customergauge/remainder

Largest Remainder Method calculation

1.1.1 2020-12-11 12:09 UTC

Requires

• php: >=7.1

Requires (Dev)

• phpunit/phpunit: ^9.0

MIT

• Marco Deleu

• method
• largest
• remainder
• Hare
• Niemeyer
• Hamilton
• Vinton

README

This library provides a simple way to calculate percentages using the Largest Remainder Method. Learn more.

Installation

composer require customergauge/remainder

Usage

use CustomerGauge\Math\Remainder\Remainder;

$remainder = new Remainder([1, 1, 1]);

$remainder->round(2); // [0.34, 0.33, 0.33]

In simple terms, the goal of the Largest Remainder Method is to make sure that when calculating the weight of each seat in the data set, the aggregated percentage will not be 99.99 or 100.01.

The first example above is arbitrary and end up rounding up only the first record so that 0.34 + 0.33 + 0.33 = 1, however not always the decision is arbitrary.

use CustomerGauge\Math\Remainder\Remainder;

$remainder = new Remainder([92, 93, 70]);

$remainder->round(2); // [0.36, 0.37, 0.27]

As we can see, 0.36 + 0.37 + 0.27 = 1, however using standard rounding, the result would have been different. To demonstrate that, let's calculate 92 + 93 + 70 = 255. Each value takes the following percentage of the whole:

Value	Percentage	Round	Largest Remainder Method
92	0.3607843137	0.36	0.36
93	0.3647058823	0.36	0.37
70	0.2745098039	0.27	0.27

As we can see from the table above, standard rounding end up losing one percentage point because all three numbers round down. The Largest Remainder Method will scan the values that will be discarded (0.3607843137, 0.3647058823, 0.2745098039) and prioritize the ones with the largest contribution. In this case, the 2nd value will discard 47058823, which is the largest value discarded. That makes it viable for round up to fill the gap.

The fact that 93 is also the largest value does not necessarily have a direct connection to the option being rounded up. We can try the same example again using a much smaller number. Take 92 + 32 + 70 = 194.

Value	Percentage	Round	Largest Remainder Method
92	0.4742268041	0.47	0.47
32	0.1649484536	0.16	0.17
70	0.3608247422	0.36	0.36