I said:
That can be shown as I described earlier. When I found out about my
Bias-Free fallacy, I set out to find the intrinsically unbiased divisor
method. Write expressions for the total number of quotas possessed, and the
total number of seats received, by the states in a some particular cycle,
between two whole numbers of Hare quotas, such as the set of states
possessing between 4 and 5 Hare quotas. Set those two expressions equal, and
solve for the rounding point between those integers.
I now comment:
Put the word "expected" in front of "total number of quotas" and "total
number of seats".
Take out the word "Hare", in both places where it occurs. The quota could be
any quota. All that's necessary is that we're talking about q as a number
between two integers. q represents a number of quotas.
Specify the assumption that the probability density of states with respect
to q is assumed uniform within a cycle.
[end of modifications to derivation]
Modified wording:
That can be shown as I described earlier. When I found out about my
Bias-Free fallacy, I set out to find the intrinsically unbiased divisor
method. Assuming that the probability density of states with respect to q is
uniform within a cycle, write expressions for the expected total number of
quotas possessed, and the expected total number of seats received, by the
states in a some particular cycle, between two whole numbers of quotas,
such as the set of states possessing between 4 and 5 quotas. Set those two
expressions equal, and solve for the rounding point between those integers.
[end of modified wording]
By the way, the only way someone could criticize what Im saying in that
posting would be if he claimed that unbias and equal expectation are
unachievable because represaentation expectation is affected by what part of
a cycle a state is in. But Ive already answered that: Yes, if were looking
at the results of states being in different parts of their cycles, then
thered be no such thing as unbias or equal representation expectation. So
we look at it only at the cycle level, and speak of unbias and equal
representation expectation with respect to cycles. If you prefer, you could
speak of it as a supposition that we dont know what part of a cycle your
state is in. Or we could speak of it as a comparison of the expected overall
s/q of the various cycles--the expected overall s/q of the cycles is equal
with the methods that I propose.
Those methods achieve unbias and equal representation for everyone in the
only sense, and in the only way, that its possible.
Milke Ossipoff
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