Dear Mike,
On Jan 24, 2007, at 3:35 AM, Michael Ossipoff wrote:
Joe says:
When it comes to bias, there are many different kinds of bias that
one might
talk about and differing ways to measure that bias. Calling
something "bias
free" does not shed extra light without more insights.
I reply:
What kind of insights does Joe want?
By way of analogy, the kind of insight that Huntington offered in
showing that Huntington-Hill minimized differences between 16
measures involving a(i) where a(i) is the number of seats given
state i and p(i) is its population, in a relative sense under
transfer of a seat between a pair of states. For Webster, the
absolute difference a(i)/p(i) - a(j)/p(j) is optimized while for
Dean p(j)/a(j) - p(i)/a(i) is optimized. For me, this gives an
insight into the difference between Huntington-Hill and Dean. (See
page 102 of Balinski and Young.)
I provided a definition of bias, and
pointed out that it's the definition that no one would disagree
with. But of
course I invite Joe to disagree with it if he wants to.
Joe says that there are many different kinds of bias that one might
talk
about, but Joe forgot to talk about any of them. So, Joe, wouild
you be
willing to name at least one different kind of bias, and tell why it
justifies giving the largest states (as defined in my most recent
post) more
s/q than the smallest states?
As for how to measure the bias empiricallly, of course that
question has to
be postponed till after a bias definiltion has been agreed-upon.
What Joe has been saying, all along, about bias seems to be, "Bias
is so
difficult to define, so many different competing definitions for it
that we
should throw up our hands and disregard it, and concentrate instead on
something else like transfer properties (and give Hill a free pass
on its
bias).
Here is your definition:
1. We’re talking about a hypothetical country that has arbitrarily
many states.
2. “The largest states” means an arbitrarily large number of states
at the top end.
3. “The smallest states” are defined similarly.
Suppose the "the largest states" which are equal or nearly equal in
population have 12 percent of the total population, and the "smallest
states" which are equal or nearly equal in population have 88 percent
of the population. Also consider many other variants of this type of
situation, both in the presence and absence of giving states some
initial distribution of seats, say 1, as required by the
Constitution. The house size is a variable here.
I am not trying to give any particular method a "free pass." I am
trying to understand complex phenomena.
Best,
Joe
Mike Ossipoff
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------------------------------------------------
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
Phone: 718-262-2551 (Voicemail available)
My new email is:
[EMAIL PROTECTED]
web page:
http://www.york.cuny.edu/~malk
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