Because one can increase the number of apportionments that are done and
averaged, theres no need to have the additional option of increasing the
number of states and the House-size. So Im 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 thats
part of the test, theres 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 Im 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),
Im 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 wont 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
theyre 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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