[EM] Touching up bias definition

[MIKE OSSIPOFF]

  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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