Source code for whalrus.matrices.matrix_ranked_pairs

# -*- 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.priorities.priority import Priority
from whalrus.utils.utils import cached_property, NiceDict
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
import numpy as np
from itertools import chain


[docs]class MatrixRankedPairs(Matrix): """ The ranked pairs 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`. tie_break : Priority The tie-break used when two duels have the same score. kwargs Cf. parent class. Examples -------- First, we compute a matrix `W` with the algorithm given in the parameter ``matrix_weighted_majority``. The ranked pair matrix represents a graph whose vertices are the candidates. In order to build it, we consider all duels between two distinct candidates `(c, d)`, by decreasing order of the value `W(c, d)`. We add an edge `(c, d)` in the ranked pairs matrix, except if it creates a cycle in the graph, and we consider the transitive closure. >>> m = MatrixRankedPairs(['a > b > c', 'b > c > a', 'c > a > b'], weights=[4, 3, 2]) >>> m.edges_order_ [('b', 'c'), ('a', 'b'), ('c', 'a')] >>> m.as_array_ array([[0, 1, 1], [0, 0, 1], [0, 0, 0]], dtype=object) In the example example above, the edge `(b, c)` is added. Then it is the edge `(a, b)` which, by transitive closure, also adds the edge `(a, c)`. Finally the edge `(c, a)` (representing the victory of `c` over `a` in the weighted majority matrix) should be added, but it would introduce a cycle in the graph, so it is ignored. If two duels have the same score, the tie-break is used. For example, with :attr:`Priority.ASCENDING`, we add a victory `(a, ...)` before a victory `(b, ...)`; and we add a victory `(a, c)` before a victory `(a, b)` (because `b` is favored over `c`). A very simple but illustrative example: >>> MatrixRankedPairs(['a > b > c'], tie_break=Priority.ASCENDING).edges_order_ [('a', 'c'), ('a', 'b'), ('b', 'c')] """ def __init__(self, *args, converter: ConverterBallot = None, matrix_weighted_majority: Matrix = None, tie_break: Priority = Priority.UNAMBIGUOUS, **kwargs): if converter is None: converter = ConverterBallotToOrder() if matrix_weighted_majority is None: matrix_weighted_majority = MatrixWeightedMajority() self.tie_break = tie_break 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 (upon which the computation of the Ranked Pairs 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 edges_order_(self) -> list: """list: The order in which edges should be added (if possible). It is a list of pairs of candidates. E.g. ``[('b', 'c'), ('c', 'a'), ('a', 'b')]``, where ('b', 'c') is the first edge to add. """ m = self.matrix_weighted_majority_ return list(chain(*[ self.tie_break.sort_pairs_rp({ (c, d) for (c, d), v in m.as_dict_.items() if v == value and c != d and m.as_dict_[(c, d)] >= m.as_dict_[(d, c)] }) for value in sorted(set(m.as_dict_.values()), reverse=True) ])) @cached_property def as_array_(self): n = len(self.candidates_) rp = np.zeros((n, n), dtype=object) for (c, d) in self.edges_order_: i = self.matrix_weighted_majority_.candidates_indexes_[c] j = self.matrix_weighted_majority_.candidates_indexes_[d] if rp[j, i] > 0: continue rp[i, j] = 1 rp[i, :] = np.maximum(rp[i, :], rp[j, :]) rp[:, j] = np.maximum(rp[:, i], rp[:, j]) return rp @cached_property def as_dict_(self): return NiceDict({(c, d): self.as_array_[self.candidates_indexes_[c], self.candidates_indexes_[d]] for c in self.candidates_ for d in self.candidates_})