself out with lots of apportionments. That means that my methods test 
unbiased with either correlation measure.

Mike Ossipoff

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