A weighted version of random.choice

I needed to write a weighted version of random.choice (each element in the list has a different probability for being selected). This is what I came up with:

def weightedChoice(choices):
    """Like random.choice, but each element can have a different chance of
    being selected.

    choices can be any iterable containing iterables with two items each.
    Technically, they can have more than two items, the rest will just be
    ignored.  The first item is the thing being chosen, the second item is
    its weight.  The weights can be any numeric values, what matters is the
    relative differences between them.
    """
    space = {}
    current = 0
    for choice, weight in choices:
        if weight > 0:
            space[current] = choice
            current += weight
    rand = random.uniform(0, current)
    for key in sorted(space.keys() + [current]):
        if rand < key:
            return choice
        choice = space[key]
    return None

This function seems overly complex to me, and ugly. I’m hoping everyone here can offer some suggestions on improving it or alternate ways of doing this. Efficiency isn’t as important to me as code cleanliness and readability.

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