def bradley_terry_dirichlet(
poc_share=0.33,
poc_support_for_poc_candidates=0.7,
poc_support_for_white_candidates=0.3,
white_support_for_white_candidates=0.8,
white_support_for_poc_candidates=0.2,
num_ballots=1000,
num_simulations=100,
seats_open=3,
num_poc_candidates=2,
num_white_candidates=3,
concentrations=[1.0, 1.0, 1.0, 1.0], # poc_for_poc, poc_for_w, w_for_poc, w_for_w
max_ballot_length=None):
if max_ballot_length == None:
max_ballot_length = num_poc_candidates+num_white_candidates
num_candidates = [num_poc_candidates, num_white_candidates]
alphas = concentrations
candidates = ['A'+str(x) for x in range(num_poc_candidates)]+['B'+str(x) for x in range(num_white_candidates)]
race_of_candidate = {x: x[0] for x in candidates}
# simulate
poc_elected = []
poc_elected_atlarge = []
for n in range(num_simulations):
# get support vectors
noise0 = list(np.random.dirichlet([alphas[0]]*num_poc_candidates))+list(np.random.dirichlet([alphas[1]]*num_white_candidates))
noise1 = list(np.random.dirichlet([alphas[2]]*num_poc_candidates))+list(np.random.dirichlet([alphas[3]]*num_white_candidates))
white_voter_support_vector = []
poc_voter_support_vector = []
for i, (c, r) in enumerate(race_of_candidate.items()):
if r == 'A':
white_voter_support_vector.append((white_support_for_poc_candidates*noise1[i]))
poc_voter_support_vector.append((poc_support_for_poc_candidates*noise0[i]))
elif r == 'B':
white_voter_support_vector.append((white_support_for_white_candidates*noise1[i]))
poc_voter_support_vector.append((poc_support_for_white_candidates*noise0[i]))
ballots = []
numballots = num_ballots
ballots = paired_comparison_mcmc(
num_ballots,
{
0: {x: poc_voter_support_vector[i] for i, x in enumerate(candidates)},
1: {x: white_voter_support_vector[i] for i, x in enumerate(candidates)}
},
None,
candidates,
{0: poc_share, 1: 1-poc_share},
[0, 1],
sample_interval=10,
verbose=False
)
# winners
ballots = [b[:max_ballot_length] for b in ballots]
winners = cw.rcv_run(ballots.copy(), candidates, seats_open, cincinnati_transfer)
poc_elected.append(len([w for w in winners if w[0] == 'A']))
atlargewinners = cw.at_large_run(ballots.copy(), candidates, seats_open)
poc_elected_atlarge.append(len([x for x in atlargewinners if x[0] == 'A']))
return poc_elected, poc_elected_atlarge
def luce_dirichlet(
poc_share=0.33,
poc_support_for_poc_candidates=0.7,
poc_support_for_white_candidates=0.3,
white_support_for_white_candidates=0.8,
white_support_for_poc_candidates=0.2,
num_ballots=1000,
num_simulations=100,
seats_open=3,
num_poc_candidates=2,
num_white_candidates=3,
concentrations=[1.0, 1.0, 1.0, 1.0], # poc_for_poc, poc_for_w, w_for_poc, w_for_w.
max_ballot_length=None):
if max_ballot_length == None:
max_ballot_length = num_poc_candidates+num_white_candidates
# alphas = poc_for_poc, poc_for_w, w_for_poc, w_for_w.
alphas = concentrations
candidates = ['A'+str(x) for x in range(num_poc_candidates)]+['B'+str(x) for x in range(num_white_candidates)]
race_of_candidate = {x: x[0] for x in candidates}
# simulate
poc_elected_luce = []
poc_elected_luce_atlarge = []
for n in range(num_simulations):
# get support vectors
noise_poc_voters = list(np.random.dirichlet([alphas[0]]*num_poc_candidates))+list(np.random.dirichlet([alphas[1]]*num_white_candidates))
noise_white_voters = list(np.random.dirichlet([alphas[2]]*num_poc_candidates))+list(np.random.dirichlet([alphas[3]]*num_white_candidates))
poc_voter_support_vector = []
white_voter_support_vector = []
# For each candidate, deetermine their support based on their race
for i, (c, r) in enumerate(race_of_candidate.items()):
# For POC candidates
if r == 'A':
white_voter_support_vector.append((white_support_for_poc_candidates*noise_white_voters[i]))
poc_voter_support_vector.append((poc_support_for_poc_candidates*noise_poc_voters[i]))
# For White candidates
elif r == 'B':
white_voter_support_vector.append((white_support_for_white_candidates*noise_white_voters[i]))
poc_voter_support_vector.append((poc_support_for_white_candidates*noise_poc_voters[i]))
ballots = []
numballots = num_ballots
sum_to_one([white_voter_support_vector, poc_voter_support_vector])
# white
for i in range(int(numballots*(1-poc_share))):
ballots.append(
np.random.choice(list(race_of_candidate.keys()), size=len(race_of_candidate), p=white_voter_support_vector, replace=False)
)
# poc
for i in range(int(numballots*poc_share)):
ballots.append(
np.random.choice(list(race_of_candidate.keys()), size=len(race_of_candidate), p=poc_voter_support_vector, replace=False)
)
# winners
ballots = [b[:max_ballot_length] for b in ballots]
winners = cw.rcv_run(ballots.copy(), candidates, seats_open, cincinnati_transfer)
poc_elected_luce.append(len([w for w in winners if w[0] == 'A']))
atlargewinners = cw.at_large_run(ballots.copy(), candidates, seats_open)
poc_elected_luce_atlarge.append(len([x for x in atlargewinners if x[0] == 'A']))
return poc_elected_luce, poc_elected_luce_atlarge
def luce_dirichlet(
poc_share = 0.33,
poc_support_for_poc_candidates = 0.7,
poc_support_for_white_candidates = 0.3,
white_support_for_white_candidates = 0.8,
white_support_for_poc_candidates = 0.2,
num_ballots = 1000,
num_simulations = 100,
seats_open = 3,
num_poc_candidates = 2,
num_white_candidates = 3,
concentrations = [1.0,1.0,1.0,1.0], #poc_for_poc, poc_for_w, w_for_poc, w_for_w.
max_ballot_length = None,
verbose=False
):
if max_ballot_length == None:
max_ballot_length = num_poc_candidates+num_white_candidates
num_candidates = [num_poc_candidates, num_white_candidates]
alphas = concentrations
candidates = ['A'+str(x) for x in range(num_poc_candidates)]+['B'+str(x) for x in range(num_white_candidates)]
race_of_candidate = {x:x[0] for x in candidates}
#simulate
poc_elected_luce = []
poc_elected_luce_atlarge = []
for n in range(num_simulations):
#get support vectors
noise0 = list(np.random.dirichlet([alphas[0]]*num_candidates[0]))+list(np.random.dirichlet([alphas[1]]*num_candidates[1]))
noise1 = list(np.random.dirichlet([alphas[2]]*num_candidates[0]))+list(np.random.dirichlet([alphas[3]]*num_candidates[1]))
white_support_vector = []
poc_support_vector = []
for i, c in enumerate(candidates):
if race_of_candidate[c] == 'A':
white_support_vector.append((white_support_for_poc_candidates*noise1[i]))
poc_support_vector.append((poc_support_for_poc_candidates*noise0[i]))
elif race_of_candidate[c] == 'B':
white_support_vector.append((white_support_for_white_candidates*noise1[i]))
poc_support_vector.append((poc_support_for_white_candidates*noise0[i]))
ballots = []
numballots = num_ballots
#white
for i in range(int(numballots*(1-poc_share))):
ballots.append(
np.random.choice(candidates, size=len(candidates), p=white_support_vector, replace=False)
)
#poc
for i in range(int(numballots*poc_share)):
ballots.append(
np.random.choice(candidates, size=len(candidates), p=poc_support_vector, replace=False)
)
#winners
ballots = [b[:max_ballot_length] for b in ballots]
winners = cw.rcv_run(ballots.copy(), candidates, seats_open, cincinnati_transfer)
poc_elected_luce.append(len([w for w in winners if w[0]=='A']))
atlargewinners = cw.at_large_run(ballots.copy(),candidates,seats_open)
poc_elected_luce_atlarge.append(len([x for x in atlargewinners if x[0] == 'A']))
if verbose and n == 1:
print(alphas)
print(white_support_vector)
print(poc_support_vector)
print("--ballots--")
for b in babababallots:
print(b)
print("-----------")
return poc_elected_luce, poc_elected_luce_atlarge
def BABABA(
poc_share = 0.33,
poc_support_for_poc_candidates = 0.7,
poc_support_for_white_candidates = 0.3,
white_support_for_white_candidates = 0.8,
white_support_for_poc_candidates = 0.2,
num_ballots = 1000,
num_simulations = 100,
seats_open = 3,
num_poc_candidates = 2,
num_white_candidates = 3,
scenarios_to_run = ['A', 'B', 'C', 'D'],
max_ballot_length = None,
verbose=False
):
if max_ballot_length == None:
max_ballot_length = num_poc_candidates+num_white_candidates
candidates = ['A'+str(x) for x in range(num_poc_candidates)]+['B'+str(x) for x in range(num_white_candidates)]
poc_candidates = [c for c in candidates if c[0]=='A']
white_candidates = [c for c in candidates if c[0]=='B']
def interleave(x,y):
'''
Interleaves two lists x and y
'''
x = list(x)
y = list(y)
minlength = min(len(x), len(y))
return [z for pair in zip(x[:minlength],y[:minlength]) for z in pair]+x[minlength:]+y[minlength:]
def white_bloc_ballots(scenario):
if scenario in ['A','B']:
return [white_candidates+poc_candidates]
else:
x = random.sample(white_candidates, len(white_candidates))
y = random.sample(poc_candidates, len(poc_candidates))
return [list(x) + list(y)]
def white_cross_ballots(scenario):
if scenario in ['A','B']:
return [interleave(poc_candidates, white_candidates)]
else:
x = random.sample(white_candidates, len(white_candidates))
y = random.sample(poc_candidates, len(poc_candidates))
return [interleave(y,x)]
def poc_bloc_ballots(scenario):
if scenario in ['A','D']:
return [poc_candidates+white_candidates]
elif scenario == 'B':
x = random.sample(white_candidates, len(white_candidates))
y = random.sample(poc_candidates, len(poc_candidates))
return [list(y)+white_candidates]
else:
x = random.sample(white_candidates, len(white_candidates))
y = random.sample(poc_candidates, len(poc_candidates))
return [list(y)+list(x)]
def poc_cross_ballots(scenario):
if scenario in ['A', 'D']:
return [interleave(white_candidates, poc_candidates)]
elif scenario == 'B':
x = random.sample(white_candidates, len(white_candidates))
y = random.sample(poc_candidates, len(poc_candidates))
return [interleave(white_candidates,y)]
else:
x = random.sample(white_candidates, len(white_candidates))
y = random.sample(poc_candidates, len(poc_candidates))
return [interleave(x,y)]
poc_elected_bababa = {}
poc_elected_bababa_atlarge = {}
for scenario in scenarios_to_run:
poc_elected_bababa[scenario] = []
poc_elected_bababa_atlarge[scenario] = []
for n in range(num_simulations):
babababallots = []
#poc bloc
a = int(num_ballots*poc_share*poc_support_for_poc_candidates)
babababallots.extend([poc_bloc_ballots(scenario)[0][:max_ballot_length] for x in range(a)])
#poc cross
a = int(num_ballots*poc_share*poc_support_for_white_candidates)
babababallots.extend([poc_cross_ballots(scenario)[0][:max_ballot_length] for x in range(a)])
#white bloc
a = int(num_ballots*(1-poc_share)*white_support_for_white_candidates)
babababallots.extend([white_bloc_ballots(scenario)[0][:max_ballot_length] for x in range(a)])
#white cross
a = int(num_ballots*(1-poc_share)*white_support_for_poc_candidates)
babababallots.extend([white_cross_ballots(scenario)[0][:max_ballot_length] for x in range(a)])
if verbose and n == 1:
print(scenario)
print("--ballots--")
for b in babababallots:
print(b)
print("-----------")
#winners
winners = cw.rcv_run(babababallots.copy(), candidates, seats_open, cincinnati_transfer)
poc_elected_bababa[scenario].append(len([w for w in winners if w[0]=='A']))
atlargewinners = cw.at_large_run(babababallots.copy(),candidates,seats_open)
poc_elected_bababa_atlarge[scenario].append(len([x for x in atlargewinners if x[0] == 'A']))
return poc_elected_bababa, poc_elected_bababa_atlarge
def Cambridge_ballot_type(
poc_share = 0.33,
poc_support_for_poc_candidates = 0.7,
poc_support_for_white_candidates = 0.3,
white_support_for_white_candidates = 0.8,
white_support_for_poc_candidates = 0.2,
num_ballots = 1000,
num_simulations = 100,
seats_open = 3,
num_poc_candidates = 2,
num_white_candidates = 3,
scenarios_to_run = ['A', 'B', 'C', 'D'],
max_ballot_length = None,
verbose=False
):
if max_ballot_length == None:
max_ballot_length = num_poc_candidates+num_white_candidates
num_candidates = [num_poc_candidates, num_white_candidates]
minority_share = poc_share
preference_strengths = [poc_support_for_poc_candidates, white_support_for_white_candidates]
num_seats = seats_open
poc_elected_Cambridge = defaultdict(list)
poc_elected_Cambridge_atlarge = defaultdict(list)
candidates = ['A'+str(x) for x in range(num_poc_candidates)]+['B'+str(x) for x in range(num_white_candidates)]
white_candidates = candidates[num_candidates[0]:]
poc_candidates = candidates[:num_candidates[0]]
#get ballot type frequencies
ballot_type_frequencies = pickle.load(open('Cambridge_09to17_ballot_types.p', 'rb'))
white_first_probs = {x:p for x,p in ballot_type_frequencies.items() if x[0]=='W'}
poc_first_probs = {x:p for x,p in ballot_type_frequencies.items() if x[0]=='C'}
sum_white_first_probs = sum(white_first_probs.values())
white_first_probs = {x:p/sum_white_first_probs for x,p in white_first_probs.items()}
sum_poc_first_probs = sum(poc_first_probs.values())
poc_first_probs = {x:p/sum_poc_first_probs for x,p in poc_first_probs.items()}
#consolidate to only prefixes that are valid based on number of candidates
consolidated_probs = {}
for pref in set([x[:sum(num_candidates)] for x in white_first_probs.keys()]):
consolidated_probs[pref] = sum(
[white_first_probs[x] for x in white_first_probs if x[:sum(num_candidates)]==pref]
)
white_first_probs = consolidated_probs
consolidated_probs = {}
for pref in set([x[:sum(num_candidates)] for x in poc_first_probs.keys()]):
consolidated_probs[pref] = sum(
[poc_first_probs[x] for x in poc_first_probs if x[:sum(num_candidates)]==pref]
)
poc_first_probs = consolidated_probs
for scenario in scenarios_to_run:
for n in range(num_simulations):
ballots = []
#white voters white first
for b in range(int(num_ballots*(1-minority_share)*preference_strengths[1])):
ballot_type = list(choice(
list(white_first_probs.keys()),
p=list(white_first_probs.values())
))[:max_ballot_length]
ballot = []
if scenario in ['C', 'D']:
candidate_ordering = {
'W':list(np.random.permutation(white_candidates)),
'C':list(np.random.permutation(poc_candidates))
}
else:
candidate_ordering = {
'W':list(reversed(white_candidates)),
'C':list(reversed(poc_candidates))
}
for j in range(len(ballot_type)):
if len(candidate_ordering[ballot_type[j]])==0:
break
else:
ballot.append(candidate_ordering[ballot_type[j]].pop())
ballots.append(ballot[:max_ballot_length])
#white voters poc first
for b in range(int(num_ballots*(1-minority_share)*(1-preference_strengths[1]))):
ballot_type = list(choice(
list(poc_first_probs.keys()),
p=list(poc_first_probs.values())
))[:max_ballot_length]
ballot = []
if scenario in ['C', 'D']:
candidate_ordering = {
'W':list(np.random.permutation(white_candidates)),
'C':list(np.random.permutation(poc_candidates))
}
else:
candidate_ordering = {
'W':list(reversed(white_candidates)),
'C':list(reversed(poc_candidates))
}
for j in range(len(ballot_type)):
if len(candidate_ordering[ballot_type[j]])==0:
break
else:
ballot.append(candidate_ordering[ballot_type[j]].pop())
ballots.append(ballot[:max_ballot_length])
#poc voters poc first
for b in range(int(num_ballots*(minority_share)*preference_strengths[0])):
ballot_type = list(choice(
list(poc_first_probs.keys()),
p=list(poc_first_probs.values())
))[:max_ballot_length]
ballot = []
if scenario in ['B']:
candidate_ordering = {
'W':list(reversed(white_candidates)),
'C':list(np.random.permutation(poc_candidates))
}
elif scenario in ['C']:
candidate_ordering = {
'W':list(np.random.permutation(white_candidates)),
'C':list(np.random.permutation(poc_candidates))
}
else:
candidate_ordering = {
'W':list(reversed(white_candidates)),
'C':list(reversed(poc_candidates))
}
for j in range(len(ballot_type)):
if len(candidate_ordering[ballot_type[j]])==0:
break
else:
ballot.append(candidate_ordering[ballot_type[j]].pop())
ballots.append(ballot[:max_ballot_length])
#poc voters white first
for b in range(int(num_ballots*(minority_share)*(1-preference_strengths[0]))):
ballot_type = list(choice(
list(white_first_probs.keys()),
p=list(white_first_probs.values())
))[:max_ballot_length]
ballot = []
if scenario in ['B']:
candidate_ordering = {
'W':list(reversed(white_candidates)),
'C':list(np.random.permutation(poc_candidates))
}
elif scenario in ['C']:
candidate_ordering = {
'W':list(np.random.permutation(white_candidates)),
'C':list(np.random.permutation(poc_candidates))
}
else:
candidate_ordering = {
'W':list(reversed(white_candidates)),
'C':list(reversed(poc_candidates))
}
for j in range(len(ballot_type)):
if len(candidate_ordering[ballot_type[j]])==0:
break
else:
ballot.append(candidate_ordering[ballot_type[j]].pop())
ballots.append(ballot[:max_ballot_length])
winners = cw.rcv_run(
ballots.copy(),
candidates,
num_seats,
cincinnati_transfer,
)
poc_elected_Cambridge[scenario].append(len([x for x in winners if x[0] == 'A']))
atlargewinners = cw.at_large_run(
ballots.copy(),
candidates,
num_seats
)
poc_elected_Cambridge_atlarge[scenario].append(len([x for x in atlargewinners if x[0] == 'A']))
if verbose and n == 1:
print(scenario)
print("--ballots--")
for b in ballots:
print(b)
print("-----------")
return poc_elected_Cambridge, poc_elected_Cambridge_atlarge
