# -*- coding: utf-8 -*-
"""
Copyright Sylvain Bouveret, Yann Chevaleyre and François Durand
sylvain.bouveret@imag.fr, yann.chevaleyre@dauphine.fr, fradurand@gmail.com
This file is part of Whalrus.
Whalrus is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Whalrus is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Whalrus. If not, see <http://www.gnu.org/licenses/>.
"""
from whalrus.rules.rule import Rule
from whalrus.converters_ballot.converter_ballot_to_order import ConverterBallotToOrder
from whalrus.utils.utils import cached_property, NiceSet
from whalrus.converters_ballot.converter_ballot import ConverterBallot
from whalrus.matrices.matrix import Matrix
from whalrus.matrices.matrix_majority import MatrixMajority
[docs]class RuleCondorcet(Rule):
"""
Condorcet Rule.
Parameters
----------
args
Cf. parent class.
converter : ConverterBallot
Default: :class:`ConverterBallotToOrder`.
matrix_majority : Matrix
The majority matrix. Default: :class:`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 :attr:`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'}]
"""
def __init__(self, *args, converter: ConverterBallot = None, matrix_majority: Matrix = None, **kwargs):
if converter is None:
converter = ConverterBallotToOrder()
if matrix_majority is None:
matrix_majority = MatrixMajority()
self.matrix_majority = matrix_majority
super().__init__(*args, converter=converter, **kwargs)
@cached_property
def matrix_majority_(self):
"""Matrix: The majority matrix (once computed with the given profile).
"""
return self.matrix_majority(self.profile_converted_)
@cached_property
def order_(self) -> list:
matrix = self.matrix_majority_
condorcet_winners = {c for c in matrix.candidates_
if min({v for (i, j), v in matrix.as_dict_.items() if i == c and j != c}) == 1}
other_candidates = self.candidates_ - condorcet_winners
return [NiceSet(tie_class) for tie_class in [condorcet_winners, other_candidates] if tie_class]