Fast Rules

Fast

class embedded_voting.RuleFast(embeddings_from_ratings=None, f=None, aggregation_rule=<function prod>)

Voting rule in which the aggregated score of a candidate is based on singular values of his score matrix.

Parameters:

• embeddings_from_ratings (EmbeddingsFromRatingsCorrelation) – If no embeddings are specified in the call, this EmbeddingsFromRatings object is use to generate the embeddings from the ratings. Default: EmbeddingsFromRatingsCorrelation(preprocess_ratings=center_and_normalize).
• f (callable) – The transformation for the ratings given by each voter. Input : (ratings_v: np.ndarray, history_mean: Number, history_std: Number). Output : modified_ratings_v: np.ndarray.
• aggregation_rule (callable) – The aggregation rule for the singular values. Input : list of float. Output : float. By default, it is the product of the singular values.

Examples

>>> ratings = np.array([[.5, .6, .3], [.7, 0, .2], [.2, 1, .8]])
>>> election = RuleFast()(ratings)
>>> election.ranking_
[1, 0, 2]
>>> election.winner_
1

modified_ratings_

Modified ratings. For each voter, f is applied to her original ratings.

Type:Ratings

Variants

class embedded_voting.RuleFastNash(embeddings_from_ratings=None, f=None)

Voting rule in which the aggregated score of a candidate is the product of the important singular values of his score matrix.

Parameters:

• embeddings_from_ratings (EmbeddingsFromRatingsCorrelation) – If no embeddings are specified in the call, this EmbeddingsFromRatings object is use to generate the embeddings from the ratings. Default: EmbeddingsFromRatingsCorrelation(preprocess_ratings=center_and_normalize).
• f (callable) – The transformation for the ratings given by each voter. Input : (ratings_v: np.ndarray, history_mean: Number, history_std: Number). Output : modified_ratings_v: np.ndarray.

Examples

>>> ratings = np.array([[.5, .6, .3], [.7, 0, .2], [.2, 1, .8]])
>>> election = RuleFastNash()(ratings)
>>> election.ranking_
[1, 0, 2]
>>> election.winner_
1

class embedded_voting.RuleFastSum(embeddings_from_ratings=None, f=None)

Voting rule in which the aggregated score of a candidate is the sum of the important singular values of his score matrix.

Parameters:

• embeddings_from_ratings (EmbeddingsFromRatingsCorrelation) – If no embeddings are specified in the call, this EmbeddingsFromRatings object is use to generate the embeddings from the ratings. Default: EmbeddingsFromRatingsCorrelation(preprocess_ratings=center_and_normalize).
• f (callable) – The transformation for the ratings given by each voter. Input : (ratings_v: np.ndarray, history_mean: Number, history_std: Number). Output : modified_ratings_v: np.ndarray.

Examples

>>> ratings = np.array([[.5, .6, .3], [.7, 0, .2], [.2, 1, .8]])
>>> election = RuleFastSum()(ratings)
>>> election.ranking_
[1, 0, 2]
>>> election.winner_
1

class embedded_voting.RuleFastMin(embeddings_from_ratings=None, f=None)

Voting rule in which the aggregated score of a candidate is the minimum of the important singular values of his score matrix.

Parameters:

• embeddings_from_ratings (EmbeddingsFromRatingsCorrelation) – If no embeddings are specified in the call, this EmbeddingsFromRatings object is use to generate the embeddings from the ratings. Default: EmbeddingsFromRatingsCorrelation(preprocess_ratings=center_and_normalize).
• f (callable) – The transformation for the ratings given by each voter. Input : (ratings_v: np.ndarray, history_mean: Number, history_std: Number). Output : modified_ratings_v: np.ndarray.

Examples

>>> ratings = np.array([[.5, .6, .3], [.7, 0, .2], [.2, 1, .8]])
>>> election = RuleFastMin()(ratings)
>>> election.ranking_
[1, 0, 2]
>>> election.winner_
1

class embedded_voting.RuleFastLog(embeddings_from_ratings=None, f=None)

Voting rule in which the aggregated score of a candidate is the log sum of the important singular values of his score matrix.

Parameters:

• embeddings_from_ratings (EmbeddingsFromRatingsCorrelation) – If no embeddings are specified in the call, this EmbeddingsFromRatings object is use to generate the embeddings from the ratings. Default: EmbeddingsFromRatingsCorrelation(preprocess_ratings=center_and_normalize).
• f (callable) – The transformation for the ratings given by each voter. Input : (ratings_v: np.ndarray, history_mean: Number, history_std: Number). Output : modified_ratings_v: np.ndarray.

Examples

>>> ratings = np.array([[.5, .6, .3], [.7, 0, .2], [.2, 1, .8]])
>>> election = RuleFastLog()(ratings)
>>> election.ranking_
[1, 0, 2]
>>> election.winner_
1