# -*- 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.utils.utils import cached_property, NiceDict, convert_number
from whalrus.converters_ballot.converter_ballot_to_order import ConverterBallotToOrder
from whalrus.converters_ballot.converter_ballot import ConverterBallot
from whalrus.matrices.matrix import Matrix
from whalrus.matrices.matrix_weighted_majority import MatrixWeightedMajority
from numbers import Number
from fractions import Fraction
[docs]class MatrixMajority(Matrix):
"""
The majority matrix.
Parameters
----------
args
Cf. parent class.
converter : ConverterBallot
Default: :class:`ConverterBallotToOrder`.
matrix_weighted_majority : Matrix.
Algorithm used to compute the weighted majority matrix `W`. Default: :class:`MatrixWeightedMajority`.
greater : Number
Value used when `W(c, d) > W(d, c)`.
lower : Number
Value used when `W(c, d) < W(d, c)`.
equal : Number
Value used when `W(c, d) = W(d, c)` (except for diagonal coefficients).
diagonal : Number
Value used for the diagonal coefficients.
kwargs
Cf. parent class.
Examples
--------
First, we compute a matrix `W` with the algorithm given in the parameter ``matrix_weighted_majority``.
Then for each pair of candidates `(c, d)`, the coefficient of the majority matrix is set to :attr:`greater`,
:attr:`lower`, :attr:`equal` or :attr:`diagonal`, depending on the values of `W(c, d)` and `W(d, c)`.
>>> MatrixMajority(ballots=['a > b ~ c', 'b > a > c', 'c > a > b']).as_array_
array([[Fraction(1, 2), 1, 1],
[0, Fraction(1, 2), Fraction(1, 2)],
[0, Fraction(1, 2), Fraction(1, 2)]], dtype=object)
Using the options:
>>> MatrixMajority(ballots=['a > b ~ c', 'b > a > c', 'c > a > b'], equal=0, diagonal=0).as_array_
array([[0, 1, 1],
[0, 0, 0],
[0, 0, 0]])
"""
def __init__(self, *args, converter: ConverterBallot = None, matrix_weighted_majority: Matrix = None,
greater: Number = 1, lower: Number = 0, equal: Number = Fraction(1, 2),
diagonal: Number = Fraction(1, 2), **kwargs):
if converter is None:
converter = ConverterBallotToOrder()
if matrix_weighted_majority is None:
matrix_weighted_majority = MatrixWeightedMajority()
self.matrix_weighted_majority = matrix_weighted_majority
self.greater = convert_number(greater)
self.lower = convert_number(lower)
self.equal = convert_number(equal)
self.diagonal = convert_number(diagonal)
super().__init__(*args, converter=converter, **kwargs)
@cached_property
def matrix_weighted_majority_(self):
"""Matrix: The weighted majority matrix (upon which the computation of the majority matrix is based), once
computed with the given profile.
"""
return self.matrix_weighted_majority(self.profile_converted_)
@cached_property
def candidates_as_list_(self) -> list:
return self.matrix_weighted_majority_.candidates_as_list_
@cached_property
def candidates_indexes_(self) -> NiceDict:
return self.matrix_weighted_majority_.candidates_indexes_
@cached_property
def as_dict_(self):
def convert(x, y):
if x == y:
return self.equal
return self.greater if x > y else self.lower
weighted_as_dict = self.matrix_weighted_majority_.as_dict_
return NiceDict({
(c, d): self.diagonal if c == d else convert(weighted_as_dict[(c, d)], weighted_as_dict[(d, c)])
for (c, d) in weighted_as_dict.keys()
})