# How Voting Systems Work 6, Exercise 2: burying under the Borda count
# Assumed, invented profile: 9 voters, three candidates. Find one honest voter who can get a
# better winner by reordering their own ballot, and show the lie and the new points.
from itertools import permutations

def borda_points(ballots):
    k = len(ballots[0])
    points = {c: 0 for c in sorted(ballots[0])}
    for b in ballots:
        for place, c in enumerate(b):
            points[c] += k - 1 - place
    return points

def winner(points):
    return max(points, key=points.get)

groups = [
    (4, ("Ana", "Bo", "Cy")),
    (3, ("Bo", "Ana", "Cy")),
    (2, ("Cy", "Bo", "Ana")),
]
ballots = [r for n, r in groups for _ in range(n)]
honest = borda_points(ballots)
print("honest points:", honest, "->", winner(honest))
found = False
for i, truth in enumerate(ballots):
    for lie in permutations(truth):
        trial = ballots[:i] + [lie] + ballots[i + 1:]
        pts = borda_points(trial)
        if truth.index(winner(pts)) < truth.index(winner(honest)):
            print(f"voter {i} (true order {truth}) lies {lie}")
            print("points after the lie:", pts, "->", winner(pts))
            found = True
            break
    if found:
        break
if not found:
    print("no single voter can gain")

# Output when run:
# honest points: {'Ana': 11, 'Bo': 12, 'Cy': 4} -> Bo
# voter 0 (true order ('Ana', 'Bo', 'Cy')) lies ('Ana', 'Cy', 'Bo')
# points after the lie: {'Ana': 11, 'Bo': 11, 'Cy': 5} -> Ana