[EM] FW: Re: Transfers of seats between states

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Dec 7 14:40:17 PST 2006

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I hadn't heard about the other methods being justified in terms of transfers
between states after the allocation. But, as for different standards for
judging the result of those transfers, by different standards of
proportional fairness, there doesn't seem to be much room for rival
standards.

The Constitution says that the seats should be allocated to the states in
proportion to their populations. "Proportion" means that seats should be
proportional to population. The (impossible) goal, therefore, is for all the
states to have the same proportion, the same ratio, of votes to seats.

So, what relation between two states should be optimized with respect to
seat transfers between them? Is there any room for disagreement? Starting
with the apportionment allocation, and then giving a seat from one state to
another, should never cause their v/s to differ by a smaller factor than it
did before the transfer. The words "proportional" and "proportion" imply
that factor is what we're talking about.

Yes, Hill's procedure looks at factor where Webster's procedure looks at
arithmetic rounding. But, as I said, no genuine justification can be found
in the procedure definitions of Webster or Hill. If you can't make the v/s
proportion the _same_ for all states, then who's to say which kind of
fudging is best? As I said, as soon as we round off to the nearest integer,
like Webster or Hill, we're going from solid justification to fudging and
word-games.

So the transfer property is what can give solid justification. A transfer
property doesn't  work for Hill, because a fixed integral number of seats
(one) is transferred. That's why Webster's arithmetic rounding, placing the
state as close to its ideal number in terms of raw seat-count, is what makes
it possible for Webster to have the transfer property. It means that any
change in that party's seat total, such as receiving or giving a seat, can
only put that party's seat total farther from the fractional seat total
corresponding to its ideal v/s. And when a state is as close as it can be to
that ideal fractional seat total, in terms of raw seat-count, then it must
also as close as possible to its ideal v/s, as measured by the factor by
which its v/s differs from the ideal. And that's true because Webster rounds

As for Jefferson or the others, I've never heard of a transfer property
claimed for them. Jefferson, for instance differs from Webster in rounding
down instead of rounding to the nearest whole seat.

Since there's no solid justification in the procedures, we can justify
according to how transfer affects the factor by which the 2 states' v/s
proportions differ. If the transfer of a seat between two states makes their
v/s differ by a smaller factor than it did before, then something is wrong
with the initial allocation.

Mike Ossipoff

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