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 0x27af8244170>

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

Voters’ utilities for the candidates:

[9]:

profile.preferences_ut

[9]:

array([[ 0.27850815, -0.28669485, -0.22244491, -0.84581486,  0.2745082 ],
       [ 0.20483466, -0.76955375,  0.48285449,  0.12511632, -0.34209243],
       [ 0.10182242,  0.69341051, -0.31735312,  0.62107686, -0.14954792],
       [ 0.39364056, -0.07883268,  0.13936726,  0.64137693,  0.63878394],
       [ 0.18832192,  0.87431586, -0.05090841,  0.44387678,  0.0220992 ],
       [-0.27510627, -0.72888585,  0.34813102, -0.18660524,  0.48685237],
       [ 0.59273353,  0.27459674,  0.23258561,  0.71828012,  0.05693147],
       [ 0.03186397,  0.34120599, -0.2585684 ,  0.75864952,  0.4900576 ],
       [ 0.84416513, -0.4321969 , -0.09895003,  0.0351225 , -0.29927643]])

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, 2, 1, 3, 1])

[13]:

profile.borda_score_c_ut

[13]:

array([22., 13., 13., 25., 17.])

[14]:

profile.total_utility_c

[14]:

array([ 2.36078407, -0.11263493,  0.25471352,  2.31107892,  1.178316  ])

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

[15]:

profile.matrix_duels_ut

[15]:

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

[16]:

profile.matrix_victories_ut_abs

[16]:

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

Condorcet winner:

[17]:

profile.condorcet_winner_ut_abs

[17]:

3

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

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