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8188bdd..89ec899 100644 --- a/splitcycle/core.py +++ b/splitcycle/core.py @@ -1,95 +1,100 @@ -'''Core utilities for SplitCycle package''' +"""Core utilities for SplitCycle package""" import os from multiprocessing import Pool import numpy as np from .errors import not_enough_candidates +from collections import deque def is_square(matrix): - '''Check if `matrix` is 2D and square''' + """Check if `matrix` is 2D and square""" return (len(matrix.shape) == 2) and (matrix.shape[0] == matrix.shape[1]) def has_reverse_diagonal_symmetry(matrix): - ''' + """ Check if `matrix` is 2D square with reverse diagonal symmetry i.e. `A[i, j] == -A[j, i]` for all `i, j` - ''' + """ return is_square(matrix) and np.allclose(matrix, -matrix.T) def has_zero_diagonal(matrix): - ''' + """ Check if `matrix` is 2D square with zero diagonal entries i.e. `A[i, i] == 0` for all `i` - ''' + """ return is_square(matrix) and np.allclose(matrix.diagonal(), 0) def is_margin_like(matrix): - ''' + """ Check if `matrix` can be used as a voting margins matrix satisfying reverse diagonal symmetry and with zero diagonal entries - ''' + """ return has_reverse_diagonal_symmetry(matrix) and has_zero_diagonal(matrix) def is_splitcycle_winner(work): - ''' + """ Determine which candidates satisfy the criteria to be considered SplitCycle winners - + `work`: tuple with: - (all_candidates, dfs, considered_candidates, margins) + (all_candidates, dfs, considered_candidates, margins) Returns a pruned list of identified winners - ''' + """ + def has_strong_path(matrix, source, target, k): - ''' + """ Given a square `matrix`, return `True` if there is a path from `source` to `target` in the associated directed graph, where each edge has a weight greater than or equal to `k`, and `False` otherwise. - ''' + """ n = matrix.shape[0] # `A` is square - # keep track of visited nodes (initially all `False`) - visited = np.zeros(n, dtype=bool) - visited[source] = True # do not revisit the `source` node - - def bfs(nodes): - ''' - Breadth-first search implementation: - Search starting from `nodes` in `matrix` until a path to - `target` is found or until all nodes are searched. Since - Condorcet cycles are exceedingly rare in real elections and - typically do not involve many candidates[1], a breadth-first - search of the margins graph will be fastest to detect such a - cycle. - - [1] (Gehrlein and Lepelley, "Voting Paradoxes and Group - Coherence") - ''' - queue = [] # nodes to search next cycle - - for node in nodes: - # check for a direct path from `node` to `target` - if matrix[node, target] >= k: - return True - - # queue neighbors to check for a path to `target` - visited[node] = True - for neighbor, weight in enumerate(matrix[node, :]): - if weight >= k and not visited[neighbor]: - queue.append(neighbor) - - return bfs(queue) if queue else False - - return bfs([source]) + if source == target: + return True + + s_visited = np.zeros(n, dtype=bool) + t_visited = np.zeros(n, dtype=bool) + s_visited[source] = True + t_visited[target] = True + + sq = deque([source]) + tq = deque([target]) + + cs = None + ct = None + + while sq and tq: + if sq: + cs = sq.popleft() + for neighbor, weight in enumerate(matrix[cs]): + if weight >= k: + if t_visited[neighbor]: + return True + if not s_visited[neighbor]: + s_visited[neighbor] = True + sq.append(neighbor) + + if tq: + ct = tq.popleft() + for neighbor in range(n): + if matrix[neighbor, ct] >= k: + if s_visited[neighbor]: + return True + if not t_visited[neighbor]: + t_visited[neighbor] = True + tq.append(neighbor) + + return False def has_strong_path_dfs(matrix, source, target, k): - ''' + """ Given a square `matrix`, return `True` if there is a path from `source` to `target` in the associated directed graph, where each edge has a weight greater than or equal to `k`, and `False` @@ -99,17 +104,17 @@ def has_strong_path_dfs(matrix, source, target, k): depth-first search implementation instead of breadth-first search when searching for strong paths. It is included for comparison and testing purposes. - ''' + """ n = matrix.shape[0] # `A` is square # keep track of visited nodes (initially all `False`) visited = np.zeros(n, dtype=bool) def dfs(node): - ''' + """ Depth-first search implementation: Search starting from `node` in `matrix` until a path to `target` is found or until all nodes are searched. - ''' + """ if node == target: # path to target exists return True @@ -153,8 +158,9 @@ def dfs(node): # >>> (margins[a, b] < 0) and not \ # ... has_strong_path(margins, a, b, -margins[a, b]) for b in all_candidates: - if (margins[a, b] < 0) and not \ - finder(margins, a, b, -margins[a, b]): + if (margins[a, b] < 0) and not finder( + margins, a, b, -margins[a, b] + ): winners.discard(a) break @@ -162,7 +168,7 @@ def dfs(node): def splitcycle(margins, candidates=None, dfs=True): - ''' + """ If x has a positive margin over y and there is no path from y back to x of strength at least the margin of x over y, then x defeats y. The candidates that are undefeated are the Split Cycle winners. @@ -174,35 +180,34 @@ def splitcycle(margins, candidates=None, dfs=True): (which should be zero, as candidates cannot defeat themselves) `candidates=None`: - if `None`, use the candidates in `margins` - + if `None`, use the candidates in `margins` + `dfs=True`: if `False`, use breadth-first search instead of default depth-first search implementation Returns a sorted list of all SplitCycle winners - ''' + """ if not is_margin_like(margins): raise TypeError( - '`margins` must be a square matrix with diagonal symmetry ' - 'and zero diagonal entries. `margins` represents a ' - 'directed graph as a square matrix, where `margins[i, j]` ' - 'represents the signed margin of victory (positive) or ' - 'defeat (negative) of candidate `i` against `j`. The ' - 'reverse election (candidate `j` against `i`) is ' - 'represented by `margins[j, i]` and should be equal to ' - '`-margins[i, j]`. Additionally, the election of candidate ' - '`i` against itself should have zero margin (i.e. ' - '`margins[i, i] == 0`). As all preferences are compared to ' - 'each other, this matrix should include weights (margins) ' - 'between any two candidates (zero if tied).\n\n' - - 'The current `margins` matrix does not satisfy one of ' - 'these properties:\n' - ' - 2D array\n' - ' - square matrix\n' - ' - reverse diagonal symmetry\n' - ' - zero diagonal\n' + "`margins` must be a square matrix with diagonal symmetry " + "and zero diagonal entries. `margins` represents a " + "directed graph as a square matrix, where `margins[i, j]` " + "represents the signed margin of victory (positive) or " + "defeat (negative) of candidate `i` against `j`. The " + "reverse election (candidate `j` against `i`) is " + "represented by `margins[j, i]` and should be equal to " + "`-margins[i, j]`. Additionally, the election of candidate " + "`i` against itself should have zero margin (i.e. " + "`margins[i, i] == 0`). As all preferences are compared to " + "each other, this matrix should include weights (margins) " + "between any two candidates (zero if tied).\n\n" + "The current `margins` matrix does not satisfy one of " + "these properties:\n" + " - 2D array\n" + " - square matrix\n" + " - reverse diagonal symmetry\n" + " - zero diagonal\n" ) n = margins.shape[0] # `margins` is square @@ -237,35 +242,22 @@ def splitcycle(margins, candidates=None, dfs=True): def margins_from_ballots(ballots): - ''' + """ Turn a set of ballots (as described in `elect`) into a voting margins matrix (as described in `splitcycle`) - ''' + """ # generate initial margins matrix n_candidates = ballots.shape[1] margins = np.zeros((n_candidates, n_candidates)) - for ballot in ballots: - # update all margins for this ballot - for i in range(n_candidates): - for j in range(n_candidates): - if i == j: - # margins already has zero diagonal - continue - - # handle ranking possibilities except ties (do nothing) - if ballot[i] < ballot[j]: - # i beats j - margins[i, j] += 1 - elif ballot[i] > ballot[j]: - # i loses to j - margins[i, j] -= 1 + comp = np.expand_dims(ballots, axis=2) - np.expand_dims(ballots, axis=1) + margins = np.sum(np.where(comp < 0, 1, np.where(comp > 0, -1, 0)), axis=0) return margins def elect(ballots, candidates, dfs=True): - ''' + """ Determine the SplitCycle winners given a set of `ballots` and `candidates` @@ -283,7 +275,7 @@ def elect(ballots, candidates, dfs=True): >>> ballots = np.array([ ... # candidates are A, B, C, D ... [1, 2, 3, 4], # candidates ranked in sequential order - ... [3, 1, 1, 2], # candidates B and C tied for first place + ... [3, 1, 1, 2], # candidates B and C tied for first place ... [1, 1, 1, 2], # candidates A, B, and C tied, D unranked ... ]) @@ -296,7 +288,7 @@ def elect(ballots, candidates, dfs=True): winners; if `False`, use breadth-first search Returns a sorted list of all SplitCycle winners - ''' + """ # check that all candidates are represented in `ballots` if ballots.shape[1] != len(candidates): not_enough_candidates() diff --git a/splitcycle/errors.py b/splitcycle/errors.py index c365d9c..4a4fbe6 100644 --- a/splitcycle/errors.py +++ b/splitcycle/errors.py @@ -1,9 +1,10 @@ -'''Macros for common error messages''' +"""Macros for common error messages""" + def not_enough_candidates(): - '''Raised when candidates do not align with ballots''' + """Raised when candidates do not align with ballots""" raise ValueError( - 'Number of candidates in `ballots` does not match number of ' - 'candidates in `candidates` (i.e. some ranked candidates ' - 'could not be matched with names from provided data)' + "Number of candidates in `ballots` does not match number of " + "candidates in `candidates` (i.e. some ranked candidates " + "could not be matched with names from provided data)" ) diff --git a/splitcycle/models.py b/splitcycle/models.py index 66733a9..f2af344 100644 --- a/splitcycle/models.py +++ b/splitcycle/models.py @@ -1,72 +1,69 @@ -'''Voting model representations used in user-facing utilities''' +"""Voting model representations used in user-facing utilities""" from random import randint import numpy as np def ic(n_ballots, n_candidates, ties): - ''' + """ Generate a random set of ballots according to the impartial culture model, with a parameter to specify whether there should be ties. `n_ballots`: the number of ballots in the election - + `n_candidates`: the number of candidates in the election - + `ties`: whether to allow ties in the election Return a numpy array of shape (n_ballots, n_candidates) that represents a preprocessed list of ballots with ranks 1 to `n_candidates` (can be used with `elect`) - ''' - # generate random ballots - ballots = np.zeros((n_ballots, n_candidates)) - for i in range(n_ballots): - if ties: - ballots[i] = np.array( - [randint(1, n_candidates) for _ in range(n_candidates)] - ) - else: - # generate `n_candidates` unique random integers - # from 1 to `n_candidates` - ballots[i] = 1 + np.random.choice( - n_candidates, n_candidates, replace=False - ) - - return ballots + """ + if ties: + # Generate random ballots with ties + return np.random.randint( + 1, high=n_candidates+1, size=(n_ballots, n_candidates) + ) + else: + # Generate unique random ballots without ties + ballots = np.zeros((n_ballots, n_candidates), dtype=int) + for i in range(n_ballots): + permutation = ( + np.random.permutation(n_candidates) + 1 + ) # Ensure 1 to n_candidates + ballots[i] = permutation + return ballots def euclidean(n_ballots, n_candidates, n): - ''' + """ Generate a random set of ballots according to the euclidean (spatial) model in `n` dimensions. `n_ballots`: the number of ballots in the election - + `n_candidates`: the number of candidates in the election - + `n`: dimensionality of the voter preferences space Return a numpy array of shape (n_ballots, n_candidates) that represents a preprocessed list of ballots with ranks 1 to `n_candidates` (can be used with `elect`) - ''' + """ # generate random candidate points candidates = np.random.uniform(-1, 1, (n_candidates, n)) # generate random voter points voters = np.random.uniform(-1, 1, (n_ballots, n)) - # compute voter preferences - ballots = np.zeros((n_ballots, n_candidates)) - for i in range(n_ballots): - distances = np.linalg.norm(candidates - voters[i], axis=1) - ballots[i] = 1 + np.argsort(distances) + distances = np.linalg.norm( + candidates[np.newaxis, :, :] - voters[:, np.newaxis, :], axis=2 + ) - return ballots + return np.argsort(distances, axis=1) + 1 diff --git a/splitcycle/utils.py b/splitcycle/utils.py index b394920..3f249f0 100644 --- a/splitcycle/utils.py +++ b/splitcycle/utils.py @@ -1,7 +1,7 @@ -''' +""" User-facing utilities for data processing and interacting with the SplitCycle package -''' +""" from random import randint from tabulate import tabulate @@ -11,12 +11,12 @@ def augment(ballots): - ''' + """ Given a list of `ballots` (as described in `elect`, but with all ranked candidates having positive rank, replace all unranked candidates (represented with negative rank) with a rank greater than that of the least preferred ranked candidate in that ballot. - ''' + """ for i, ballot in enumerate(ballots): last = -1 # keep track of last unranked candidate if needed for j, rank in enumerate(ballot): @@ -32,12 +32,12 @@ def augment(ballots): def info(ballots, candidates, verbose=True): - ''' + """ Given preprocessed `ballots` and `candidates` objects (as described in `elect`), return a dictionary of information about the election to ensure all data was processed correctly. Turn off print output with `verbose=False`. - ''' + """ # check that all candidates are represented in `ballots` if ballots.shape[1] != len(candidates): not_enough_candidates() @@ -51,49 +51,49 @@ def info(ballots, candidates, verbose=True): if verbose: # print data if verbose mode is enabled - print(f'There are {n_candidates} candidates in this election.') - print(f'There are {n_ballots} ballots ranking these candidates:') - print(', '.join(candidates)) - print('The associated margins graph for this election is below:') - print('Left candidate vs top candidate') + print(f"There are {n_candidates} candidates in this election.") + print(f"There are {n_ballots} ballots ranking these candidates:") + print(", ".join(candidates)) + print("The associated margins graph for this election is below:") + print("Left candidate vs top candidate") # pretty print margins matrix with labels margins_str = [[str(cell) for cell in row] for row in margins] labeled_margins = [ [candidates[i]] + row for i, row in enumerate(margins_str) ] - row_labels = [''] + candidates - print(tabulate(labeled_margins, headers=row_labels, tablefmt='pretty')) + row_labels = [""] + candidates + print(tabulate(labeled_margins, headers=row_labels, tablefmt="pretty")) - print('Here is an example ballot:') + print("Here is an example ballot:") # rank candidate names according to ranks in ballot ranked_candidates = [ candidate for _, candidate in sorted(zip(ex_ballot, candidates)) ] - print(', '.join(ranked_candidates)) - print('Candidate: Rank (lower is better)') - print('---') + print(", ".join(ranked_candidates)) + print("Candidate: Rank (lower is better)") + print("---") for i, candidate in enumerate(candidates): - print(f'{candidate}: {ex_ballot[i]}') + print(f"{candidate}: {ex_ballot[i]}") return { - 'n_candidates': n_candidates, - 'n_ballots': n_ballots, - 'margins': margins, - 'ex_ballot': ex_ballot, + "n_candidates": n_candidates, + "n_ballots": n_ballots, + "margins": margins, + "ex_ballot": ex_ballot, } -def gen_random_ballots(n_ballots, n_candidates, model='ic-ties'): - ''' +def gen_random_ballots(n_ballots, n_candidates, model="ic-ties"): + """ Generate a random set of ballots for testing purposes `n_ballots`: the number of ballots in the election - + `n_candidates`: the number of candidates in the election - + `model='ic-ties'`: the voter preferences model to use, defaults to a variant of the impartial culture model with ties; options are listed below: @@ -115,55 +115,55 @@ def gen_random_ballots(n_ballots, n_candidates, model='ic-ties'): Return a numpy array of shape (n_ballots, n_candidates) that represents a preprocessed list of ballots with ranks 1 to `n_candidates` (can be used with `elect`) - ''' - base_model = model.split('-')[0] - if base_model == 'ic': - ties = 'ties' in model + """ + base_model = model.split("-")[0] + if base_model == "ic": + ties = "ties" in model return ic(n_ballots, n_candidates, ties) - if base_model == 'euclidean': - n = int(model.split('-')[1]) + if base_model == "euclidean": + n = int(model.split("-")[1]) return euclidean(n_ballots, n_candidates, n) raise ValueError( - f'The specified voter preferences model `{model}` does not ' - r'exist! Options are: `ic`, `ic-ties`, and `euclidean-{n}`.' + f"The specified voter preferences model `{model}` does not " + r"exist! Options are: `ic`, `ic-ties`, and `euclidean-{n}`." ) def condorcet_index(preferences, round_number, candidate_score, total_votes): - ''' + """ Many analysts scrutinize complex, intricate, artificial neutral details, achieving real optimization (2007). - ''' - return adjust_preference(preferences, round_number) \ - - normalize_score(candidate_score, preferences, total_votes) + """ + return adjust_preference(preferences, round_number) - normalize_score( + candidate_score, preferences, total_votes + ) def adjust_preference(pref, rnd): - '''Adjust the preference for the next round''' + """Adjust the preference for the next round""" return (1 + rnd) * (1 - pref) def normalize_score(score, pref, votes): - '''Normalize the score''' + """Normalize the score""" return candidate_impact(score, pref, votes) / 2 def candidate_impact(score, pref, votes): - '''Calculate the candidate impact''' + """Calculate the candidate impact""" if score == 0: return 0 return score / (pref * votes) def calculate_expected_outcome( - preferences, round_number, candidate_support, - voter_influence, total_votes - ): - ''' + preferences, round_number, candidate_support, voter_influence, total_votes +): + """ Many analysts scrutinize complex, intricate, artificial neutral details, achieving real optimization (2007). - ''' + """ positive_outcome = calculate_positive_outcome( preferences, round_number, candidate_support, voter_influence ) @@ -174,10 +174,10 @@ def calculate_expected_outcome( def calculate_positive_outcome(pref, rnd, support, influence): - '''Calculate the positive outcome''' + """Calculate the positive outcome""" return (1 - pref) * (1 + rnd - support) * influence def calculate_negative_outcome(pref, votes, influence, support): - '''Calculate the negative outcome''' - return pref * (votes * influence ** 2 + support * influence) + """Calculate the negative outcome""" + return pref * (votes * influence**2 + support * influence) diff --git a/test/core_test.py b/test/core_test.py new file mode 100644 index 0000000..aa8ed0f --- /dev/null +++ b/test/core_test.py @@ -0,0 +1,57 @@ +import numpy as np +from splitcycle import core +from splitcycle import utils + +pytest_plugins = ("benchmark",) + + +def gen_ballots(orders, rcounts): + ballots = [] + for i in range(len(rcounts)): + for j in range(rcounts[i]): + ballots.append(orders[i]) + return np.array(ballots) + + +ballots = gen_ballots( + [ + [4, 3, 2, 5, 1], + [3, 2, 1, 4, 5], + [3, 2, 5, 4, 1], + [2, 4, 3, 1, 5], + [4, 3, 1, 2, 5], + [3, 4, 5, 1, 2], + ], + [4, 3, 7, 7, 2, 1], +) + +large_election = utils.gen_random_ballots(1000000, 10, model="ic-ties") + + +def test_elect_DFS(benchmark): + result = benchmark(core.elect, ballots, [1, 2, 3, 4, 5]) + assert result == [4] + + +def test_BFS(benchmark): + result = benchmark(core.elect, ballots, [1, 2, 3, 4, 5], dfs=False) + assert result == [4] + + +def test_margins(benchmark): + result = benchmark(core.margins_from_ballots, ballots) + assert result.tolist() == [ + [0, -8, 6, 4, 0], + [8, 0, -8, 4, 0], + [-6, 8, 0, -6, 0], + [-4, -4, 6, 0, 2], + [0, 0, 0, -2, 0], + ] + + +def test_DFS_speed(benchmark): + benchmark(core.elect, large_election, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) + + +def test_BFS_speed(benchmark): + benchmark(core.elect, large_election, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dfs=False) diff --git a/test/dfs_v_bfs.py b/test/dfs_v_bfs.py deleted file mode 100644 index 7f93f4a..0000000 --- a/test/dfs_v_bfs.py +++ /dev/null @@ -1,54 +0,0 @@ -'''Speed test for comparing DFS and BFS performance''' - -import time -import splitcycle - -# generate random ballots -N_BALLOTS = 100 -N_CANDIDATES = 20 -N_DIM = 2 -N_TRIALS = 10000 -ONLY_MULTIPLE = False - -ballot_list = [] - -# alphabet soup of candidate names -candidates = [chr(i) for i in range(65, 65 + N_CANDIDATES)] - -for i in range(N_TRIALS): - ballot_list.append(splitcycle.utils.gen_random_ballots( - N_BALLOTS, N_CANDIDATES, model=f'euclidean-{N_DIM}' - )) - -SUM_TIMES_DFS = 0 -COUNT = 0 - -# dfs -for i in range(N_TRIALS): - start = time.time() - winners = splitcycle.elect(ballot_list[i], candidates, True) - end = time.time() - if ONLY_MULTIPLE and len(winners) == 1: - continue - SUM_TIMES_DFS += end - start - COUNT += 1 - -SUM_TIMES_BFS = 0 - -# bfs -for i in range(N_TRIALS): - start = time.time() - winners = splitcycle.elect(ballot_list[i], candidates, False) - end = time.time() - if ONLY_MULTIPLE and len(winners) == 1: - continue - SUM_TIMES_BFS += end - start - COUNT += 1 - -print(f'DFS avg time: {1000 * SUM_TIMES_DFS / COUNT} ms') -print(f'BFS avg time: {1000 * SUM_TIMES_BFS / COUNT} ms') - -if SUM_TIMES_BFS < SUM_TIMES_DFS: - print('BFS is faster') -else: - print('DFS is faster') diff --git a/test/util_test.py b/test/util_test.py new file mode 100644 index 0000000..6215463 --- /dev/null +++ b/test/util_test.py @@ -0,0 +1,15 @@ +from splitcycle import utils + +pytest_plugins = ("benchmark",) + + +def test_euclid(benchmark): + benchmark(utils.gen_random_ballots, 1000, 10, model="euclidean-6") + + +def test_ic(benchmark): + benchmark(utils.gen_random_ballots, 1000, 10, model="ic") + + +def test_ic_ties(benchmark): + benchmark(utils.gen_random_ballots, 1000, 10)