# How Voting Systems Work 2, Exercise 2: how often does a loser change the result?
# One-dimensional race (assumed model): voters and candidates sit at random
# points on a line from 0 to 1, and each voter ranks candidates by distance.
# Count how often removing a losing candidate changes the plurality winner.
import random
from collections import Counter

def plurality_winner(positions, voters):
    counts = Counter(min(positions, key=lambda c: abs(positions[c] - v)) for v in voters)
    top = max(counts.values())
    return sorted(c for c, n in counts.items() if n == top)

random.seed(31)
trials = 3000
for k in (3, 4, 5):
    changed = 0
    for _ in range(trials):
        voters = [random.random() for _ in range(101)]
        positions = {f"C{i}": random.random() for i in range(k)}
        base = plurality_winner(positions, voters)
        loser = next(c for c in sorted(positions) if c not in base)
        smaller = {c: p for c, p in positions.items() if c != loser}
        if plurality_winner(smaller, voters) != base:
            changed += 1
    print(f"{k} candidates: withdrawing one loser changed the winner in {changed / trials:.1%} of {trials} races")

# Output when run:
# 3 candidates: withdrawing one loser changed the winner in 24.1% of 3000 races
# 4 candidates: withdrawing one loser changed the winner in 23.3% of 3000 races
# 5 candidates: withdrawing one loser changed the winner in 23.5% of 3000 races