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Largest Remainder

The largest remainder method (also known as Hare–Niemeyer method, Hamilton method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with voting systems.

Installation

yarn add largest-remainder

Usage

const largestRemainder = require('largest-remainder')

const votes = {
	Conservatives: 13636684,
	Labour: 12877918,
	SNP: 977568,
	'Liberal Democrats': 2371861,
	Green: 525665,
	Other: 746144
}
const seats = 650

let government = largestRemainder(votes, seats, 'hare')
console.table(government)

Results

┌─────────┬────────┬─────────────────────┬──────────┬──────────────────────┬────────────────────┬─────────────────────┬───────┬──────────────────────┬──────────────────────┐
│ (index) │  type  │        party        │  votes   │      percentage      │    distribution    │      remainder      │ seats │        error         │   percentageSeats    │
├─────────┼────────┼─────────────────────┼──────────┼──────────────────────┼────────────────────┼─────────────────────┼───────┼──────────────────────┼──────────────────────┤
│    0    │ 'hare' │   'Conservatives'   │ 13636684 │  0.437973859064024   │ 284.6830083916156  │ 0.6830083916155445  │  285  │ 0.31699160838439866  │ 0.43846153846153846  │
│    1    │ 'hare' │      'Labour'       │ 12877918 │ 0.41360432222159416  │ 268.8428094440362  │ 0.8428094440361633  │  269  │ 0.15719055596377984  │ 0.41384615384615386  │
│    2    │ 'hare' │ 'Liberal Democrats' │ 2371861  │ 0.07617783878642748  │ 49.51559521117786  │ 0.5155952111778532  │  49   │  0.5155952111778603  │ 0.07538461538461538  │
│    3    │ 'hare' │        'SNP'        │  977568  │ 0.031396872543024375 │ 20.407967152965842 │ 0.40796715296584196 │  20   │ 0.40796715296584196  │ 0.03076923076923077  │
│    4    │ 'hare' │       'Other'       │  746144  │ 0.02396415192267175  │ 15.576698749736638 │ 0.5766987497366376  │  16   │  0.4233012502633624  │ 0.024615384615384615 │
│    5    │ 'hare' │       'Green'       │  525665  │ 0.016882955462258285 │ 10.973921050467885 │ 0.9739210504678848  │  11   │ 0.026078949532115203 │ 0.016923076923076923 │
└─────────┴────────┴─────────────────────┴──────────┴──────────────────────┴────────────────────┴─────────────────────┴───────┴──────────────────────┴──────────────────────┘

Quotas

Available quotas are hare, droop, hagenbach-bischoff and imperiali. See Quotas

Not providing a quota, rounds the seats down before ordering by the largest remainder and incrementally increasing.

droop quota defaults to hare quota when quota <= seats

Results object

  • type the quota used
  • party the original key name
  • votes the original key value
  • percentage the overall percentage of votes received
  • distribution how the seats should be distributed
  • remainder the remainder used to order the results before addition of new seats
  • seats the seats allocated to the party
  • error how far off the distribution is the seats
  • percentageSeats what percentage the seats now represent

Credits

Written by Nic Mulvaney @ Normally

Inspired by https://github.com/juliuste/hare-niemeyer