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pyRCV2/pyRCV2/method/base_stv.py

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Python

# pyRCV2: Preferential vote counting
# Copyright © 2020–2021 Lee Yingtong Li (RunasSudo)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program 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 Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
__pragma__ = lambda x: None
from pyRCV2.model import CandidateState, CountCard, CountCompleted, CountStepResult
import pyRCV2.numbers
from pyRCV2.numbers import Num
from pyRCV2.safedict import SafeDict
import pyRCV2.ties
class STVException(Exception):
def __init__(self, message):
Exception.__init__(self)
self.message = message
class BaseSTVCounter:
"""
Basic STV counter for various different variations
"""
def __init__(self, election, options=None):
self.election = election
# Default options
self.options = {
'bulk_elect': True, # Bulk election?
'bulk_exclude': False, # Bulk exclusion?
'defer_surpluses': False, # Defer surpluses?
'quota': 'droop', # 'droop', 'droop_exact', 'hare' or 'hare_exact'
'quota_criterion': 'geq', # 'geq' or 'gt'
'quota_mode': 'static', # 'static', 'progressive' or 'ers97'
'surplus_order': 'size', # 'size' or 'order'
'papers': 'both', # 'both' or 'transferable'
'exclusion': 'one_round', # 'one_round', 'parcels_by_order', 'by_value' or 'wright'
'ties': [], # List of tie strategies (e.g. TiesRandom)
'round_quota': None, # Number of decimal places or None
'round_votes': None, # Number of decimal places or None
'round_tvs': None, # Number of decimal places or None
'round_weights': None, # Number of decimal places or None
}
if options is not None:
self.options.update(options)
self.candidates = SafeDict([(c, CountCard()) for c in self.election.candidates])
self.exhausted = CountCard()
self.loss_fraction = CountCard()
self.total_orig = sum((b.value for b in self.election.ballots), Num('0'))
self.logs = []
self.step_results = []
self.num_elected = 0
self.num_excluded = 0
self.num_withdrawn = 0
# Withdraw candidates
for candidate in self.election.withdrawn:
__pragma__('opov')
self.candidates[candidate].state = CandidateState.WITHDRAWN
__pragma__('noopov')
self.num_withdrawn += 1
def reset(self):
"""
Public function:
Perform the first step (distribute first preferences)
Does not reset the states of candidates, etc.
"""
self._exclusion = None # Optimisation to avoid re-collating/re-sorting ballots
self.distribute_first_preferences()
self.logs.append('First preferences distributed.')
self.quota = None
self.vote_required_election = None # For ERS97
self.compute_quota()
self.elect_meeting_quota()
return self.make_result('First preferences')
def distribute_first_preferences(self):
"""
Distribute first preferences (called as part of the reset() step)
"""
for ballot in self.election.ballots:
__pragma__('opov')
candidate = next((c for c in ballot.preferences if self.candidates[c].state == CandidateState.HOPEFUL), None)
if candidate is not None:
self.candidates[candidate].transfers += ballot.value
if len(self.candidates[candidate].parcels) == 0:
self.candidates[candidate].parcels.append([(ballot, Num(ballot.value))])
else:
self.candidates[candidate].parcels[0].append((ballot, Num(ballot.value)))
else:
self.exhausted.transfers += ballot.value
#self.exhausted.parcels[0].append((ballot, Num(ballot.value)))
__pragma__('noopov')
def step(self):
"""
Public function:
Perform one step of the STV count
"""
# Step count cards
self.step_count_cards()
# Check if done
result = self.before_surpluses()
if result:
return result
# Distribute surpluses
result = self.distribute_surpluses()
if result:
return result
# Check if done (2)
result = self.before_exclusion()
if result:
return result
# Insufficient winners and no surpluses to distribute
# Exclude the lowest ranked hopeful(s)
result = self.exclude_candidates()
if result:
return result
raise STVException('Unable to complete step') # pragma: no cover
def step_count_cards(self):
"""
Reset the count cards for the beginning of a new step
"""
for candidate, count_card in self.candidates.items():
count_card.step()
self.exhausted.step()
self.loss_fraction.step()
def before_surpluses(self):
"""
Check if the count can be completed before distributing surpluses
"""
# Have sufficient candidates been elected?
if self.num_elected >= self.election.seats:
__pragma__('opov')
return CountCompleted(
'Count complete',
self.logs,
self.candidates,
self.exhausted,
self.loss_fraction,
self.total + self.exhausted.votes + self.loss_fraction.votes,
self.quota,
self.vote_required_election,
)
__pragma__('noopov')
# Are there just enough candidates to fill all the seats?
if self.options['bulk_elect']:
# Include EXCLUDING to avoid interrupting an exclusion
if len(self.election.candidates) - self.num_withdrawn - self.num_excluded + sum(1 for c, cc in self.candidates.items() if cc.state == CandidateState.EXCLUDING) <= self.election.seats:
# Declare elected all remaining candidates
candidates_elected = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.HOPEFUL]
if len(candidates_elected) == 1:
self.logs.append(candidates_elected[0][0].name + ' is elected to fill the remaining vacancy.')
else:
self.logs.append(self.pretty_join([c.name for c, cc in candidates_elected]) + ' are elected to fill the remaining vacancies.')
for candidate, count_card in candidates_elected:
count_card.state = CandidateState.PROVISIONALLY_ELECTED
self.num_elected += 1
count_card.order_elected = self.num_elected
return self.make_result('Bulk election')
def can_defer_surpluses(self, has_surplus):
"""
Determine if the specified surpluses can be deferred
"""
# Do not defer if this could change the last 2 candidates
__pragma__('opov')
total_surpluses = sum((cc.votes - self.quota for c, cc in has_surplus), Num(0))
__pragma__('noopov')
hopefuls = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.HOPEFUL]
hopefuls.sort(key=lambda x: x[1].votes)
__pragma__('opov')
if total_surpluses > hopefuls[1][1].votes - hopefuls[0][1].votes:
return False
__pragma__('noopov')
# Do not defer if this could affect a bulk exclusion
if self.options['bulk_exclude']:
to_bulk_exclude = self.candidates_to_bulk_exclude(hopefuls)
if len(to_bulk_exclude) > 0:
total_excluded = sum((cc.votes for c, cc in to_bulk_exclude), Num(0))
__pragma__('opov')
if total_surpluses > hopefuls[len(to_bulk_exclude) + 1][1].votes - total_excluded:
return False
__pragma__('opov')
# Can defer surpluses
self.logs.append('Distribution of surpluses totalling ' + total_surpluses.pp(2) + ' votes will be deferred.')
return True
def distribute_surpluses(self):
"""
Distribute surpluses, if any
"""
# Do not interrupt an exclusion
if any(cc.state == CandidateState.EXCLUDING for c, cc in self.candidates.items()):
return
candidate_surplus, count_card = None, None
# Are we distributing a surplus?
has_surplus = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.DISTRIBUTING_SURPLUS]
if len(has_surplus) > 0:
candidate_surplus, count_card = has_surplus[0]
else:
# Do surpluses need to be distributed?
__pragma__('opov')
has_surplus = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.PROVISIONALLY_ELECTED and cc.votes > self.quota]
__pragma__('noopov')
if len(has_surplus) > 0:
# Distribute surpluses in specified order
if self.options['surplus_order'] == 'size':
has_surplus.sort(key=lambda x: x[1].votes, reverse=True)
elif self.options['surplus_order'] == 'order':
has_surplus.sort(key=lambda x: x[1].order_elected)
else: # pragma: no cover
raise STVException('Invalid surplus order option')
# Attempt to defer all remaining surpluses if possible
if self.options['defer_surpluses']:
if self.can_defer_surpluses(has_surplus):
has_surplus = []
if len(has_surplus) > 0:
# Cannot defer any surpluses
if self.options['surplus_order'] == 'size':
candidate_surplus, count_card = self.choose_highest(has_surplus) # May need to break ties
elif self.options['surplus_order'] == 'order':
candidate_surplus, count_card = has_surplus[0] # Ties were already broken when these were assigned
if candidate_surplus is not None:
count_card.state = CandidateState.DISTRIBUTING_SURPLUS
__pragma__('opov')
surplus = count_card.votes - self.quota
__pragma__('noopov')
# Transfer surplus
self.do_surplus(candidate_surplus, count_card, surplus)
# Declare elected any candidates meeting the quota as a result of surpluses
self.compute_quota()
self.elect_meeting_quota()
return self.make_result('Surplus of ' + candidate_surplus.name)
def do_surplus(self, candidate_surplus, count_card, surplus):
"""
Transfer the surplus of the given candidate
Subclasses must override this function
"""
raise NotImplementedError('Method not implemented') # pragma: no cover
def before_exclusion(self):
"""
Check before excluding a candidate
"""
# If we did not perform bulk election in before_surpluses: Are there just enough candidates to fill all the seats?
if not self.options['bulk_elect']:
if len(self.election.candidates) - self.num_withdrawn - self.num_excluded <= self.election.seats:
# Declare elected one remaining candidate at a time
hopefuls = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.HOPEFUL]
hopefuls.sort(key=lambda x: x[1].votes, reverse=True)
candidate_elected, count_card = self.choose_highest(hopefuls)
count_card.state = CandidateState.PROVISIONALLY_ELECTED
self.num_elected += 1
count_card.order_elected = self.num_elected
return self.make_result('Bulk election')
def exclude_candidates(self):
"""
Exclude the lowest ranked hopeful(s)
"""
candidates_excluded = self.candidates_to_exclude()
for candidate, count_card in candidates_excluded:
if count_card.state != CandidateState.EXCLUDING:
count_card.state = CandidateState.EXCLUDING
self.num_excluded += 1
count_card.order_elected = -self.num_excluded
# Handle Wright STV
if self.options['exclusion'] == 'wright':
for candidate, count_card in candidates_excluded:
count_card.state = CandidateState.EXCLUDED
# Reset the count
# Carry over certain candidate states
new_candidates = SafeDict()
for candidate, count_card in self.candidates.items():
new_count_card = CountCard()
if count_card.state == CandidateState.WITHDRAWN:
new_count_card.state = CandidateState.WITHDRAWN
elif count_card.state == CandidateState.EXCLUDED:
new_count_card.state = CandidateState.EXCLUDED
__pragma__('opov')
new_candidates[candidate] = new_count_card
__pragma__('noopov')
self.candidates = new_candidates
self.exhausted = CountCard()
self.loss_fraction = CountCard()
self.num_elected = 0
step_results = self.step_results # Carry over step results
result = self.reset()
self.step_results = step_results
result.comment = 'Exclusion of ' + ', '.join([c.name for c, cc in candidates_excluded])
return result
# Exclude this candidate
self.do_exclusion(candidates_excluded)
# Declare any candidates meeting the quota as a result of exclusion
self.compute_quota()
self.elect_meeting_quota()
return self.make_result('Exclusion of ' + ', '.join([c.name for c, cc in candidates_excluded]))
def candidates_to_bulk_exclude(self, hopefuls):
"""
Determine which candidates can be bulk excluded
Returns List[Tuple[Candidate, CountCard]]
"""
remaining_candidates = len(self.election.candidates) - self.num_withdrawn - self.num_excluded
__pragma__('opov')
total_surpluses = sum((cc.votes - self.quota for c, cc in self.candidates.items() if cc.votes > self.quota), Num(0))
__pragma__('noopov')
# Attempt to exclude as many candidates as possible
for i in range(0, len(hopefuls)):
try_exclude = hopefuls[0:len(hopefuls)-i]
# Do not exclude if this splits tied candidates
__pragma__('opov')
if i != 0 and try_exclude[len(hopefuls)-i-1][1].votes == hopefuls[len(hopefuls)-i][1].votes:
continue
__pragma__('noopov')
# Do not exclude if this leaves insufficient candidates
if remaining_candidates - len(try_exclude) < self.election.seats:
continue
# Do not exclude if this could change the order of exclusion
total_votes = sum((cc.votes for c, cc in try_exclude), Num(0))
__pragma__('opov')
if i != 0 and total_votes + total_surpluses > hopefuls[len(hopefuls)-i][1].votes:
continue
__pragma__('noopov')
# Can bulk exclude
return try_exclude
return []
def candidates_to_exclude(self):
"""
Determine the candidate(s) to exclude
Returns List[Tuple[Candidate, CountCard]]
"""
# Continue current exclusion if applicable
if self._exclusion is not None:
self.logs.append('Continuing exclusion of ' + self.pretty_join([c.name for c, cc in self._exclusion[0]]) + '.')
__pragma__('opov')
return self._exclusion[0]
__pragma__('noopov')
hopefuls = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.HOPEFUL]
hopefuls.sort(key=lambda x: x[1].votes)
candidates_excluded = []
# Bulk exclusion
if self.options['bulk_exclude']:
if self.options['exclusion'] == 'parcels_by_order':
# Ordering of parcels is not defined in this case
raise STVException('Cannot use bulk_exclude with parcels_by_order')
candidates_excluded = self.candidates_to_bulk_exclude(hopefuls)
if len(candidates_excluded) > 0:
if len(candidates_excluded) == 1:
self.logs.append('No surpluses to distribute, so ' + candidates_excluded[0][0].name + ' is excluded.')
else:
self.logs.append('No surpluses to distribute, so ' + self.pretty_join([c.name for c, cc in candidates_excluded]) + ' are excluded.')
else:
candidates_excluded = [self.choose_lowest(hopefuls)]
self.logs.append('No surpluses to distribute, so ' + candidates_excluded[0][0].name + ' is excluded.')
return candidates_excluded
def do_exclusion(self, candidates_excluded):
"""
Exclude the given candidate and transfer the votes
Subclasses must override this function
"""
raise NotImplementedError('Method not implemented') # pragma: no cover
def compute_quota(self):
"""
Recount total votes and (if applicable) recalculate the quota
"""
__pragma__('opov')
self.total = sum((cc.votes for c, cc in self.candidates.items()), Num('0'))
self.loss_fraction.transfers += (self.total_orig - self.total - self.exhausted.votes) - self.loss_fraction.votes
if self.quota is None or self.options['quota_mode'] == 'progressive':
if self.options['quota'] == 'droop' or self.options['quota'] == 'droop_exact':
self.quota = self.total / Num(self.election.seats + 1)
elif self.options['quota'] == 'hare' or self.options['quota'] == 'hare_exact':
self.quota = self.total / Num(self.election.seats)
else:
raise STVException('Invalid quota option') # pragma: no cover
if self.options['round_quota'] is not None:
if self.options['quota'] == 'droop' or self.options['quota'] == 'hare':
# Increment to next available increment
factor = Num(10).__pow__(self.options['round_quota'])
__pragma__('opov')
self.quota = ((self.quota * factor).__floor__() + Num(1)) / factor
__pragma__('noopov')
else:
# Round up (preserving the original quota if exact)
self.quota = self.quota.round(self.options['round_quota'], self.quota.ROUND_UP)
self.logs.append(self.total.pp(2) + ' usable votes, so the quota is ' + self.quota.pp(2) + '.')
__pragma__('noopov')
if self.options['quota_mode'] == 'ers97' and self.num_elected < self.election.seats:
# Calculate the total active vote
__pragma__('opov')
orig_vre = self.vote_required_election
total_active_vote = \
sum((cc.votes for c, cc in self.candidates.items() if cc.state == CandidateState.HOPEFUL or cc.state == CandidateState.EXCLUDING), Num('0')) + \
sum((cc.votes - self.quota for c, cc in self.candidates.items() if (cc.state == CandidateState.PROVISIONALLY_ELECTED or cc.state == CandidateState.DISTRIBUTING_SURPLUS or cc.state == CandidateState.ELECTED) and cc.votes > self.quota), Num('0'))
self.vote_required_election = total_active_vote / Num(self.election.seats - self.num_elected + 1)
if self.options['round_votes'] is not None:
self.vote_required_election = self.vote_required_election.round(self.options['round_votes'], self.vote_required_election.ROUND_UP)
if (orig_vre is None or self.vote_required_election != orig_vre) and self.vote_required_election < self.quota:
self.logs.append('Total active vote is ' + total_active_vote.pp(2) + ', so the vote required for election is ' + self.vote_required_election.pp(2) + '.')
__pragma__('noopov')
def meets_quota(self, count_card):
"""
Determine if the given candidate meets the quota
"""
if self.options['quota_criterion'] == 'geq':
__pragma__('opov')
return count_card.votes >= self.quota or (self.options['quota_mode'] == 'ers97' and count_card.votes >= self.vote_required_election)
__pragma__('noopov')
elif self.options['quota_criterion'] == 'gt':
__pragma__('opov')
return count_card.votes > self.quota or (self.options['quota_mode'] == 'ers97' and count_card.votes > self.vote_required_election)
__pragma__('noopov')
else:
raise STVException('Invalid quota criterion') # pragma: no cover
def elect_meeting_quota(self):
"""
Elect all candidates meeting the quota
"""
# Does a candidate meet the quota?
meets_quota = [(c, cc) for c, cc in self.candidates.items() if cc.state == CandidateState.HOPEFUL and self.meets_quota(cc)]
if len(meets_quota) > 0:
meets_quota.sort(key=lambda x: x[1].votes, reverse=True)
if len(meets_quota) == 1:
self.logs.append(meets_quota[0][0].name + ' meets the quota and is elected.')
else:
self.logs.append(self.pretty_join([c.name for c, cc in meets_quota]) + ' meet the quota and are elected.')
# Declare elected any candidate who meets the quota
while len(meets_quota) > 0:
x = self.choose_highest(meets_quota)
candidate, count_card = x[0], x[1]
count_card.state = CandidateState.PROVISIONALLY_ELECTED
self.num_elected += 1
count_card.order_elected = self.num_elected
meets_quota.remove(x)
if self.options['quota_mode'] == 'ers97':
self.compute_quota() # Vote required for election may have changed
if self.options['quota_mode'] == 'ers97':
self.elect_meeting_quota() # Repeat as the vote required for election may have changed
return
def describe_options(self):
result = []
if self.options['quota'] != 'droop':
result.append('--quota ' + self.options['quota'])
if self.options['quota_criterion'] != 'geq':
result.append('--quota-criterion ' + self.options['quota_criterion'])
if self.options['quota_mode'] != 'static':
result.append('--quota-mode ' + self.options['quota_mode'])
if not self.options['bulk_elect']:
result.append('--no-bulk-elect')
if self.options['bulk_exclude']:
result.append('--bulk-exclude')
if self.options['defer_surpluses']:
result.append('--defer-surpluses')
if pyRCV2.numbers._numclass is pyRCV2.numbers.Rational:
result.append('--numbers rational')
elif pyRCV2.numbers._numclass is pyRCV2.numbers.Native:
result.append('--numbers native')
elif pyRCV2.numbers._numclass is pyRCV2.numbers.FixedGuarded:
result.append('--numbers gfixed')
if pyRCV2.numbers.get_dps() != 5:
result.append('--decimals ' + str(pyRCV2.numbers.get_dps()))
else:
# Fixed
if pyRCV2.numbers.get_dps() != 5:
result.append('--decimals ' + str(pyRCV2.numbers.get_dps()))
if self.options['round_quota'] is not None:
result.append('--round-quota ' + str(self.options['round_quota']))
if self.options['round_votes'] is not None:
result.append('--round-votes ' + str(self.options['round_votes']))
if self.options['round_tvs'] is not None:
result.append('--round-tvs ' + str(self.options['round_tvs']))
if self.options['round_weights'] is not None:
result.append('--round-weights ' + str(self.options['round_weights']))
if self.options['surplus_order'] != 'size':
result.append('--surplus-order ' + self.options['surplus_order'])
if self.options['papers'] == 'transferable':
result.append('--transferable-only')
if self.options['exclusion'] != 'one_round':
result.append('--exclusion ' + self.options['exclusion'])
if len(self.options['ties']) == 1 and isinstance(self.options['ties'][0], pyRCV2.ties.TiesPrompt):
pass
else:
for t in self.options['ties']:
if isinstance(t, pyRCV2.ties.TiesBackwards):
result.append('--ties backwards')
elif isinstance(t, pyRCV2.ties.TiesForwards):
result.append('--ties forwards')
elif isinstance(t, pyRCV2.ties.TiesRandom):
result.append('--ties random')
result.append('--random-seed ' + t.random.seed)
elif isinstance(t, pyRCV2.ties.TiesPrompt):
result.append('--ties prompt')
return ' '.join(result)
# -----------------
# UTILITY FUNCTIONS
# -----------------
def next_preferences(self, parcels):
"""
Examine the specified ballots and group ballot papers by next available preference
"""
# SafeDict: Candidate -> [List[Ballot], ballots, votes]
next_preferences = SafeDict([(c, [[], Num('0'), Num('0')]) for c, cc in self.candidates.items()])
total_ballots = Num('0')
total_votes = Num('0')
next_exhausted = []
exhausted_ballots = Num('0')
exhausted_votes = Num('0')
for parcel in parcels:
for ballot, ballot_value in parcel:
__pragma__('opov')
total_ballots += ballot.value
total_votes += ballot_value
candidate = next((c for c in ballot.preferences if self.candidates[c].state == CandidateState.HOPEFUL), None)
if candidate is not None:
next_preferences[candidate][0].append((ballot, ballot_value))
next_preferences[candidate][1] += ballot.value
next_preferences[candidate][2] += ballot_value
else:
next_exhausted.append((ballot, ballot_value))
exhausted_ballots += ballot.value
exhausted_votes += ballot_value
__pragma__('noopov')
return next_preferences, total_ballots, total_votes, next_exhausted, exhausted_ballots, exhausted_votes
def choose_lowest(self, l):
"""
Provided a list of tuples (Candidate, CountCard), sorted in ASCENDING order of votes, choose the tuple with the fewest votes, breaking ties appropriately
"""
if len(l) == 1:
return l[0]
__pragma__('opov')
# Do not use (c, cc) for c, cc in ... as this will break equality in JS
tied = [x for x in l if x[1].votes == l[0][1].votes]
__pragma__('noopov')
if len(tied) == 1:
return tied[0]
# A tie exists
for tie in self.options['ties']:
result = tie.choose_lowest(tied)
if result is not None:
self.logs.append('A tie for last place was resolved ' + tie.adverb + ' against ' + result[0].name + '.')
return result
raise STVException('Unable to resolve tie')
def choose_highest(self, l):
"""
Provided a list of tuples (Candidate, CountCard), sorted in DESCENDING order of votes, choose the tuple with the most votes, breaking ties appropriately
"""
if len(l) == 1:
return l[0]
__pragma__('opov')
# Do not use (c, cc) for c, cc in ... as this will break equality in JS
tied = [x for x in l if x[1].votes == l[0][1].votes]
__pragma__('noopov')
if len(tied) == 1:
return tied[0]
# A tie exists
for tie in self.options['ties']:
result = tie.choose_highest(tied)
if result is not None:
self.logs.append('A tie for first place was resolved ' + tie.adverb + ' in favour of ' + result[0].name + '.')
return result
raise STVException('Unable to resolve tie')
def round_votes(self, num):
if self.options['round_votes'] is None:
return num
return num.round(self.options['round_votes'], num.ROUND_DOWN)
def round_weight(self, num):
if self.options['round_weights'] is None:
return num
return num.round(self.options['round_weights'], num.ROUND_DOWN)
def round_tv(self, num):
if self.options['round_tvs'] is None:
return num
return num.round(self.options['round_tvs'], num.ROUND_DOWN)
def make_result(self, comment):
__pragma__('opov')
result = CountStepResult(
comment,
self.logs,
self.candidates,
self.exhausted,
self.loss_fraction,
self.total + self.exhausted.votes + self.loss_fraction.votes,
self.quota,
self.vote_required_election,
)
__pragma__('noopov')
self.logs = []
self.step_results.append(result)
return result
def pretty_join(self, strs):
if len(strs) == 0:
return ''
if len(strs) == 1:
return strs[0]
if len(strs) == 2:
return strs[0] + ' and ' + strs[1]
return ', '.join(strs[0:-1]) + ' and ' + strs[len(strs)-1]