chores.py

import random

N = 4 # Number of chores
p = 2 # Number of players

preferences = []
for i in range(p):
    vs = list(range(N))
    random.shuffle(vs)
    preferences.append(vs)

def _vectors(xs, n_entries):
    if n_entries == 0:
        yield xs
    else:
        for i in range(p):
            for v in _vectors(xs+[i], n_entries-1):
                yield v


def vectors(n_entries):
    return _vectors([], n_entries)


def score(vs, preferences):
    sums = [0 for _ in preferences]
    for chore, person in enumerate(vs):
        rank = preferences[person][chore]
        sums[person] += rank
    return sum(x*x for x in sums)

sorted_allocations = sorted(vectors(N), key=lambda vs: score(vs, preferences))
for vs in sorted_allocations:
    print(f'{score(vs, preferences)}\t{vs}')