[EM] I propose Bias-Free, Cycle-Webster, and Adjusted-Rounding

MIKE OSSIPOFF nkklrp at hotmail.com
Mon Jan 15 22:30:49 PST 2007

Though Cycle-Webster started out as Adjusted-Rounding, CW & AR are two 
dilstinct methods, as is evident from their definitions.

As I said in the subject-line, I propose Bias-Free, Cycle-Webster, and 

Each has its advantages and disadvantages.

BF's bias-freeness, as measured by correlation tests on its apportionments, 
is affected by the state-size frequency distribution. This, of course is 
true of every method except for Cycle-Webster and Adjusted-Rounding, which 
are unconditionally completely unbiased. But BF is still less biased than 
Webster or (especially) Hill.

Cycle-Webster may (rarely) give one more seat to a smaller state than to a 
larger state. I don't know if that can happen in CW, but maybe it can. If 
so, it isn't a fatal problem. It can be dealt with by a specvial rule that 
modifies a pair-nonmonotonic result to get rid of the pair-nonmonotonicity. 
But that's a disadvantage, because that rule is something of an 
embarrassment to have to have.

Adjusted-Rounding's only disadvantage, apparently, is that it's much more 
work to apply. Instead of having a formula for the rounding point in a 
particular cycle, AR must find the rounding point that gives that cycle 1 
seat for each of its quotas, as nearly as possible. The rounding point that 
puts the sum of that cycle's states' seats as close as possible to the sum 
of that cycle's states' quotas.
Of course, as different quotas are tried, a particular cycle mighst not 
contain the same seats. The iterative systematic procedures so convenient in 
Jefferson, Webster, Hill, Bias-Free, Cycle-Webster, etc., won't work in AR. 
Trial and error is needed to find the quota that gives 435 seats.
Mike Ossipoff

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