RuleBlack¶

class whalrus.RuleBlack(*args, rule_condorcet: whalrus.rules.rule.Rule = None, rule_borda: whalrus.rules.rule.Rule = None, **kwargs)[source]¶

Black’s rule.

Parameters:	args – Cf. parent class. rule_condorcet (Rule) – Used as the main victory criterion. Default: `RuleCondorcet`. rule_borda (Rule) – Used as the secondary victory criterion. Default: `RuleBorda`. kwargs – Cf. parent class.

Examples

As a main victory criterion, the Condorcet winner is elected (even if it does not have the highest Borda score):

>>> rule = RuleBlack(ballots=['a > b > c', 'b > c > a'], weights=[3, 2])
>>> rule.rule_condorcet_.matrix_majority_.matrix_weighted_majority_.as_array_
array([[0, Fraction(3, 5), Fraction(3, 5)],
       [Fraction(2, 5), 0, 1],
       [Fraction(2, 5), 0, 0]], dtype=object)
>>> rule.order_
[{'a'}, {'b'}, {'c'}]

When there is no Condorcet winner, candidates are sorted according to their Borda scores:

>>> rule = RuleBlack(ballots=['a > b > c', 'b > c > a', 'c > a > b'], weights=[3, 2, 2])
>>> rule.rule_condorcet_.matrix_majority_.matrix_weighted_majority_.as_array_
array([[0, Fraction(5, 7), Fraction(3, 7)],
       [Fraction(2, 7), 0, Fraction(5, 7)],
       [Fraction(4, 7), Fraction(2, 7), 0]], dtype=object)
>>> rule.order_
[{'a'}, {'b'}, {'c'}]

cotrailers_¶

“Cotrailers” of the election, i.e. the candidates that fare worst in the election. This is the last equivalence class in order_. For example, in RuleScoreNum, it is the candidates that are tied for the worst score.

Type:	NiceSet

cowinners_¶

Cowinners of the election, i.e. the candidates that fare best in the election.. This is the first equivalence class in order_. For example, in RuleScoreNum, it is the candidates that are tied for the best score.

Type:	NiceSet

n_candidates_¶

Number of candidates.

Type:	int

rule_borda_¶

The Borda rule (once applied to the profile).

Examples

>>> rule = RuleBlack(ballots=['a > b > c', 'b > c > a'], weights=[3, 2])
>>> rule.rule_borda_.scores_
{'a': Fraction(6, 5), 'b': Fraction(7, 5), 'c': Fraction(2, 5)}

Type:	Rule

rule_condorcet_¶

The Condorcet rule (once applied to the profile).

Examples

>>> rule = RuleBlack(ballots=['a > b > c', 'b > c > a'], weights=[3, 2])
>>> rule.rule_condorcet_.matrix_majority_.as_array_
array([[Fraction(1, 2), 1, 1],
       [0, Fraction(1, 2), 1],
       [0, 0, Fraction(1, 2)]], dtype=object)

Type:	Rule

rules_¶

The rules (once applied to the profile).

Type:	list

strict_order_¶

Result of the election as a strict order over the candidates. The first element is the winner, etc. This may use the tie-breaking rule.

Type:	list

trailer_¶

The “trailer” of the election. This is the last candidate in strict_order_ and also the unfavorable choice of the tie-breaking rule in cotrailers_.

Type:	object

winner_¶

The winner of the election. This is the first candidate in strict_order_ and also the choice of the tie-breaking rule in cowinners_.

Type:	object