def test_strict_majority(tiebreaker):
A, B, C = 0, 1, 2
election = [
[A, B, C],
[B, C, A],
[A, C, B],
]
assert coombs(election, tiebreaker) == A
election = [
*3 * [[A, B, C]],
*7 * [[B, C, A]],
*2 * [[C, B, A]],
]
assert coombs(election, tiebreaker) == B
def test_no_tiebreak_tied_losers():
A, B, C = 0, 1, 2
election = [
[A, B, C],
[B, C, A],
[A, C, B],
[B, C, A],
[C, B, A],
[C, A, B],
[C, A, B],
]
assert coombs(election) is None
def test_one_round():
# 60% majority, tie between others
election = np.array([[2, 0, 1], [0, 1, 2], [2, 0, 1], [1, 2, 0], [2, 1, 0],
[2, 0, 1], [1, 0, 2], [2, 0, 1], [2, 1, 0], [0, 2,
1]])
assert coombs(election) == 2
assert coombs(election, tiebreaker='order') == 2
assert coombs(election, tiebreaker='random') == 2
# 50% winner, 30%, 20% for others
# In this case, Candidate 2 picks up an additional vote in the runoff,
# making it unambiguous.
election = np.array([[2, 0, 1], [0, 1, 2], [1, 0, 2], [2, 0, 1], [2, 1, 0],
[0, 1, 2], [2, 0, 1], [1, 2, 0], [2, 1, 0], [0, 2,
1]])
assert coombs(election) == 2
assert coombs(election, tiebreaker='order') == 2
assert coombs(election, tiebreaker='random') == 2
# 50%, 30%, 20%
# This is ambiguous. It would make sense for the 50% candidate to win
# outright, but technically they don't have a majority, so we have to
# eliminate another, so there's now a 50/50 split, and then tiebreak
# between the two, which might pick a different candidate, even though they
# got fewer first-preference votes.
election = np.array([[2, 0, 1], [0, 1, 2], [1, 0, 2], [2, 0, 1], [2, 1, 0],
[0, 1, 2], [2, 0, 1], [1, 0, 2], [2, 0, 1], [0, 2,
1]])
assert coombs(election) is None
assert coombs(election, tiebreaker='order') == 0
assert collect_random_results(coombs, election) == {0, 2}
# 50% exact tie
election = np.array([[2, 1, 0], [1, 2, 0], [1, 2, 0], [2, 1, 0]])
assert coombs(election) is None
assert coombs(election, tiebreaker='order') == 1
assert collect_random_results(coombs, election) == {1, 2}
# Complete cycle, anyone can win
election = np.array([[0, 1, 2], [1, 2, 0], [2, 0, 1]])
assert coombs(election) is None
assert coombs(election, tiebreaker='order') == 0
assert collect_random_results(coombs, election) == {0, 1, 2}
def test_legit_winner_none(election):
election = np.asarray(election)
n_cands = election.shape[1]
assert coombs(election) in {None} | set(range(n_cands))
def test_legit_winner_order(election, tiebreaker):
election = np.asarray(election)
n_cands = election.shape[1]
assert coombs(election, tiebreaker) in range(n_cands)
def test_examples(tiebreaker):
# Standard Tennessee example (two-round)
# https://en.wikipedia.org/wiki/Template:Tenn_voting_example
Memphis, Nashville, Chattanooga, Knoxville = 0, 1, 2, 3
election = [
*42 * [[Memphis, Nashville, Chattanooga, Knoxville]],
*26 * [[Nashville, Chattanooga, Knoxville, Memphis]],
*15 * [[Chattanooga, Knoxville, Nashville, Memphis]],
*17 * [[Knoxville, Chattanooga, Nashville, Memphis]],
]
assert coombs(election, tiebreaker) == Nashville
# Four-round example from Ques 9
# http://www.yorku.ca/bucovets/4380/exercises/exercises_1_a.pdf
v, w, x, y, z = 0, 1, 2, 3, 4
election = [
*11 * [[v, w, x, y, z]],
*12 * [[w, x, y, z, v]],
*13 * [[x, v, w, y, z]],
*14 * [[y, w, v, z, x]],
*15 * [[z, v, x, w, y]],
]
assert coombs(election, tiebreaker) == v
# Two-round example from
# http://pi.math.cornell.edu/~ismythe/Lec_04_web.pdf#page=16
A, B, C = 0, 1, 2
election = [
[A, C, B],
[A, C, B],
[B, C, A],
[B, C, A],
[C, A, B],
]
assert coombs(election, tiebreaker) == C # "? C wins under Coombs "?
# Homework example from
# https://www.slader.com/discussion/question/the-coombs-method-this-method-is-just-like-the-plurality-with-elimination-method-except-that-in-each/#
A, B, C, D = 0, 1, 2, 3
election = [
*14 * [[A, B, C, D]],
*10 * [[C, B, D, A]],
*8 * [[D, C, B, A]],
*4 * [[B, D, C, A]],
*1 * [[C, D, B, A]],
]
assert coombs(election, tiebreaker) == C
# Example from http://pi.math.cornell.edu/~ismythe/Lec_05_web.pdf#page=2
A, B, C, D, E = 0, 1, 2, 3, 4
election = [
*4 * [[A, C, D, B, E]],
*3 * [[B, E, D, C, A]],
*2 * [[C, B, D, A, E]],
*1 * [[D, B, E, C, A]],
*1 * [[E, D, B, A, C]],
]
assert coombs(election, tiebreaker) == C
# Example from
# https://medium.com/@t2ee6ydscv/how-ranked-choice-voting-elects-extremists-fa101b7ffb8e
r, b, g, o, y = 0, 1, 2, 3, 4
election = [
*31 * [[r, b, g, o, y]],
*5 * [[b, r, g, o, y]],
*8 * [[b, g, r, o, y]],
*1 * [[b, g, o, r, y]],
*6 * [[g, b, o, r, y]],
*1 * [[g, b, o, y, r]],
*6 * [[g, o, b, y, r]],
*2 * [[o, g, b, y, r]],
*5 * [[o, g, y, b, r]],
*7 * [[o, y, g, b, r]],
*28 * [[y, o, g, b, r]],
]
assert coombs(election) == g