[EM] Touching up bias definition
MIKE OSSIPOFF
nkklrp at hotmail.com
Wed Dec 13 11:48:54 PST 2006
The definition of bias should specify that we're comparing cycles (from
one integer to the next), rather than comparing places within a cycle.
Whether the method is Largest-Remainder/Hamilton or any one of the quota and
rounding methods, a state in the higher part of a cycle has a better s/q
expectation than a state in the lower part of a cycle. So it only makes
sense for bias to compare whole cycles to eachother. That's really the
unspoken intention when we speak of bias.
Maybe the reason why bias is less popular to discuss is the notion that it
needs an assumption about a probability distribution. Some of us, including
me, have been a little apologetic about that.
But you don't really know in advance which part of a cycle your state will
be in. And, in the spirit of comparing whole cycles, discussed in the
paragraph before last, you have meaningful comparison without weighting the
parts of a cycle in comparison to eachother.
By the way, though Bias-Free dosn't have either of the transfer properties
of Webster or Hill, it can be regarded as a compromise between them, since
BF's round-off points are between those of Hill and Webster. Not either
transfer property, but reduced violation of both. And zero bias.
I told yesterday why I claim that bias is more important than random,
undirected small deviations from proportionaly, and I pointed out that even
Hill and Webster, with their transfer properties, can't eliminate deviation
from perfect proportionality, but can only reduce it in degree--while BF
completely eliminates bias, when we compare cycles, without unequally
weighting the places within a cycle.
By the way, my easy access to a computer might end in a day or so. Then I'll
only be able to get to a computer every few weeks. So if I take a long time
to reply to something, that's why.
Mike Ossipoff
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