# How Voting Systems Work 5, Exercise 3: how often do plurality and Borda pick the Condorcet winner?
# Two assumed models, 3,000 seeded elections each, 5 candidates, 51 voters.
import random
from collections import Counter

def pairwise(ballots):
    names = sorted(ballots[0])
    return {(x, y): sum(1 for b in ballots if b.index(x) < b.index(y))
            for x in names for y in names if x != y}

def condorcet(ballots):
    wins, n = pairwise(ballots), len(ballots)
    for x in ballots[0]:
        if all(wins[x, y] > n / 2 for y in ballots[0] if y != x):
            return x
    return None

random.seed(5)
trials, voters, k = 3000, 51, 5
names = [f"C{i}" for i in range(k)]
print("model            has CW   plurality picks CW   Borda picks CW")
for model in ("line", "random ballots"):
    found = plural_hits = borda_hits = 0
    for _ in range(trials):
        if model == "line":
            pos = {c: random.random() for c in names}
            ballots = []
            for _ in range(voters):
                v = random.random()
                ballots.append(tuple(sorted(names, key=lambda c: abs(pos[c] - v))))
        else:
            ballots = [tuple(random.sample(names, k)) for _ in range(voters)]
        cw = condorcet(ballots)
        if cw is None:
            continue
        found += 1
        plural = Counter(b[0] for b in ballots)
        borda = Counter()
        for b in ballots:
            for place, c in enumerate(b):
                borda[c] += k - 1 - place
        plural_hits += max(plural, key=plural.get) == cw
        borda_hits += max(borda, key=borda.get) == cw
    print(f"{model:<15} {found / trials:7.1%} {plural_hits / found:14.1%} {borda_hits / found:20.1%}")

# Output when run:
# model            has CW   plurality picks CW   Borda picks CW
# line             100.0%          40.7%                78.9%
# random ballots    74.6%          60.4%                85.3%