Polarized Embeddings

class embedded_voting.EmbeddingsGeneratorPolarized(n_voters, n_dim, prob=None)

Generates parametrized embeddings with n_dim groups of voters. This class creates two embeddings: one according to uniform distribution, the other one fully polarized (with groups of voters on the canonical basis), and we can parametrize the embeddings to get one distribution between these two extremes.

Parameters:

• n_voters (int) – Number of voters in the embeddings.
• n_dim (int) – Number of dimensions for the embeddings.
• prob (list) – The probabilities for each voter to be in each group. Default is uniform distribution.

Examples

>>> np.random.seed(42)
>>> generator = EmbeddingsGeneratorPolarized(10, 2)
>>> generator(polarisation=1)
Embeddings([[1., 0.],
            [0., 1.],
            [1., 0.],
            [0., 1.],
            [0., 1.],
            [1., 0.],
            [0., 1.],
            [1., 0.],
            [1., 0.],
            [0., 1.]])
>>> generator(polarisation=0)
Embeddings([[0.96337365, 0.26816265],
            [0.39134578, 0.92024371],
            [0.70713157, 0.70708199],
            [0.89942118, 0.43708299],
            [0.65433791, 0.75620229],
            [0.70534506, 0.70886413],
            [0.1254653 , 0.99209801],
            [0.95076   , 0.30992809],
            [0.95508537, 0.29633078],
            [0.54080587, 0.84114744]])
>>> generator(polarisation=0.5)
Embeddings([[0.9908011 , 0.13532618],
            [0.19969513, 0.97985808],
            [0.92388624, 0.38266724],
            [0.53052663, 0.84766827],
            [0.34914017, 0.93707051],
            [0.92340269, 0.38383261],
            [0.06285695, 0.99802255],
            [0.98761328, 0.15690762],
            [0.98870758, 0.14985764],
            [0.28182668, 0.95946533]])

class embedded_voting.EmbeddingsGeneratorFullyPolarized(n_voters, n_dim, prob=None)

Create embeddings that are random vectors of the canonical basis.

Parameters:

• n_voters (int) – Number of voters in the embeddings.
• n_dim (int) – Number of dimensions for the embeddings.
• prob (list) – The probabilities for each voter to be in each group. Default is uniform distribution.

Examples

>>> np.random.seed(42)
>>> generator = EmbeddingsGeneratorFullyPolarized(10, 5)
>>> generator()
Embeddings([[0., 1., 0., 0., 0.],
            [0., 0., 0., 0., 1.],
            [0., 0., 0., 1., 0.],
            [0., 0., 1., 0., 0.],
            [1., 0., 0., 0., 0.],
            [1., 0., 0., 0., 0.],
            [1., 0., 0., 0., 0.],
            [0., 0., 0., 0., 1.],
            [0., 0., 0., 1., 0.],
            [0., 0., 0., 1., 0.]])