# How Voting Systems Work 1, Exercise 1: a club vote, counted two ways
# A club of 15 members ranks four candidates (assumed, invented numbers).
# Find the plurality winner and its share, say whether it is a majority,
# then play every head-to-head contest and look for a Condorcet winner.
from collections import Counter
from itertools import combinations

profile = (
    [("Ann", "Ben", "Cat", "Dan")] * 5
    + [("Ben", "Cat", "Ann", "Dan")] * 4
    + [("Cat", "Ben", "Dan", "Ann")] * 3
    + [("Dan", "Cat", "Ben", "Ann")] * 3
)
names = sorted({c for b in profile for c in b})
total = len(profile)

firsts = Counter(b[0] for b in profile)
winner, top = firsts.most_common(1)[0]
print("first choices:", dict(firsts))
print(f"plurality winner: {winner} with {top / total:.1%}; majority: {top > total / 2}")

wins = {n: 0 for n in names}
for x, y in combinations(names, 2):
    vx = sum(1 for b in profile if b.index(x) < b.index(y))
    vy = total - vx
    print(f"{x} vs {y}: {vx} to {vy}")
    if vx > vy:
        wins[x] += 1
    elif vy > vx:
        wins[y] += 1

print("head-to-head wins:", wins)
condorcet = [n for n in names if wins[n] == len(names) - 1]
print("Condorcet winner:", condorcet[0] if condorcet else "none")

# Output when run:
# first choices: {'Ann': 5, 'Ben': 4, 'Cat': 3, 'Dan': 3}
# plurality winner: Ann with 33.3%; majority: False
# Ann vs Ben: 5 to 10
# Ann vs Cat: 5 to 10
# Ann vs Dan: 9 to 6
# Ben vs Cat: 9 to 6
# Ben vs Dan: 12 to 3
# Cat vs Dan: 12 to 3
# head-to-head wins: {'Ann': 1, 'Ben': 3, 'Cat': 2, 'Dan': 0}
# Condorcet winner: Ben