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# my proposed solution to the fair share problem

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here's how i would handle the problem

so step 1, take the total population and divide by the number of seats. let's call this value D.

then assign each state 1 seat, and subtract from each, D

then again from top to bottom, assign 1 seat, subtracting D. if any are negative don't assign it a seat, obviously.

using the numbers in the video;

40075 population, 43 seats. that 932 representatives per seat.

new triangle 21878

circula  9713

squaryland 4167

octiana 3252

rhombus 1065

assign 1 seat for each state, and subtract 932.

new triangle 20946 reps 1

circula  8781 reps 1

squaryland 3,235 reps 1

octiana 2320 reps 1

rhombus 133 reps 1

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new triangle 20014 reps 2

circula  7849 reps 2

squaryland 2303 reps 2

octiana 1388 reps 2

rhombus 133 reps 1; no further reps.

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new triangle 19,082 reps 3

circula 6,917 reps 3

squaryland 1,371 reps 3

octiana 456 reps 3; no further reps.

rhombus 133 reps 1; no further reps.

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new triangle 18150 reps 4

circula 5985 reps 4

squaryland 439 reps 4 no further reps.

octiana 456 reps 3; no further reps.

rhombus 133 reps 1; no further reps.

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new triangle 442 reps 23

circula 393 reps 10

squaryland 439 reps 4

octiana 456 reps 3

rhombus 133 reps 1

with 2 reps left over. they go to the highest remaining. in this case, octiana and new triangle.

new triangle 442 reps 24

circula 393 reps 10

squaryland 439 reps 4

octiana 456 reps 4

rhombus 133 reps 1

now going from 43 to 44, we get the following

new triangle 14 reps 24

circula 603 reps 10

squaryland 523 reps 4

octiana 519 reps 3

rhombus 154 reps 1

again with 2 left over; they get assigned to curricular and squaryland.

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so the problem is if the number of chairs increases by one, sometimes you lose a seat by most round methods.

if this is the problem, then this seems fairly simple to fix, just "remember" the previous setup.

at 43, we have the following

new triangle 442 reps 24

circula 393 reps 10

squaryland 439 reps 4

octiana 456 reps 4

rhombus 133 reps 1

so at 44;

new triangle 14  with 24 seats

circula  603 with 10 seat

squaryland 523 with 4 seat

octiana 0    with 4 seats

rhombus 154 with 1 seat

and then curricula get the next seat.

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