-
Notifications
You must be signed in to change notification settings - Fork 0
/
gerrymander.py
504 lines (411 loc) · 18.8 KB
/
gerrymander.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
"""File: gerrymander.py
Authors: MBWhitestone, csirika & stefanklut
UvA Computational Social Choice Project.
This file contains an implementations of gerrymandering
models & algorithms with uncertain voters.
May 2020
"""
import operator as op
from functools import reduce
from itertools import combinations
import numpy as np
from tqdm import tqdm
from astar import a_star
class Model():
"""Main model class."""
def __init__(self, n_dims=0, n_dists=15, units_in_dist=100, unit_size=1,
shape=(15, 100)):
"""Initialize a model."""
assert n_dims in [0, 1, 2]
self.n_dims = n_dims
self.n_dists = n_dists
self.units_in_dist = units_in_dist
self.total_units = n_dists * units_in_dist
model = [Unit(n=unit_size) for u in range(self.total_units)]
# For 0D use set of Units, 1D & 2D use numpy array of Units
if n_dims == 1:
model = np.array(model)
elif n_dims == 2:
assert shape[0] * shape[1] == self.total_units
model = np.array(model).reshape(shape)
for x, y in np.ndindex(shape):
model[x, y].set_x_y(x, y)
self.model = model
def resample(self):
"""Resample voter preferences in all units of the model."""
for unit in self.model:
if isinstance(unit, Unit):
unit.sample()
else:
for u in unit:
u.sample()
class Unit():
"""Neighbourhood."""
def __init__(self, n=1, distribution='uniform'):
"""Initialize neighbourhood."""
self.n = n
self.distribution = distribution
self.sample()
def sample(self):
"""Sample voter preferences."""
if self.distribution == 'uniform':
self.voters = np.random.uniform(0, 1, self.n)
self.average = np.mean(self.voters)
self.median = np.median(self.voters)
else:
raise "Unknown distribution."
def vote(self):
"""Return votes according to preferences."""
return np.random.binomial(1, self.voters)
def get(self, attribute):
"""Return attribute of Unit."""
if attribute == 'average':
return self.average
else:
return self.median
def set_x_y(self, x, y):
self.x = x
self.y = y
def __repr__(self):
"""Returns representation of Unit."""
return f"U(n={self.n}, μ={round(self.average, 2)} " + \
f"~={round(self.median, 2)})"
def __lt__(self, other):
"""Needed for A* queue."""
if isinstance(other, Unit):
other = other.average
return self.average < other
def __str__(self):
"""Returns representation of Unit."""
return self.__repr__()
class GerryMander():
"""Defines different gerrymandering attempts."""
def __init__(self, winner=1, n_samples=100, algorithm='brute-force',
tie_breaking='coin'):
"""Inits the GerryMander with algorithm, tie and samples."""
assert winner in [0, 1], "Winner should be 0 or 1"
self.winner = winner
self.n_samples = n_samples
self.algorithm = algorithm
self.tie_breaking = tie_breaking
@staticmethod
def partitions(n_agents, items):
"""Return partitions of items for n agents.
Based on: https://stackoverflow.com/questions/42290859/
generate-all-equal-sized-partitions-of-a-set.
"""
if n_agents == 1:
yield [items]
else:
quota = len(items) // n_agents
for indexes in combinations(range(len(items)), quota):
remainder = items[:]
selection = [remainder.pop(i) for i in reversed(indexes)]
for result in GerryMander.partitions(n_agents - 1, remainder):
result.append(selection)
yield result
def wins(self, votes):
"""Returns a winner based on votes."""
mean = np.mean(votes)
if mean == .5 and self.tie_breaking == "coin":
return np.random.randint(0, 2)
return mean > .5
def score(self, districts):
"""Returns winner after samples elections in all districts."""
wins = self.wins
return np.mean([wins([wins([unit.vote() for unit in district])
for district in districts])
for sample in range(self.n_samples)])
@staticmethod
def nCr(n, r):
"""Returns nCr.
See https://stackoverflow.com/questions/4941753/
is-there-a-math-ncr-function-in-python.
"""
r = min(r, n - r)
numer = reduce(op.mul, range(n, n - r, -1), 1)
denom = reduce(op.mul, range(1, r + 1), 1)
return numer / denom
def _brute_force(self, partitions):
"""Returns brute force best partition in model."""
winning_score = 1 - self.winner
winning_partition = None
losing_partition = None
losing_score = self.winner
rel = op.gt if self.winner else op.lt
for districts in tqdm(partitions):
score = self.score(districts)
if rel(score, winning_score):
winning_score = score
winning_partition = districts
if rel(losing_score, score):
losing_score = score
losing_partition = districts
return winning_score, winning_partition, losing_score, losing_partition
def _sort(self, units, param):
"""Sort units based on param."""
return np.array(sorted(units, key=lambda unit: unit.get(param),
reverse=not self.winner))
def _packing(self, model, n_packs=1, units=None, param='median'):
"""Implements packing technique packing voters of party x together."""
assert model.n_dists >= n_packs, "Not enough districts for packs."
if units is None:
units = model.model
sorted_units = self._sort(units, param)
pu = n_packs * model.units_in_dist
w_score, w_districts = self._score_stack(sorted_units[:pu],
sorted_units[pu:], model)
l_score, l_districts = self._score_stack(sorted_units[-pu:],
sorted_units[:-pu], model)
return w_score, w_districts, l_score, l_districts
def _score_stack(self, made_districts, rest, model):
"""Randomly assign the not already assigned."""
made_districts = made_districts.reshape(-1, model.units_in_dist)
todo = (np.random.permutation(rest)).reshape(-1, model.units_in_dist)
districts = np.vstack((made_districts, todo))
score = self.score(districts)
return score, districts
def _cracking(self, model, n_cracks=1, units=None, param='median'):
"""Implements cracking technique maximizing wasted votes."""
assert model.n_dists >= n_cracks, "Not enough districts for cracks."
if units is None:
units = model.model
cracks = self._sort(units, param).reshape(model.units_in_dist, -1)
w_score, w_districts = self._score_stack(cracks[:, -n_cracks:].T,
cracks[:, :-n_cracks].T,
model)
l_score, l_districts = self._score_stack(cracks[:, :n_cracks].T,
cracks[:, n_cracks:].T, model)
return w_score, w_districts, l_score, l_districts
def _pack_n_crack(self, model, packs=1, cracks=None, param='median'):
"""First pack then crack the remaining districts."""
if cracks is None:
cracks = model.n_dists - packs
_, wp_districts, _, lp_districts = self._packing(model, packs,
param=param)
w_packs = wp_districts[:packs]
l_packs = lp_districts[:packs]
w_units = wp_districts[packs:].flatten()
l_units = lp_districts[packs:].flatten()
_, wc_districts, _, _ = self._cracking(model, cracks, w_units,
param=param)
_, _, _, lc_districts = self._cracking(model, cracks, l_units,
param=param)
w_score, w_districts = self._score_stack(w_packs, wc_districts, model)
l_score, l_districts = self._score_stack(l_packs, lc_districts, model)
return w_score, w_districts, l_score, l_districts
def _solve_0D(self, model, ratio=None, param=None):
"""Returns optimal 0D partitioning for winner."""
if ratio is None:
ratio = round(.25 * model.n_dists)
else:
ratio = round(ratio * model.n_dists)
if self.algorithm == 'brute-force':
n, s = model.total_units, 1
while n != model.units_in_dist:
s *= GerryMander.nCr(n, model.units_in_dist)
n -= model.units_in_dist
print(f'This will take me {s} iterations...')
partitions = GerryMander.partitions(model.n_dists, model.model)
return self._brute_force(partitions)
elif self.algorithm == "packing":
return self._packing(model, ratio, param)
elif self.algorithm == "cracking":
return self._cracking(model, param=param, n_cracks=ratio)
elif self.algorithm == "pracking":
return self._pack_n_crack(model, ratio, param=param)
raise NotImplementedError
def _solve_1D(self, model):
"""Returns optimal 1D (circle) partitioning for winner."""
if self.algorithm == 'brute-force':
circ = model.model.reshape(model.n_dists, model.units_in_dist)
partitions = [np.roll(circ, i) for i in range(model.units_in_dist)]
return self._brute_force(partitions)
raise NotImplementedError
def _solve_2D(self, model):
"""Returns optimal 2D partitioning for winner."""
if self.algorithm == "a_star":
initial = [[] for _ in range(model.n_dists)]
nodes = list(model.model.flatten())
w_solution = a_star((initial, nodes), model.model, self.winner,
model.total_units)
w_score = self.score(w_solution[0])
print(w_solution[0])
l_solution = a_star((initial, nodes), model.model, 1 - self.winner,
model.total_units)
l_score = self.score(l_solution[0])
print(l_solution[0])
return w_score, w_solution, l_score, l_solution
raise NotImplementedError
def solve(self, model, algorithm=None, ratio=None, param=None):
"""Returns optimal partioning in model for winner."""
if algorithm is not None:
self.algorithm = algorithm
if model.n_dims == 1:
return self._solve_1D(model)
elif model.n_dims == 2:
return self._solve_2D(model)
return self._solve_0D(model, param=param, ratio=ratio)
def round_print(array):
"""Prints mean and array."""
print(round(np.mean(array), 2), '\t', array)
def run_0D(model, gm, brute_force=True, ratio=.25, rounds=5):
"""Do multiple test with the 0D model. Don't cry when reading this."""
assert model.n_dims == 0, "Not 0D"
w_scores, l_scores = [], []
wp_scores, lp_scores = [], []
wc_scores, lc_scores = [], []
mw_scores, ml_scores = [], []
mwp_scores, mlp_scores = [], []
mwc_scores, mlc_scores = [], []
bw_scores, bl_scores = [], []
for _ in tqdm(range(rounds)):
if brute_force:
bw_score, bw_part, bl_score, bl_part = gm.solve(model,
'brute-force',
ratio)
bw_scores.append(bw_score)
bl_scores.append(bl_score)
else:
gm.param = 'average'
w_score, w_part, l_score, l_part = gm.solve(model, 'packing',
ratio)
wc_score, wc_part, lc_score, lc_part = gm.solve(model, 'cracking',
ratio)
wp_score, wp_part, lp_score, lp_part = gm.solve(model, 'pracking',
ratio)
w_scores.append(w_score)
l_scores.append(l_score)
wp_scores.append(wp_score)
lp_scores.append(lp_score)
wc_scores.append(wc_score)
lc_scores.append(lc_score)
gm.param = 'median'
mw_score, mw_part, ml_score, ml_part = gm.solve(model,
'packing',
ratio)
mwc_score, mwc_part, mlc_score, mlc_part = gm.solve(model,
'cracking',
ratio)
mwp_score, mwp_part, mlp_score, mlp_part = gm.solve(model,
'pracking',
ratio)
mw_scores.append(w_score)
ml_scores.append(l_score)
mwp_scores.append(wp_score)
mlp_scores.append(lp_score)
mwc_scores.append(wc_score)
mlc_scores.append(lc_score)
model.resample()
# Brute-force results.
if brute_force:
round_print(bw_scores)
round_print(bl_scores)
bavg = round(np.mean(np.array(bw_scores) - np.array(bl_scores)), 2)
print(f'\nAverage brute-force difference best and worst: {bavg}')
return bavg
# Average results.
for s in [w_scores, l_scores, wp_scores, lp_scores, wc_scores, lc_scores]:
round_print(s)
avg = round(np.mean(np.array(w_scores) - np.array(l_scores)), 2)
avg2 = round(np.mean(np.array(wp_scores) - np.array(lp_scores)), 2)
avg3 = round(np.mean(np.array(wc_scores) - np.array(lc_scores)), 2)
print(f'\nAverage packing difference best and worst: {avg}')
print(f'\nAverage pracking difference best and worst: {avg2}')
print(f'\nAverage cracking difference best and worst: {avg3}')
# Median results.
for s in [mw_scores, ml_scores, mwp_scores, mlp_scores, mwc_scores,
mlc_scores]:
round_print(s)
mavg = round(np.mean(np.array(mw_scores) - np.array(ml_scores)), 2)
mavg2 = round(np.mean(np.array(mwp_scores) - np.array(mlp_scores)), 2)
mavg3 = round(np.mean(np.array(mwc_scores) - np.array(mlc_scores)), 2)
print(f'\nAverage median packing difference best and worst: {mavg}')
print(f'\nAverage median pracking difference best and worst: {mavg2}')
print(f'\nAverage median cracking difference best and worst: {mavg3}')
return avg, avg2, avg3, mavg, mavg2, mavg3
def run_1D_2D(model, gm, rounds=5, D=1):
"""Do multiple test with the 1D or 2D model."""
assert D in [1, 2]
if D == 1:
assert model.n_dims == 1, "Not 1D"
assert gm.algorithm == 'brute-force', "1D only supports brute-force."
elif D == 2:
assert model.n_dims == 2, "Not 2D"
assert gm.algorithm == "a_star", "Use \"a star\""
assert model.total_units < 30, "better don't do this"
w_scores, l_scores = [], []
for _ in tqdm(range(rounds)):
w_score, w_part, l_score, l_part = gm.solve(model)
w_scores.append(w_score)
l_scores.append(l_score)
model.resample()
# Results.
round_print(w_scores)
round_print(l_scores)
avg = round(np.mean(np.array(w_scores) - np.array(l_scores)), 2)
print(f'\nAverage {D}D difference best and worst: {avg}')
return avg
def write_to(data, path='results.txt'):
"""Append data to path."""
with open(path, 'a') as f:
f.write(data + "\n")
def do_2D(g=GerryMander(algorithm="a_star")):
""" """
for n_dists in [3, 5, 7]:
for units_in_dist in [3, 5, 7]:
for unit_size in [1, 10, 100]:
if n_dists * units_in_dist < 25:
m = Model(n_dims=2, unit_size=unit_size, n_dists=n_dists,
units_in_dist=units_in_dist,
shape=(n_dists, units_in_dist))
# a*
avg = run_1D_2D(m, g, D=2)
line1 = f"2D dists {n_dists} units_in_dist {units_in_dist}"
line2 = f" unit_size {unit_size} avg_score {avg}"
write_to(line1+line2, "results_2D.txt")
def do_1D(g=GerryMander(algorithm="brute-force"), rounds=5):
""" """
for n_dists in [3, 9, 27]:
for units_in_dist in [3, 5, 9, 27]:
for unit_size in [1, 10, 100]:
m = Model(n_dims=1, unit_size=unit_size, n_dists=n_dists,
units_in_dist=units_in_dist)
avg = run_1D_2D(m, g, D=1, rounds=rounds)
line1 = f"1D dists {n_dists} units_in_dist {units_in_dist} "
line2 = f"unit_size {unit_size} avg_score {avg}"
write_to(line1+line2, "results_1D.txt")
def do_0D(g=GerryMander(algorithm="brute-force"), rounds=5):
""" """
for n_dists in [3, 5, 7]:
for units_in_dist in [3, 5, 7]:
for unit_size in [1, 10, 100]:
line1 = f"0D dists {n_dists} units_in_dist {units_in_dist} " +\
f"unit_size {unit_size} "
m = Model(n_dims=0, unit_size=unit_size, n_dists=n_dists,
units_in_dist=units_in_dist)
# brute-force
if n_dists * units_in_dist < 10:
line2 = f"avg_score {run_0D(m, g, True, rounds=rounds)}"
write_to(line1+line2, "results_0D.txt")
# Packing, Cracking & Pracking
for ratio in [0.25, .5, 1]:
line2 = f"ratio {ratio}"
if unit_size > 1:
avgs = run_0D(m, g, False, ratio=ratio, rounds=rounds)
line3 = f" mean pack {avgs[0]}" +\
f" mean crack {avgs[2]}" +\
f" mean prack {avgs[1]}" +\
f" median pack{avgs[3]}" +\
f" median crack {avgs[5]}" +\
f" median prack {avgs[4]}"
write_to(line1+line2+line3, "results_0D.txt")
else:
avgs = run_0D(m, g, False, ratio=ratio)
line3 = f" mean pack {avgs[0]} mean crack {avgs[2]}" +\
f" mean prack {avgs[1]}"
write_to(line1+line2+line3, "results_0D.txt")
if __name__ == '__main__':
do_1D(rounds=10)
do_0D()
do_2D()