# How Voting Systems Work 4, Exercise 3: how often do Copeland and Minimax disagree?
# Random profiles: 5 groups of 2 to 8 voters, 4 candidates, seeded (assumed model).
# Count profiles with no Condorcet winner, and among those, how often the two methods
# pick different single winners.
import itertools
import random

def pairwise(ballots):
    names = sorted(ballots[0])
    return {(x, y): sum(1 for b in ballots if b.index(x) < b.index(y))
            for x in names for y in names if x != y}

random.seed(4)
perms = list(itertools.permutations(("Ana", "Bo", "Cy", "Di")))
trials = 5000
no_winner = differ = 0
for _ in range(trials):
    groups = [(random.randint(2, 8), random.choice(perms)) for _ in range(5)]
    ballots = [r for count, r in groups for _ in range(count)]
    wins, n = pairwise(ballots), len(ballots)
    names = sorted(ballots[0])
    if any(all(wins[x, y] > n / 2 for y in names if y != x) for x in names):
        continue
    no_winner += 1
    cope = {x: sum((wins[x, y] > wins[y, x]) - (wins[x, y] < wins[y, x]) for y in names if y != x)
            for x in names}
    mini = {x: max([wins[y, x] for y in names if y != x and wins[y, x] > wins[x, y]], default=0)
            for x in names}
    c = [x for x in names if cope[x] == max(cope.values())]
    m = [x for x in names if mini[x] == min(mini.values())]
    if len(c) == 1 and len(m) == 1 and c != m:
        differ += 1
print("profiles with no Condorcet winner:", no_winner, "of", trials)
print("single winners that differ:", differ)

# Output when run:
# profiles with no Condorcet winner: 892 of 5000
# single winners that differ: 6