# How Voting Systems Work 3, Exercise 1: a two-round runoff on a four-candidate club vote
# 30 members rank four candidates (assumed, invented numbers).
# Report round 1, whether anyone has a majority, and the runoff if needed.
# Then check: does the runoff winner also win every head-to-head contest?
from collections import Counter

profile = (
    [("Ana", "Bo", "Cy", "Di")] * 9
    + [("Bo", "Cy", "Ana", "Di")] * 7
    + [("Cy", "Bo", "Di", "Ana")] * 8
    + [("Di", "Cy", "Bo", "Ana")] * 6
)
n = len(profile)
first = Counter(b[0] for b in profile)
print("round 1:", dict(sorted(first.items())), f"(majority needs more than {n / 2:g})")
ranked = sorted(first, key=lambda c: (-first[c], c))
if first[ranked[0]] > n / 2:
    winner = ranked[0]
    print("outright winner:", winner)
else:
    a, b = ranked[:2]
    a_votes = sum(1 for x in profile if x.index(a) < x.index(b))
    print(f"no majority; runoff {a} vs {b}: {a_votes} to {n - a_votes}")
    winner = a if a_votes > n - a_votes else b
    print("runoff winner:", winner)

beats_all = all(
    sum(1 for x in profile if x.index(winner) < x.index(y)) > n / 2
    for y in profile[0] if y != winner
)
print("beats every rival head to head:", beats_all)
for y in sorted(profile[0]):
    if y != winner:
        w = sum(1 for x in profile if x.index(winner) < x.index(y))
        print(f"  {winner} vs {y}: {w} to {n - w}")

# Output when run:
# round 1: {'Ana': 9, 'Bo': 7, 'Cy': 8, 'Di': 6} (majority needs more than 15)
# no majority; runoff Ana vs Cy: 9 to 21
# runoff winner: Cy
# beats every rival head to head: False
#   Cy vs Ana: 21 to 9
#   Cy vs Bo: 14 to 16
#   Cy vs Di: 24 to 6