Mallows 4 last#
[1]:
from math import prod
import sympy
import numpy as np
from actinvoting import *
[2]:
m = 4
phi = sympy.Rational(50, 100)
rho = - np.log(float(phi))
rho
[2]:
np.float64(0.6931471805599453)
[3]:
tau = [-2*rho, -rho, 0, 0]
[4]:
culture = CultureMallows(m=m, phi=phi)
session = WorkSession(culture=culture, c=m-1, tau=tau)
rate = session.p_of_zeta / prod([session.zeta[j]**(1/2) for j in session.adversaries])
float(rate)
[4]:
0.7003724308895327
Runtimes#
[5]:
%%timeit
equivalent_probas = equivalent_batch(session=session, ns=[25], n_jobs=1, force_recompute=True)
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361 μs ± 8.82 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
[6]:
exact_probas = exact_batch(session=session, ns=[25], n_jobs=1, force_recompute=True)
run_time_str='4m34s'
[7]:
monte_carlo_probas = monte_carlo_batch(session=session, ns=[25], n_samples=10000, n_jobs=1, force_recompute=True)
run_time_str='16s'
Plot#
[8]:
ns_equivalent_probas = list(range(2, 51))
ns_exact_probas = list(range(2, 26))
ns_monte_carlo_probas = list(range(2, 21))
n_samples = 10000
n_jobs = -1
[9]:
equivalent_probas = equivalent_batch(session=session, ns=ns_equivalent_probas, n_jobs=n_jobs)
Loading Mallows_m=4_phi=1_2_c=3_ns=[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]_equiv.pkl
[10]:
monte_carlo_probas = monte_carlo_batch(session=session, ns=ns_monte_carlo_probas, n_samples=n_samples, n_jobs=n_jobs)
Loading Mallows_m=4_phi=1_2_c=3_ns=[2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,_13,_14,_15,_16,_17,_18,_19,_20]_n_samples=10000_mc.pkl
[11]:
exact_probas = exact_batch(session=session, ns=ns_exact_probas, n_jobs=n_jobs)
Loading Mallows_m=4_phi=1_2_c=3_ns=[2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,_13,_14,_15,_16,_17,_18,_19,_20,_21,_22,_23,_24,_25]_exact.pkl
[12]:
plot_simu_and_theo(
equivalent_probas=equivalent_probas, monte_carlo_probas=monte_carlo_probas, exact_probas=exact_probas,
ns_equivalent_probas=ns_equivalent_probas, ns_monte_carlo_probas=ns_monte_carlo_probas, ns_exact_probas=ns_exact_probas,
log_scale=True, file_name='mallows_4_last.tex', y_label=r"$\mathbb{P}(4 \text{ is CW})$", verbose=False
)

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