Divided Preferences: Approval (5.2.3)

from fractions import Fraction
from matplotlib import pyplot as plt
from poisson_approval import *

SCALE = 25
SAMPLES_PER_POINT = 1000
N_MAX_EPISODES = 1000

divided_majority_av = SimplexToProfile(
    ProfileHistogram,
    right_type=('cab', (1, )),
    top_type=('abc', (1, )),
    left_type=('bac', (1, )),
    d_type_fixed_share={('cba', (1, )): 0.2},
    voting_rule=APPROVAL
)

fig, tax = ternary_plot_winning_frequencies(
    divided_majority_av,
    scale=SCALE,
    init='random_tau',
    samples_per_point=SAMPLES_PER_POINT,
    n_max_episodes=N_MAX_EPISODES,
    title='',
    legend_title='Winners',
    file_save_data='sav/DM_AV.sav',
)
plt.savefig('img/fDM_AV.png', dpi=600, bbox_inches="tight")

tax.f_point_values_(right=0.02, top=0.69, left=0.29)

array([1.0, 0.0, 0.0], dtype=object)

An example where the CW may not be elected under AV:

profile = ProfileHistogram({
    ('abc', (1, )): Fraction(55, 100),
    ('bac', (1, )): Fraction(25, 100),
    ('cba', (1, )): Fraction(20, 100)
})

profile.analyzed_strategies_ordinal

Equilibria:
<abc: a, bac: b, cba: bc> ==> a (FF)
<abc: ab, bac: b, cba: c> ==> b (D)

Non-equilibria:
<abc: a, bac: b, cba: c> ==> a (D)
<abc: a, bac: ab, cba: c> ==> a (D)
<abc: a, bac: ab, cba: bc> ==> a (FF)
<abc: ab, bac: b, cba: bc> ==> b (D)
<abc: ab, bac: ab, cba: c> ==> a, b (FF)
<abc: ab, bac: ab, cba: bc> ==> b (D)