# -*- 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_score_num import RuleScoreNum
from whalrus.converters_ballot.converter_ballot_to_order import ConverterBallotToOrder
from whalrus.utils.utils import cached_property, NiceDict, convert_number
from whalrus.converters_ballot.converter_ballot import ConverterBallot
from whalrus.matrices.matrix import Matrix
from whalrus.matrices.matrix_weighted_majority import MatrixWeightedMajority
[docs]class RuleSimplifiedDodgson(RuleScoreNum):
"""
Simplified Dodgson rule.
The score of a candidate is the sum of the negative non-diagonal coefficient on its raw of
:attr:`matrix_weighted_majority_`.
Parameters
----------
args
Cf. parent class.
converter : ConverterBallot
Default: :class:`ConverterBallotToOrder`.
matrix_weighted_majority : Matrix
Default: :class:`MatrixWeightedMajority` with ``antisymmetric=True``.
kwargs
Cf. parent class.
Examples
--------
>>> rule = RuleSimplifiedDodgson(ballots=['a > b > c', 'b > a > c', 'c > a > b'],
... weights=[3, 3, 2])
>>> rule.matrix_weighted_majority_.as_array_
array([[0, Fraction(1, 4), Fraction(1, 2)],
[Fraction(-1, 4), 0, Fraction(1, 2)],
[Fraction(-1, 2), Fraction(-1, 2), 0]], dtype=object)
>>> rule.scores_
{'a': 0, 'b': Fraction(-1, 4), 'c': -1}
>>> rule.winner_
'a'
"""
def __init__(self, *args, converter: ConverterBallot = None, matrix_weighted_majority: Matrix = None, **kwargs):
if converter is None:
converter = ConverterBallotToOrder()
if matrix_weighted_majority is None:
matrix_weighted_majority = MatrixWeightedMajority(antisymmetric=True)
self.matrix_weighted_majority = matrix_weighted_majority
super().__init__(*args, converter=converter, **kwargs)
@cached_property
def matrix_weighted_majority_(self):
"""Matrix: The weighted majority matrix (once computed with the given profile).
"""
return self.matrix_weighted_majority(self.profile_converted_)
@cached_property
def scores_(self) -> NiceDict:
matrix = self.matrix_weighted_majority_
return NiceDict({
c: convert_number(sum([v for (i, j), v in matrix.as_dict_.items() if i == c and j != c and v < 0]))
for c in matrix.candidates_})