RuleCondorcet

class whalrus.RuleCondorcet(*args, converter: whalrus.converters_ballot.converter_ballot.ConverterBallot = None, matrix_majority: whalrus.matrices.matrix.Matrix = None, **kwargs)

Condorcet Rule.

Parameters

• args – Cf. parent class.

• converter (ConverterBallot) – Default: ConverterBallotToOrder.

• matrix_majority (Matrix) – The majority matrix. Default: MatrixMajority.

• kwargs – Cf. parent class.

Examples

If there is a Condorcet winner, then it it the winner and all other candidates are tied. If there is no Condorcet winner, then all candidates are tied.

>>> RuleCondorcet(ballots=['a > b > c', 'b > a > c', 'c > a > b']).order_
[{'a'}, {'b', 'c'}]
>>> RuleCondorcet(ballots=['a > b > c', 'b > c > a', 'c > a > b']).order_
[{'a', 'b', 'c'}]

More precisely, and in all generality, a candidate is considered a Condorcet winner if all the non-diagonal coefficients on its raw of matrix_majority_ are equal to 1. With the default setting of matrix_majority = MatrixMajority(), the Condorcet winner is necessarily unique when it exists, but that might not be the case with some more exotic settings:

>>> rule = RuleCondorcet(ballots=['a ~ b > c'], matrix_majority=MatrixMajority(equal=1))
>>> rule.matrix_majority_.as_array_
array([[Fraction(1, 2), 1, 1],
       [1, Fraction(1, 2), 1],
       [0, 0, Fraction(1, 2)]], dtype=object)
>>> rule.order_
[{'a', 'b'}, {'c'}]

property 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

property 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

property matrix_majority_

The majority matrix (once computed with the given profile).

Type

Matrix

property n_candidates_

Number of candidates.

Type

int

property 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

property 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

property 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