[EM] Juho: Bias

Michael Ossipoff email9648742 at gmail.com
Mon Jul 2 17:51:09 PDT 2012

Here is what I mean by "bias". I claim that my meaning for bias is
consistent with the usual understood meaning for bias::

For any two consecutive integers N and N+1,  the interval between those two
integers is "Interval N"

If it is equally likely to find a party with its final quotient anywhere in
interval N, then determine the expected s/v for parties in interval N.

Compare that expected s/v for some small value of N, with the expected
value of s/v for some large value of N.

If the latter expected s/v is greater than the former, when using a certain
seat allocation method, then that allocation method is large-biased.

If the opposite is true, then the method is small-biased.

If the expected s/v is equal for the two values of N, then the method is
unbaised, under the assumption that a party is equally likely to be found
within whichever interval that you're considering.

That's what I mean by bias, under the above-stated assumption.

What if that assumption isn't quite correct? Then Sainte-Lague is very
slightly large-biased.

Bias compares the expected s/v, in two intervals such as I described above.

Mike Ossipoff
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