import numpy as np
from embedded_voting.embeddings.embeddings import Embeddings
from embedded_voting.ratings.ratings import Ratings
from embedded_voting.rules.singlewinner_rules.rule_svd import RuleSVD
[docs]class RuleSVDNash(RuleSVD):
"""
Voting rule in which the aggregated score of a candidate is the product of the singular values
of his embedding matrix (cf :meth:`~embedded_voting.Embeddings.times_ratings_candidate`).
Parameters
----------
square_root: boolean
If True, use the square root of score in the matrix.
By default, it is True.
use_rank : boolean
If True, consider the rank of the matrix when doing the ranking.
By default, it is False.
embedded_from_ratings: EmbeddingsFromRatings
If no embeddings are specified in the call, this `EmbeddingsFromRatings` object is use to generate
the embeddings from the ratings. Default: `EmbeddingsFromRatingsIdentity()`.
Examples
--------
>>> ratings = Ratings(np.array([[.5, .6, .3], [.7, 0, .2], [.2, 1, .8]]))
>>> embeddings = Embeddings(np.array([[1, 1], [1, 0], [0, 1]]), norm=True)
>>> election = RuleSVDNash()(ratings, embeddings)
>>> election.scores_ # DOCTEST: +ELLIPSIS
[0.6041522986797..., 0.547722557505..., 0.5567764362830...]
>>> election.ranking_
[0, 2, 1]
>>> election.winner_
0
>>> election.welfare_ # DOCTEST: +ELLIPSIS
[1.0, 0.0, 0.16044515869439...]
"""
def __init__(self, square_root=True, use_rank=False, embedded_from_ratings=None):
super().__init__(aggregation_rule=np.prod, square_root=square_root, use_rank=use_rank,
embedded_from_ratings=embedded_from_ratings)