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

Thu Dec 7 14:40:17 PST 2006

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 
arithmetically instead of geometrically.

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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