python - Distributing integers using weights? How to calculate?

Question

I need to distribute a value based on some weights. For example, if my weights are 1 and 2, then I would expect the column weighted as 2 to have twice the value as the column weighted 1.

I have some Python code to demonstrate what I'm trying to do, and the problem:

def distribute(total, distribution):
    distributed_total = []
    for weight in distribution:
        weight = float(weight)
        p = weight/sum(distribution)
        weighted_value = round(p*total)
        distributed_total.append(weighted_value)
    return distributed_total

for x in xrange(100):
    d = distribute(x, (1,2,3))
    if x != sum(d):
        print x, sum(d), d

There are many cases shown by the code above where distributing a value results in the sum of the distribution being different than the original value. For example, distributing 3 with weights of (1,2,3) results in (1,1,2), which totals 4.

What is the simplest way to fix this distribution algorithm?

UPDATE:

I expect the distributed values to be integer values. It doesn't matter exactly how the integers are distributed as long as they total to the correct value, and they are "as close as possible" to the correct distribution.

(By correct distribution I mean the non-integer distribution, and I haven't fully defined what I mean by "as close as possible." There are perhaps several valid outputs, so long as they total the original value.)

Answer 1

Distribute the first share as expected. Now you have a simpler problem, with one fewer participants, and a reduced amount available for distribution. Repeat until there are no more participants.

>>> def distribute2(available, weights):
...     distributed_amounts = []
...     total_weights = sum(weights)
...     for weight in weights:
...         weight = float(weight)
...         p = weight / total_weights
...         distributed_amount = round(p * available)
...         distributed_amounts.append(distributed_amount)
...         total_weights -= weight
...         available -= distributed_amount
...     return distributed_amounts
...
>>> for x in xrange(100):
...     d = distribute2(x, (1,2,3))
...     if x != sum(d):
...         print x, sum(d), d
...
>>>