def __monroe_bruteforce(profile, committeesize, resolute):
"""Brute-force computation of Monroe's rule"""
opt_committees = []
opt_monroescore = -1
for comm in combinations(list(range(profile.num_cand)), committeesize):
score = scores.monroescore(profile, comm)
if score > opt_monroescore:
opt_committees = [comm]
opt_monroescore = score
elif scores.monroescore(profile, comm) == opt_monroescore:
opt_committees.append(comm)
committees = sort_committees(opt_committees)
if resolute:
committees = [committees[0]]
return committees
def compute_monroe(profile, committeesize, algorithm="brute-force",
resolute=False, verbose=0):
"""Monroe's rule"""
enough_approved_candidates(profile, committeesize)
# optional output
if verbose:
print(header(rules["monroe"].longname))
if resolute:
print("Computing only one winning committee (resolute=True)\n")
if verbose >= 3:
if algorithm == "gurobi":
print("Using the Gurobi ILP solver\n")
if algorithm == "brute-force":
print("Using a brute-force algorithm\n")
# end of optional output
if not profile.has_unit_weights():
raise ValueError(rules["monroe"].shortname +
" is only defined for unit weights (weight=1)")
if algorithm == "gurobi":
committees = abcrules_gurobi.__gurobi_monroe(
profile, committeesize, resolute)
committees = sort_committees(committees)
elif algorithm == "brute-force":
committees = __monroe_bruteforce(
profile, committeesize, resolute)
else:
raise NotImplementedError(
"Algorithm " + str(algorithm)
+ " not specified for compute_monroe")
# optional output
if verbose:
print("Optimal Monroe score: "
+ str(scores.monroescore(profile, committees[0])) + "\n")
print(str_committees_header(committees, winning=True))
print(str_candsets(committees, names=profile.names))
# end of optional output
return committees
"""Example 7 (Greedy Monroe)
from the survey: "Approval-Based Multi-Winner Voting:
Axioms, Algorithms, and Applications"
by Martin Lackner and Piotr Skowron
"""
from __future__ import print_function
import sys
sys.path.insert(0, '..')
from abcvoting import abcrules
from survey import example01 as ex1
from abcvoting.scores import monroescore
from abcvoting import misc
print(misc.header("Example 7", "*"))
print(misc.header("Input (election instance from Example 1):"))
print(ex1.profile.str_compact())
committees = abcrules.compute_greedy_monroe(ex1.profile, 4, verbose=2)
# verify correctness
a, b, c, d, e, f, g = list(range(7)) # a = 0, b = 1, c = 2, ...
assert committees == [[a, c, d, f]]
assert monroescore(ex1.profile, committees[0]) == 10
{a, b},
{a, c},
{a, c},
{a, c},
{a, d},
{a, d},
{b, c, f},
{e},
{f},
{g},
]
profile = Profile(num_cand, cand_names="abcdefgh")
profile.add_voters(approval_sets)
committeesize = 4
#
print(misc.header("Example 7", "*"))
print(misc.header("Input (election instance from Example 1):"))
print(profile.str_compact())
committees = abcrules.compute_monroe(profile, 4)
# verify correctness
a, b, c, d, e, f, g = range(7) # a = 0, b = 1, c = 2, ...
assert len(committees) == 6
# Monroe-score of all committees is the same
score = monroescore(profile, committees[0])
for committee in committees:
assert score == monroescore(profile, committee)
def compute_greedy_monroe(profile, committeesize,
algorithm="standard", resolute=True, verbose=0):
""""Greedy Monroe"""
enough_approved_candidates(profile, committeesize)
if not profile.has_unit_weights():
raise ValueError(rules["greedy-monroe"].shortname +
" is only defined for unit weights (weight=1)")
if not resolute:
raise NotImplementedError(
"compute_greedy_monroe does not support resolute=False.")
if algorithm != "standard":
raise NotImplementedError(
"Algorithm " + str(algorithm)
+ " not specified for compute_greedy_monroe")
num_voters = len(profile)
committee = []
# remaining voters
remaining_voters = list(range(num_voters))
remaining_cands = set(range(profile.num_cand))
assignment = []
for t in range(committeesize):
maxapprovals = -1
selected = None
for c in remaining_cands:
approvals = len([i for i in remaining_voters
if c in profile[i]])
if approvals > maxapprovals:
maxapprovals = approvals
selected = c
# determine how many voters are removed (at most)
if t < num_voters - committeesize * (num_voters // committeesize):
num_remove = num_voters // committeesize + 1
else:
num_remove = num_voters // committeesize
# only voters that approve the chosen candidate
# are removed
to_remove = [i for i in remaining_voters
if selected in profile[i]]
if len(to_remove) > num_remove:
to_remove = to_remove[:num_remove]
assignment.append((selected, to_remove))
remaining_voters = [i for i in remaining_voters
if i not in to_remove]
committee.append(selected)
remaining_cands.remove(selected)
committees = sort_committees([committee])
# optional output
if verbose:
print(header(rules["greedy-monroe"].longname))
if verbose >= 2:
score1 = scores.monroescore(profile, committees[0])
score2 = len(profile) - len(remaining_voters)
print("The Monroe assignment computed by Greedy Monroe")
print("has a Monroe score of " + str(score2) + ".")
if score1 > score2:
print("Monroe assignment found by Greedy Monroe is not "
+ "optimal for the winning committee,")
print("i.e., by redistributing voters to candidates a higher "
+ "satisfaction is possible "
+ "(without changing the committee).")
print("Optimal Monroe score of the winning committee is "
+ str(score1) + ".")
# build actual Monroe assignment for winning committee
for t, district in enumerate(assignment):
cand, voters = district
if t < num_voters - committeesize * (num_voters // committeesize):
missing = num_voters // committeesize + 1 - len(voters)
else:
missing = num_voters // committeesize - len(voters)
for _ in range(missing):
v = remaining_voters.pop()
voters.append(v)
print("Assignment (unsatisfatied voters marked with *):\n")
for cand, voters in assignment:
print(" candidate " + profile.names[cand]
+ " assigned to: ", end="")
output = ""
for v in sorted(voters):
output += str(v)
if cand not in profile[v].approved:
output += "*"
output += ", "
print(output[:-2])
print()
if verbose:
print(str_committees_header(committees, winning=True))
print(str_candsets(committees, names=profile.names))
# end of optional output
return committees