Profile

[1]:

import svvamp

Define a random generator of profiles using the Spheroid model (which extends Impartial Culture to utilities), with 9 voters and 5 candidates:

[2]:

random_profile = svvamp.GeneratorProfileSpheroid(n_v=9, n_c=5)
random_profile

[2]:

<svvamp.preferences.generator_profile_spheroid.GeneratorProfileSpheroid at 0x227236d1310>

Use the generator to create a random profile:

[3]:

profile = random_profile()

If you wish, you can give a label to each candidate:

[4]:

profile.labels_candidates = ['Alice', 'Bob', 'Catherine', 'Dave', 'Ellen']

Basic information about the profile:

[5]:

profile.n_v

[5]:

9

[6]:

profile.n_c

[6]:

5

[7]:

profile.labels_candidates

[7]:

['Alice', 'Bob', 'Catherine', 'Dave', 'Ellen']

Voters’ rankings of preference:

[8]:

profile.preferences_rk

[8]:

array([[0, 3, 1, 2, 4],
       [2, 0, 1, 3, 4],
       [3, 0, 2, 1, 4],
       [2, 3, 0, 4, 1],
       [0, 4, 1, 2, 3],
       [4, 2, 1, 3, 0],
       [2, 1, 3, 0, 4],
       [3, 1, 4, 2, 0],
       [3, 2, 4, 0, 1]])

Voters’ utilities for the candidates:

[9]:

profile.preferences_ut

[9]:

array([[ 0.56962423,  0.23147669, -0.10420753,  0.46170276, -0.63080752],
       [-0.10565873, -0.38552417,  0.22279825, -0.55394695, -0.6954934 ],
       [-0.26048526, -0.43251655, -0.41065507,  0.28538753, -0.70355756],
       [ 0.26890645, -0.52263056,  0.58980142,  0.55356667,  0.01564742],
       [ 0.04576047, -0.46090844, -0.48370682, -0.59680883, -0.44194607],
       [-0.27629285,  0.37454992,  0.44890641,  0.25299888,  0.71961741],
       [-0.02726965,  0.30157615,  0.75419276,  0.13546169, -0.56670239],
       [-0.13770358,  0.62540861, -0.0909895 ,  0.73785947,  0.192837  ],
       [-0.03753725, -0.29808471,  0.34075518,  0.88258878,  0.12107605]])

Plot the restriction of the population to 3 candidates, for example [0, 2, 3] (Alice, Catherine and Dave), in the utility space:

[10]:

profile.plot3(indexes=[0, 2, 3])
../_images/tutorials_tutorial_profile_17_0.png

Plot the restriction of the population to 4 candidates, for example [0, 1, 2, 4] (Alice, Bob, Catherine and Ellen), in the utility space:

[11]:

profile.plot4(indexes=[0, 1, 2, 4])
../_images/tutorials_tutorial_profile_19_0.png

Plurality score, Borda score and total utility of each candidate:

[12]:

profile.plurality_scores_ut

[12]:

array([2, 0, 3, 3, 1])

[13]:

profile.borda_score_c_ut

[13]:

array([18., 15., 23., 22., 12.])

[14]:

profile.total_utility_c

[14]:

array([ 0.03934382, -0.56665305,  1.2668951 ,  2.15881001, -1.98932905])

Matrix of duels (weighted majority graph) and matrix of victories (unweighted majority graph):

[15]:

profile.matrix_duels_ut

[15]:

array([[0, 6, 3, 3, 6],
       [3, 0, 3, 4, 5],
       [6, 6, 0, 5, 6],
       [6, 5, 4, 0, 7],
       [3, 4, 3, 2, 0]])

[16]:

profile.matrix_victories_ut_abs

[16]:

array([[0., 1., 0., 0., 1.],
       [0., 0., 0., 0., 1.],
       [1., 1., 0., 1., 1.],
       [1., 1., 0., 0., 1.],
       [0., 0., 0., 0., 0.]])

Condorcet winner:

[17]:

profile.condorcet_winner_ut_abs

[17]:

2

By convention, if there is no Condorcet winner, then SVVAMP returns nan (not a number).