# How Voting Systems Work 9, Exercise 1: dictators, veto holders and dummies
# Assumed systems (invented): each is (weights, quota).

def roles(weights, quota):
    n = len(weights)
    total = sum(weights)
    out = []
    for i in range(n):
        alone = weights[i] >= quota                      # wins with nobody else
        veto = total - weights[i] < quota                # the rest cannot reach the quota without i
        dummy = True                                     # never critical in any winning coalition
        for mask in range(1 << n):
            if mask >> i & 1:
                t = sum(weights[j] for j in range(n) if mask >> j & 1)
                if t >= quota and t - weights[i] < quota:
                    dummy = False
                    break
        out.append("dictator" if alone else "veto" if veto else "dummy" if dummy else "ordinary")
    return out

systems = {
    "one big shareholder": ([51, 25, 24], 51),
    "unanimity":           ([40, 30, 30], 100),
    "49/48/3 parliament":  ([49, 48, 3], 51),
    "board 9,9,7,3,1,1":   ([9, 9, 7, 3, 1, 1], 16),
    "quota 60 of 100":    ([30, 20, 20, 15, 15], 60),
}
for name, (w, q) in systems.items():
    print(f"{name:<20} quota {q:>3}/{sum(w):<3} ->", ", ".join(roles(w, q)))

# Output when run:
# one big shareholder  quota  51/100 -> dictator, dummy, dummy
# unanimity            quota 100/100 -> veto, veto, veto
# 49/48/3 parliament   quota  51/100 -> ordinary, ordinary, ordinary
# board 9,9,7,3,1,1    quota  16/30  -> ordinary, ordinary, ordinary, dummy, dummy, dummy
# quota 60 of 100      quota  60/100 -> ordinary, ordinary, ordinary, ordinary, ordinary