Generator

apportion

A generator in the applied library, called 9 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

apportion is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

Hamilton's method on 27 seats and 5 regionsA worksheet of populations, exact quotas, floors, remainders and the seats Hamilton's method awards to 5 regions.quota = population × 27 ÷ 10000populationexact quotaquotafloorremainderseatsABCDEsum571015417/100015.41715417/10001526707209/10007.2097209/10007650351/2001.7551151/20025301431/10001.4311431/10002440297/2501.188147/2501100002727.00025227rounded up from its floorHamilton: floors, then the largest remainders, over 27 seats and 5 regions of 10000 peoplethe exact quotas sum to 27 and so do the awarded seats; the floors account for 25, leaving 2the 2 spare seats went to the largest remainders: C and D

show: "quota"

Hamilton's method on 27 seats and 5 regionsA worksheet of populations, exact quotas, floors, remainders and the seats Hamilton's method awards to 5 regions.quota = population × 27 ÷ 10000populationexact quotaquotafloorremainderseatsABCDEsum571015417/100015.41715417/10001526707209/10007.2097209/10007650351/2001.7551151/20025301431/10001.4311431/10002440297/2501.188147/2501100002727.00025227rounded up from its floorHamilton: floors, then the largest remainders, over 27 seats and 5 regions of 10000 peoplethe exact quotas sum to 27 and so do the awarded seats; the floors account for 25, leaving 2the 2 spare seats went to the largest remainders: C and D

show: "alabama"

Hamilton's seats for each region as the house grows from 20 to 34One step line per region of seats against house size, with the step at which a region's seat count falls marked.5 regions · 10000 people · house 20 to 341213141516171819A56789B12C12D12E202122232425262728293031323334house sizethe seat region D loses at 29Hamilton run at every house size from 20 to 34, one band per region, 20 pixels tothe seatregion D holds 2 seats in a house of 28 and 1 in a house of 29 — the house grewand its share of it fellthat is the only fall in the 15 house sizes swept, and the total is exactly right atevery one of them

show: "divisor"

Jefferson's divisor searched exactly for 27 seatsA divisor axis showing the interval that awards 27 seats, above a table of shares, awarded seats and exact quotas for 5 regions.the divisor d, and the seats Jefferson's rule awards at it28 seats27 seats26 seats1335/4333.750, excluded5710/17335.882, includedpopulationpopulation ÷ dseatsexact quotaquota allowsverdictABCDEsum571017.000171715.41715417/100015 … 161 over26707.9494539/57177.2097209/10007 … 8within6501.9351105/57111.755351/2001 … 2within5301.578901/57111.4311431/10001 … 2within4401.310748/57111.188297/2501 … 2within100002727seats awarded at the divisoroutside ⌊quota⌋ … ⌈quota⌉Jefferson: round every share down, and the divisor is searched rather than guessed — every divisor above1335/4 and at most 5710/17 awards exactly 27 seatsat 1335/4 the same rule awards 28, and above 5710/17 it awards fewer, so that interval is the whole ofthe answerregion A is awarded 17 seats against an exact quota of 15417/1000 — 1 above the ceiling of its own quota

show: "population"

The same 27 seats before and after a censusTwo censuses side by side with exact growth ratios, quotas and seats, and the seat that moves against the growth.first censussecond censuspopulationquotaseatspopulationgrowthquotaseatsABCDEsum571015.417155760576/5710.876%15.4591626707.2097267010.000%7.16676501.755265010.000%1.74525301.431254054/531.887%1.44914401.188144010.000%1.18111000027.0027100601.006027.00271 seatD grew faster; A gained the seatD lost a seattwo censuses, the same 27 seats, and the second found by walking all 59049 censuses in which each region grows by 0 to80 people in steps of 10region D grew by 54/53 and region A by 576/571 — D the faster of the two, and D is the one that lost a seat to Athe ratios are compared as whole numbers, never as decimals: 54 × 571 = 30834 against 576 × 53 = 30528

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

The whole library · What the figures prove