[FIXED] Calculate the prorata weight of a list of numbers (including negative) in Python

Issue

I am looking for a way to distribute a positive number proportionally to a list of numbers based on their value (higher gets more). Think of it as distributing a fixed bonus amount based on everyone's performance (pnl).

This is simple if the numbers are all positive. The prorata weight of [1,2,3] would be [1/6, 2/6, 3/6]. But I am not sure how to handle the case for something like [-1, 2, 3] in code?

Solution

In the absence of additional information: if the weights for [1,2,3] are [1/6, 2/6, 3/6], then for [-1,2,3] they would be [-1/4, 2/4, 3/4].

Example:

def get_weights(p, nums):
    total = sum(nums)
    return [p * num / total for num in nums]
    
print(get_weights(1, [1, 2, 3]))
print(get_weights(1, [-1, 2, 3]))

Output:

[0.16666666666666666, 0.3333333333333333, 0.5]
[-0.25, 0.5, 0.75]

UPDATED:

Based on OP's updated question and comments, one "bonus" policy that could be adopted is:

• allocate a "base bonus" pool from which everyone receives an equal base bonus
• in addition, allocate a "rank bonus" pool from which everyone receives an additional bonus pro rata with their performance ranking
• for the balance of the bonus pool, everyone with positive performance receives an additional bonus pro rata with their performance.

Example:

performance = [-1,2,3,-1]
bonus_pool = 1
base_bonus = 0.1
rank_bonus = 0.1
# rank items in the list `performance` and allocate the rank_bonus pro rata to rank
from collections import Counter
c = Counter(performance)
rank = {x[1][0][0]:(x[0] + 1, x[1][0][1]) for x in enumerate(zip(sorted(c.items())))}
total_rank = sum(v[0]*v[1] for v in rank.values())

pro_rata_bonus = 1 - base_bonus - rank_bonus
total_pro_rata = sum(x for x in performance if x > 0)
n = len(performance)
bonus_base = [bonus_pool * base_bonus / n for k in performance]
bonus_rank = [bonus_pool * rank_bonus * rank[k][0] / total_rank for k in performance]
bonus_pro_rata = [bonus_pool * pro_rata_bonus * max(k, 0) / total_pro_rata for k in performance]
bonus = [bonus_pool * (base_bonus / n + rank_bonus * rank[k][0] / total_rank + 
    pro_rata_bonus * max(k, 0) / total_pro_rata) for k in performance]


print(f'performance   :', end=''); [print(f' {x:5}',end='') for x in performance]; print(f' TOTAL: {sum(performance):5}')
print(f'bonus_base    :', end=''); [print(f' {x:0.3f}',end='') for x in bonus_base]; print(f' TOTAL: {sum(bonus_base):0.3f}')
print(f'bonus_rank    :', end=''); [print(f' {x:0.3f}',end='') for x in bonus_rank];  print(f' TOTAL: {sum(bonus_rank):0.3f}')
print(f'bonus_pro_rata:', end=''); [print(f' {x:0.3f}',end='') for x in bonus_pro_rata];  print(f' TOTAL: {sum(bonus_pro_rata):0.3f}')
print(f'---------------', end=''); [print(f'------',end='') for x in bonus]; print()
print(f'bonus         :', end=''); [print(f' {x:0.3f}',end='') for x in bonus];  print(f' TOTAL: {sum(bonus):0.3f}')

Output:

performance   :    -1     2     3    -1 TOTAL:     3
bonus_base    : 0.025 0.025 0.025 0.025 TOTAL: 0.100
bonus_rank    : 0.014 0.029 0.043 0.014 TOTAL: 0.100
bonus_pro_rata: 0.000 0.320 0.480 0.000 TOTAL: 0.800
---------------------------------------
bonus         : 0.039 0.374 0.548 0.039 TOTAL: 1.000

Answered By - constantstranger