Dear Election List,
The issue of whether or not a particular method of apportionment is
biased is rather complex it seems to me. Although I greatly respect
the work of Balinski and Young I do not find the discussion they have
about bias totally compelling. (Look at the diagram on page 72 of the
revised edition of their book to see data for the apportionment of
the House of the Representative using the Balinski-Young measure of
bias.) One problem for me is that the Constitution requires that each
state get one seat. Thus, a state can get a set even if in some sense
it might not be entitled to this in a pairwise comparison framework.
The Constitution gives small (and large) states one seat
automatically. Thus, it seems to me that one has to "sort out" the
effects due to the Constitutional requirement of 1 seat for each
state and the effects of the method of apportionment. Balinski and
Young do take this issue into account but it is not clear to me if
their way is the only reasonable one. In the year 2000, Huntington-
Hill and Webster gave the same apportionment. In 1990, they differed
with regard to 1 seat between two states. (Webster gave one more seat
to MA. at the expense of Oklahoma, and Huntington-Hill the other
other way around.)
Best,
Joe
On Dec 8, 2006, at 2:29 PM, MIKE OSSIPOFF wrote:
I accidentally said that Hill has "unbias". I meant to say that it
has bias.
Mike Ossipoff
p.s. Right now is close to the anniversary of the date when Webster
was
replaced by Hill, for apportioning the House.
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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:
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web page:
http://www.york.cuny.edu/~malk
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