# How Voting Systems Work 4, Exercise 2: Copeland and Minimax on a cycle
# Three groups with rotated rankings (assumed numbers: 12, 9 and 6 voters).
# Compute Copeland scores and Minimax worst defeats, and see what each method does.
ballots = (
    [("Ann", "Ben", "Cat")] * 12
    + [("Ben", "Cat", "Ann")] * 9
    + [("Cat", "Ann", "Ben")] * 6
)
names = sorted(ballots[0])
wins = {(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}
for x in names:
    for y in names:
        if x < y:
            print(f"{x} vs {y}: {wins[x, y]} to {wins[y, x]}")
copeland = {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}
minimax = {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}
print("Copeland scores:", copeland)
print("Minimax worst defeats:", minimax)
best = min(minimax.values())
print("Copeland winners:", [x for x in names if copeland[x] == max(copeland.values())])
print("Minimax winners:", [x for x in names if minimax[x] == best])

# Output when run:
# Ann vs Ben: 18 to 9
# Ann vs Cat: 12 to 15
# Ben vs Cat: 21 to 6
# Copeland scores: {'Ann': 0, 'Ben': 0, 'Cat': 0}
# Minimax worst defeats: {'Ann': 15, 'Ben': 18, 'Cat': 21}
# Copeland winners: ['Ann', 'Ben', 'Cat']
# Minimax winners: ['Ann']