Dynamic Process: Robustness to the Share of Updating Voters (C.2)

import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from poisson_approval import *

N_SAMPLES = 10000
N_MAX_EPISODES = 1000

update_ratios = {
    '1': 1,
    '0.5': 0.5,
    'one_over_log_log_t_plus_fourteen': one_over_log_log_t_plus_fourteen,
    'one_over_log_t_plus_one': one_over_log_t_plus_one,
    'one_over_sqrt_t': one_over_sqrt_t,
    'one_over_t': one_over_t,
}

update_ratios_legend = {
    '1': '1',
    '0.5': '0.5',
    'one_over_log_log_t_plus_fourteen': '1 / log(log(t + 14))',
    'one_over_log_t_plus_one': '1 / log(t + 1)',
    'one_over_sqrt_t': '1 / sqrt(t)',
    'one_over_t': '1 / t',
}

rand_profile = RandProfileHistogramUniform(n_bins=1)

Convergence Rate

table_cv = pd.DataFrame()
table_cv.index.name = 'Share of updating voters'
d_update_ratio_name_results = {}
for update_ratio_name, update_ratio in update_ratios.items():
    results = monte_carlo_fictitious_play(
        factory=rand_profile,
        n_samples=N_SAMPLES,
        n_max_episodes=N_MAX_EPISODES,
        voting_rules=VOTING_RULES,
        init='random_tau',
        ballot_update_ratio=update_ratio,
        monte_carlo_settings=[
            MCS_N_EPISODES,
            MCS_CONVERGES,
        ],
        file_save='sav/ballot_update_%s.sav' % update_ratio_name,
    )
    d_update_ratio_name_results[update_ratio_name] = results
    for voting_rule in VOTING_RULES:
        table_cv.loc[update_ratio_name, voting_rule] = float(results[voting_rule]['mean_converges'])
table_cv

	Approval	Plurality	Anti-plurality
Share of updating voters
1	0.9390	1.0	0.0
0.5	0.9461	1.0	0.0
one_over_log_log_t_plus_fourteen	0.9492	1.0	0.0
one_over_log_t_plus_one	0.9472	1.0	0.0
one_over_sqrt_t	0.9503	1.0	0.0
one_over_t	0.0558	1.0	0.0

Convergence Speed

fig, ax = plt.subplots(figsize=(8, 4))
for update_ratio_name, update_ratio in update_ratios.items():
    plt_cdf(
        data=d_update_ratio_name_results[update_ratio_name]['Approval']['n_episodes'],
        weights=np.ones(N_SAMPLES) / N_SAMPLES,
        n_samples=N_SAMPLES,
        data_min=0,
        data_max=N_MAX_EPISODES,
        label=update_ratios_legend[update_ratio_name]
    )
plt.grid(True)
plt.legend()
plt.xlabel('Number of episodes')
plt.ylabel('Cumulative likelihood of occurrence')
plt.xlim(0, N_MAX_EPISODES)
plt.ylim(0, 1.05)
plt.savefig('img/fspeedCV_ballot_update_ratio.png', dpi=600, bbox_inches="tight")