[EM] Hamilton vs Webster (Sainte-Lague)
Juho
juho4880 at yahoo.co.uk
Thu Dec 14 10:07:51 PST 2006
Yes, this one works. But there are still some interesting peculiarities.
Example:
We have three sates with population A:5, B:3 and C:3 (millions I guess).
Seats will be allocated in the following order: A, B*, C, A, B*, A,
C,...
- Three first seats go to the three states either based on the "at
least one seat per state" rule or by starting the algorithm from
"zero seats"
- I used * to indicate where B wins the seat by lottery (instead of C)
The strange thing is that the fifth seat goes to B by lottery but C
will not get the next seat although it was already entitled (tie) to
the previous seat (and B and C are identical states in the sense that
they have exactly the same population).
Divisor methods like SL/Webster provide ordering of the candidates/
seats by default and they may be nicer to use in places where such
ordering is needed. I however tend to think that the Alabama paradox
is not a sufficient reason to abandon use of LR/Hamilton in seat
allocation to the states. LR/Hamilton does the allocation in a
perfectly rational way that can be considered to be ideal (at least
from one point of view). LR/Hamilton (Alabama paradox) may look bad
to the audience if presented so, but it is another question if it is
bad or if it looks bad to mathematicians.
Juho Laatu
On Dec 14, 2006, at 6:16 , Dan Bishop wrote:
> MIKE OSSIPOFF wrote:
> ...
>> Are there other reasons
>> why LR/Hamilton is not favoured?
>>
>> I reply:
>>
>> That's reason enough. Two kinds of nonmonotonicity: Population
>> nonmonotonicity and House-size nonmonotonicitly. Your state can
>> lose a seat
>> because of a population change favoring your state with respect to
>> the
>> others, or because of an increase in the House's total number of
>> seats.
>
> There's a pretty simple modification to LR/Hamilton that would
> eliminate
> the Alabama Paradox. Give seats one at a time (except at the
> beginning,
> when each state is assigned one seat), such that the nth seat goes to
> the state for which the quantity
> (state's proportion of population) * n - (state's seats so far)
> is the greatest.
> ----
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