[EM] SL vs LR--Rounding is unavoidalbe because allocations are integer

[Dan Bishop]

raphfrk at netscape.net wrote:
>  > From: juho4880 at yahoo.co.uk
>  > On Dec 10, 2006, at 20:50 , MIKE OSSIPOFF wrote:
>  > > But
>  > > rounding is quite unavoidable, since fractional seats can't be
>  > > given (or at least are against the rules).
>  >
>  > I agree. All methods lead to rounding errors (unless we cut the
>  > candidates in fractions or give them unequal voting power :-).
> 
> What about charging each State 1 seat for every seat they are
> allocated.  If a State receives to few seats in one election,
> they will receive a compensating one in a future election.
> 
> The long term average number of seats allocated to the State
> would be exactly proportional.
> 
> For example:
> 
> Each State has a seat total that is not cleared from election to
> election.  This total counts in fractional seats.
> 
> When a seat is allocated, the State that receives the seat's total
> is decreased by 1 seat.  All States, including the one that
> received the seat, then have their total increased by State
> Population divided by National Population.
> 
> A seat is always allocated to the State with the highest total, or
> using some tie-break rule if there is a tie.
> 
> ...
> 
> Finally, handling small States would require a kludge.  Perhaps,
> make a rule that they must be allocated a seat at the end, but that
> it isn't included as part of the totals.  This would mean that
> sometimes they would get a seat directly and sometimes they would
> get a seat due to the exception to the normal rules.

One way to avoid this problem is to start by apportioning E*S seats, 
where E is the number of elections between reapportionments and S is the 
number of seats in the legislative body, with the constraint that no 
state can receive fewer than E seats.

Alabama: 34
Alaska: 5
Arizona: 40
Arkansas: 21
California: 262
Colorado: 33
Connecticut: 26
Delaware: 6
Florida: 124
Georgia: 63
Hawaii: 9
Idaho: 10
Illinois: 96
Indiana: 47
Iowa: 23
Kansas: 21
Kentucky: 31
Louisiana: 35
Maine: 10
Maryland: 41
Massachusetts: 49
Michigan: 77
Minnesota: 38
Mississippi: 22
Missouri: 43
Montana: 7
Nebraska: 13
Nevada: 15
New Hampshire: 10
New Jersey: 65
New Mexico: 14
New York: 147
North Carolina: 62
North Dakota: 5
Ohio: 88
Oklahoma: 27
Oregon: 26
Pennsylvania: 95
Rhode Island: 8
South Carolina: 31
South Dakota: 6
Tennessee: 44
Texas: 162
Utah: 17
Vermont: 5
Virginia: 55
Washington: 46
West Virginia: 14
Wisconsin: 42
Wyoming: 5

Then, apply your algorithm to these numbers rather than to the 
populations directly.