Math::Round::Fair Distribute rounding errors fairly
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Math::Round::Fair Ranking & Summary

Math::Round::Fair Tags

Perl module distributing rounding errors rounding errors exportable function

Math::Round::Fair Description

Distribute rounding errors fairly Math::Round::Fair is a Perl module that provides a single, exportable function, round_fair, which allocates an integer value, fairly distributing rounding errors.round_fair rounds up, or down, randomly, where the probability of rounding up is equal to the fraction to round. For example, round_fair will round 0.5 to 1.0 with a probability of 0.5. It will round 0.3 to 1.0 3 out of 10 times and to zero 7 out of 10 times, on average.Consider the problem of distributing one indivisible item, for example a penny, across three evenly weighted accounts, A, B, and C.Using a naive approach, none of the accounts will receive an allocation since the allocated portion to each is 1/3 and 1/3 rounds to zero. We are left with 1 unallocated item.Another approach is to adjust the basis at each step. We start with 1 item to allocate to 3 accounts. 1/3 rounds to 0, so account A receives no allocation, and we drop it from consideration. Now, we have 2 accounts and one item to allocate. 1/2 rounds to 1, so we allocate 1 item to account B. Account C gets no allocation since there is nothing left to allocate.But what happens if we allocate one item to the same three accounts 10,000 times? Ideally, two accounts should end up with 3,333 items and one should end up with 3,334 items.Using the naive approach, all three accounts receive no allocation since at each round the allocation is 1/3 which rounds to zero. Using the second method, account A and account C will receive no allocation, and account B will receive a total allocation of 10,000 items. Account B always receives the benefit of the rounding errors using the second method.round_fair uses an algorithm with randomness to ensure a fair distribution of rounding errors. In our example problem, we start with 1 item to allocate. We calculate account A's share, 1/3. Since it is less than one item, we give it a 1/3 chance of rounding up (and, therefore, a 2/3 chance of rounding down). It wins the allocation 1/3 of the time. 2/3 of the time we continue to B. We calculate B's allocation as 1/2 (since there are only 2 accounts remaining and one item to allocate). B rounds up 1/2 of 2/3 (or 1/3) of the time and down 1/2 of 2/3 (or 1/3) of the time. If neither A nor B rounds up (which occurs 2/3 * 1/2, or 1/3 of the time), C's allocation is calculated as 1/1 since we have one item to allocate and only one account to allocate it to. So, 1/3 of the time C receives the benefit of the rounding error. We never end up with any unallocated items.This algorithm works for any number of weighted allocations.round_fair($value, @weights) Returns a list of integer values that sum to $value where each return value is a portion of $value allocated by the respective weights in @weights. The number of return values is equal to the number of elements in @weights $value must be an integer.SYNOPSIS use Math::Round::Fair 'round_fair'; my $cents = 7; my @weights = (1, 2, 3, 2, 1); my @allocation = round_fair($cents, @weights); print "@allocation "; # output will be one of the following: # 0 1 3 2 1 # 0 2 2 2 1 # 0 2 3 1 1 # 0 2 3 2 0 # 1 1 2 2 1 # 1 1 3 1 1 # 1 1 3 2 0 # 1 2 2 1 1 # 1 2 2 2 0 my @total; for ( 1..900 ) { @allocation = round_fair($cents, @weights); @total += @allocation for 0..$#allocation; } print "@total "; # output will be *near* 700 1400 2100 1400 700, e.g.: # 698 1411 2096 1418 677 Requirements: · Perl

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