I'm simulating US governmental structure and I have a list of n voters (random length between 10,000 and 100,000).
I'd like to create constituencies, which means subdividing that into states, and thence into districts.
All of these are randomly sized.
How can I take a list of n elements and create m lists of random size, which together constitute the original n?
import numpy as np
from numpy.random import multinomial, shuffle
from more_itertools import split_into
# Create test data
x = np.array(range(20))
# Shuffle test data
shuffle(x)
# Split into 5 constituencies
m = 5
constituencies = multinomial(len(x), [1/m] * m)
result = list(split_into(x, constituencies))
# [[3, 16, 9, 8, 15, 2, 6], [4], [12, 18, 5], [1, 11, 0, 17, 14, 19], [13, 7, 10]]
The multinomial function here tells us how many times each of m results occurs after len(x) experiments have been performed, given that the result of an experiment is one of the m results. Thus, the sum of all of the values is equal to the number of experiments -- len(x). Then, we use split_into, which will split the data up into groups, where the size of group i is equal to the value at constituencies[i].
This next part of the code is the "easy" part, but I couldn't find a way to write it nicely. Obviously we don't want zero person constituencies, so if anyone has a better way of redistributing the values to ensure there are no zeroes, please suggest them! With that said, this code works:
zero_count = 0
for idx, value in enumerate(constituencies):
if value == 0:
constituencies[idx] += 1
zero_count += 1
elif zero_count > 0 and value > 1:
constituencies[idx] -= 1
zero_count -= 1
while zero_count > 0:
for idx, value in enumerate(constituencies):
if value > 1:
constituencies[idx] -= 1
zero_count -= 1
if zero_count == 0:
break
You'll want to insert this block right below the constituencies definition to ensure no constituencies have a size of zero.
Note: This only works if your x has at least m elements: it will get stuck in an infinite loop otherwise.
After further thought, I realized that we could write the code for constituencies with at least min_size people in the following way:
import numpy as np
from numpy.random import multinomial, shuffle
from more_itertools import split_into
# Create test data
x = np.array(range(20))
# Shuffle test data
shuffle(x)
# Split into 5 constituencies
m = 5
min_size = 2
# List of length m, where the ith entry is the number
# of people in the ith constituency
constituencies = multinomial(len(x) - m * min_size, [1/m] * m)
constituencies = [const_size + min_size for const_size in constituencies]
result = list(split_into(x, constituencies))
print(result)
In this case, if the size of your population -- len(x) -- is too small for your minimum population size, then the program will raise a ValueError going into multinomial. This method works by holding out min_size * m people, and then adding min_size to each constituency, ensuring randomness (given that x is sufficiently large) and a minimum constituency size.
As I've noticed the comments discuss the chosen probability distribution for constituency size, note that the final argument of multinomial: [1/m] * m, is the probability distribution. Here, I use a uniform probability distribution, but you can provide whichever works best for you (so long as it has m elements).
