Created
March 30, 2016 09:42
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Updated geryrmandering code
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import z3 | |
import pulp | |
def validate(districts, pro): | |
if not districts: | |
raise ValueError("Must have at least one district") | |
for v in districts: | |
if v <= 0: | |
raise ValueError("Invalid district size %r" % (v,)) | |
population = sum(districts) | |
if pro <= 0: | |
raise ValueError("Invalid pro population %r" % (pro,)) | |
if pro > population: | |
raise ValueError("Can't have more people pro that population") | |
if pro == population: | |
raise ValueError("Can't have everyone pro") | |
def gerrymanderz3(districts, pro): | |
districts = list(districts) | |
validate(districts, pro) | |
solver = z3.Optimize() | |
populations = [z3.Int('Pop%d' % (i,)) for i in range(len(districts))] | |
wins = [] | |
for i, (p, d) in enumerate(zip(populations, districts)): | |
solver.add(p >= 0) | |
solver.add(p <= d) | |
win = z3.Int('Win%d' % (i,)) | |
solver.add(z3.Implies( | |
p * 2 > d, win == 1 | |
)) | |
solver.add(z3.Implies( | |
p * 2 <= d, win == 0 | |
)) | |
wins.append(win) | |
solver.add(sum(populations) == pro) | |
wincount = z3.Int('wincount') | |
solver.add(wincount == sum(wins)) | |
assert solver.check() == z3.sat | |
lo = 0 | |
hi = len(districts) + 1 | |
# Invariant: There is a partition with at least lo districts majority pro | |
# Invariant: There is no partition with at least hi districts majority pro | |
while lo + 1 < hi: | |
mid = (lo + hi) // 2 | |
solver.push() | |
solver.add(wincount >= mid) | |
check = solver.check() | |
if check == z3.unsat: | |
hi = mid | |
else: | |
lo = mid | |
solver.pop() | |
solver.add(wincount >= lo) | |
res = solver.check() | |
assert res == z3.sat, res | |
m = solver.model() | |
return [m[p] for p in populations], lo | |
def gerrymanderlp(districts, pro): | |
validate(districts, pro) | |
problem = pulp.LpProblem('gerrymander', pulp.LpMaximize) | |
votes = [ | |
pulp.LpVariable( | |
'Pop%d' % (i,), cat='Integer', | |
lowBound=0, upBound=v | |
) | |
for i, v in enumerate(districts) | |
] | |
wins = [] | |
for i, (population, count) in enumerate(zip(districts, votes)): | |
win = pulp.LpVariable( | |
'Win%d' % (i,), cat='Integer', lowBound=0, upBound=1) | |
wins.append(win) | |
loss_ceiling = population // 2 | |
if loss_ceiling > 0: | |
loss = pulp.LpVariable( | |
'Loss%d' % (i,), cat='Integer', lowBound=0, | |
upBound=loss_ceiling) | |
problem.add(loss * (1.0 / loss_ceiling) >= win) | |
else: | |
loss = 0 | |
problem.add(loss + win <= count) | |
assert len(wins) == len(votes) == len(districts) | |
problem.add(sum(votes) == pro) | |
problem.objective = sum(wins) | |
problem.solve() | |
votes_per_district = [int(p.varValue) for p in votes] | |
votes_per_district.sort(reverse=True) | |
return ( | |
votes_per_district, | |
int(sum(w.varValue for w in wins)) | |
) | |
def gerrymandergreedy(districts, pro): | |
districts = sorted(districts) | |
wins = 0 | |
results = [] | |
for d in districts: | |
win = (d // 2) + 1 | |
if win <= pro: | |
pro -= win | |
results.append(win) | |
wins += 1 | |
else: | |
pro = 0 | |
results.append(pro) | |
return results, wins |
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from gerry import gerrymanderz3, gerrymanderlp, gerrymandergreedy | |
from hypothesis import given, assume, example | |
from hypothesis import strategies as st | |
import pytest | |
@st.composite | |
def problem(draw): | |
districts = draw( | |
st.lists( | |
st.integers(min_value=1, max_value=100), | |
min_size=1, max_size=5) | |
) | |
population = sum(districts) | |
assert population >= 1 | |
assume(population >= 2) | |
return districts, draw(st.integers(1, population - 1)) | |
implementations = [gerrymanderz3, gerrymanderlp, gerrymandergreedy] | |
gerrytest = pytest.mark.parametrize( | |
'gerrymander', implementations) | |
@gerrytest | |
def test_can_gerrymander_majority_to_total(gerrymander): | |
_, count = gerrymander([3] * 3, 6) | |
assert count == 3 | |
@gerrytest | |
def test_can_arrange_a_win_for_a_minority(gerrymander): | |
_, count = gerrymander([3] * 3, 2) | |
assert count == 1 | |
@gerrytest | |
@given(problem()) | |
def test_handles_arbitrary_data(gerrymander, problem): | |
gerrymander(*problem) | |
@gerrytest | |
@given(problem()) | |
def test_increasing_population_increases_maximum(gerrymander, problem): | |
districts, pro = problem | |
assume(pro + 1 < sum(districts)) | |
_, c1 = gerrymander(districts, pro) | |
_, c2 = gerrymander(districts, pro + 1) | |
assert c1 <= c2 | |
@example(([2, 2], 2)) | |
@example(([1, 1], 1)) | |
@given(problem()) | |
def test_counts_agree(problem): | |
cs = [g(*problem) for g in implementations] | |
assert len({c for _, c in cs}) == 1 |
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