Source code for whalrus.rules.rule_condorcet

# -*- coding: utf-8 -*-
"""
Copyright Sylvain Bouveret, Yann Chevaleyre and Fran├žois 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]