mirror of
https://github.com/pezkuwichain/consensus.git
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A S
588 lines
24 KiB
Python
588 lines
24 KiB
Python
#from itertools import count
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import math
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class edge:
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def __init__(self,voterid,canid):
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self.voterid=voterid
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self.canid=canid
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#self.index
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#self.voterindex
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#self.canindex
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class voter:
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def __init__(self,votetuple):
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self.voterid=votetuple[0]
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self.budget=votetuple[1]
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self.edges=[edge(self.voterid,canid) for canid in votetuple[2]]
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#self.index
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class candidate:
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def __init__(self,canid,index):
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self.canid = canid
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self.index=index
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import itertools
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class assignment:
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def __init__(self,voterlist,candidates, copyassignment=None):
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self.voterlist=voterlist
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self.candidates=candidates
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if copyassignment is None:
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#create edgelist here at cost O(votes size)
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self.edgelist = list(itertools.chain.from_iterable((nom.edges for nom in voterlist)))
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numvoters = len(voterlist)
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numcandidates = len(candidates)
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numedges=len(self.edgelist)
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self.voterload=[0.0 for x in range(numvoters)]
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self.edgeload = [0.0 for x in range(numedges)]
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self.edgeweight = [0.0 for x in range(numedges)]
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self.cansupport=[0.0 for x in range(numcandidates)]
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self.canelected=[False for x in range(numcandidates)]
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self.electedcandidates=set()
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self.canapproval= [0.0 for x in range(numcandidates)]
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#calculate approval here at cost O(numedges)
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for voter in voterlist:
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for edge in voter.edges:
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self.canapproval[edge.canindex] += voter.budget
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self.canscore = [0.0 for x in range(numcandidates)]
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self.canscorenumerator = [0.0 for x in range(numcandidates)]
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self.canscoredenominator = [0.0 for x in range(numcandidates)]
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else:
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self.edgelist = copyassignment.edgelist
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self.voterload=copyassignment.voterload.copy()
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self.edgeload = copyassignment.edgeload.copy()
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self.edgeweight=copyassignment.edgeweight.copy()
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self.cansupport=copyassignment.cansupport.copy()
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self.canelected=copyassignment.canelected.copy()
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self.electedcandidates=copyassignment.electedcandidates.copy()
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self.canapproval=copyassignment.canapproval.copy()
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self.canscore=copyassignment.canscore.copy()
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self.canscorenumerator = copyassignment.canscorenumerator.copy()
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self.canscoredenominator = copyassignment.canscoredenominator.copy()
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def setload(self, edge,load):
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oldload=self.edgeload[edge.index]
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self.edgeload[edge.index]=load
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self.voterload[edge.voterindex] +=load-oldload
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def setweight(self,edge,weight):
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oldweight=self.edgeweight[edge.index]
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self.edgeweight[edge.index]=weight
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self.cansupport[edge.canindex] +=weight-oldweight
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def setscore(self,candidate,score):
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self.canscore[candidate.index] = score
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def loadstoweights(self):
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for voter in self.voterlist:
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for edge in voter.edges:
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if(self.voterload[voter.index] > 0.0):
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self.setweight(edge, voter.budget * self.edgeload[edge.index] / self.voterload[voter.index])
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def weightstoloads(self):
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for edge in self.edgelist:
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self.setload(edge, self.edgeweight[edge.index]/self.cansupport[edge.canindex])
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def elect(self,candidate):
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self.canelected[candidate.index]=True
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self.electedcandidates.add(candidate)
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def unelect(self,candidate):
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self.canelected[candidate.index]=False
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self.electedcandidates.remove(candidate)
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def setuplists(votelist):
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#Instead of Python's dict here, you can use anything with O(log n) addition and lookup.
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#We can also use a hashmap, by generating a random constant r and useing H(canid+r)
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#since the naive thing is obviously attackable.
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voterlist = [voter(votetuple) for votetuple in votelist]
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candidatedict=dict()
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candidatearray=list()
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numcandidates=0
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numvoters=0
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numedges=0
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#Get an array of candidates that we can reference these by index
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for nom in voterlist:
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nom.index=numvoters
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numvoters+= 1
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for edge in nom.edges:
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edge.index=numedges
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edge.voterindex=nom.index
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numedges += 1
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canid = edge.canid
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if canid in candidatedict:
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edge.candidate=candidatearray[candidatedict[canid]]
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edge.canindex=edge.candidate.index
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else:
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candidatedict[canid]=numcandidates
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newcandidate=candidate(canid,numcandidates)
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candidatearray.append(newcandidate)
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edge.candidate=newcandidate
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edge.canindex=numcandidates
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numcandidates += 1
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return(voterlist,candidatearray)
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def seqPhragmén(votelist,numtoelect):
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nomlist,candidates=setuplists(votelist)
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#creating an assignment now also computes the total possible stake for each candidate
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a=assignment(nomlist,candidates)
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for round in range(numtoelect):
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for canindex in range(len(candidates)):
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if not a.canelected[canindex]:
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a.canscore[canindex]=1/a.canapproval[canindex]
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for nom in a.voterlist:
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for edge in nom.edges:
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if not a.canelected[edge.canindex]:
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a.canscore[edge.canindex] += nom.budget * a.voterload[nom.index] / a.canapproval[edge.canindex]
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bestcandidate=0
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bestscore = 1000 #should be infinite but I'm lazy
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for canindex in range(len(candidates)):
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if not a.canelected[canindex] and a.canscore[canindex] < bestscore:
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bestscore=a.canscore[canindex]
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bestcandidate=canindex
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electedcandidate=candidates[bestcandidate]
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a.canelected[bestcandidate]=True
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#electedcandidate.electedpos=round
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a.elect(electedcandidate)
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for nom in a.voterlist:
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for edge in nom.edges:
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if edge.canindex == bestcandidate:
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a.setload(edge,a.canscore[bestcandidate]-a.voterload[nom.index])
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a.loadstoweights()
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return a
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def calculateScores(a,cutoff):
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for canindex in range(len(a.candidates)):
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if not a.canelected[canindex]:
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a.canscorenumerator[canindex]=0
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a.canscoredenominator[canindex]=1
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for nom in a.voterlist:
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numeratorcontrib=nom.budget
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denominatorcontrib=0
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for edge in nom.edges:
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if a.canelected[edge.canindex]:
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if a.cansupport[edge.canindex] > cutoff:
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denominatorcontrib += a.edgeweight[edge.index]/a.cansupport[edge.canindex]
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else:
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numeratorcontrib -= a.edgeweight[edge.index]
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for edge in nom.edges:
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if not a.canelected[edge.canindex]:
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a.canscorenumerator[edge.canindex] +=numeratorcontrib
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a.canscoredenominator[edge.canindex] +=denominatorcontrib
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for canindex in range(len(a.candidates)):
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if not a.canelected[canindex]:
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a.canscore[canindex] = a.canscorenumerator[canindex]/a.canscoredenominator[canindex]
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#for canindex in range(len(a.candidates)):
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#if not a.canelected[canindex]:
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#print(a.candidates[canindex].canid," has score ", a.canscore[canindex]," with cutoff ",cutoff)
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#print("Approval stake: ", a.canapproval[canindex]," support: ",a.cansupport[canindex]," denominator: ",a.canscoredenominator[canindex], " numerator: ",a.canscorenumerator[canindex])
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def calculateMaxScore(a):
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supportList=[a.cansupport[can.index] for can in a.electedcandidates]
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supportList.append(0.0)
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supportList.sort()
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lowerindex=0
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upperindex=len(a.electedcandidates)+1
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currentindex=0
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while(True):
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#print(len(supportList), currentindex, len(a.electedcandidates),upperindex,lowerindex)
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cutoff=supportList[currentindex]
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calculateScores(a,cutoff)
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scores=[(can, a.canscore[can.index]) for can in a.candidates if not a.canelected[can.index]]
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bestcandidate,score=max(scores,key=lambda x: x[1])
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if score > cutoff:
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# In this case both score and cutoff are lower bounds to the max score
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lowerindex=len([s for s in supportList if s <= score]) - 1
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#print("lowerindex ",lowerindex, " upperindex ",upperindex, " cutoff ", cutoff, "score ",score, " candidate ",bestcandidate.canid)
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#print("bottom support ",supportList[0], " real lowest support ",supportList[1], " highest support ",supportList[-1])
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if currentindex == upperindex-1 or currentindex==lowerindex:
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return bestcandidate,score
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elif score < cutoff:
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# In this case, cutoff is an upper bounf for the max score
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upperindex=currentindex
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else:
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# If they are magically equal, this is the score
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return bestcandidate,score
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currentindex=(lowerindex + upperindex) // 2
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def insertWithScore(a,candidate,cutoff):
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oldcansupport=a.cansupport.copy()
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a.elect(candidate)
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for nom in a.voterlist:
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for newedge in nom.edges:
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if newedge.canindex== candidate.index:
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usedbudget = sum([a.edgeweight[edge.index] for edge in nom.edges])
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a.setweight(newedge, nom.budget-usedbudget)
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for edge in nom.edges:
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if edge.canindex != candidate.index and a.edgeweight[edge.index] > 0.0:
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if oldcansupport[edge.canindex] > cutoff:
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fractiontotake = cutoff / oldcansupport[edge.canindex]
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a.setweight(newedge, a.edgeweight[newedge.index] + a.edgeweight[edge.index]* fractiontotake)
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a.setweight(edge, a.edgeweight[edge.index] * (1-fractiontotake))
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def approvalvoting(votelist,numtoelect):
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nomlist,candidates=setuplists(votelist)
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#creating an assignment now also computes the total possible stake for each candidate
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a=assignment(nomlist,candidates)
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candidatessorted=sorted(candidates, key = lambda x : a.canapproval[x.index], reverse=True)
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for candidate in candidatessorted[0:numtoelect]:
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a.elect(candidate)
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for nom in a.voterlist:
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numbelected=len([edge for edge in nom.edges if a.canelected[edge.canindex]])
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if (numbelected > 0):
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for edge in nom.edges:
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a.setweight(edge,nom.budget/numbelected)
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return a
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def printresult(a,listvoters=True,listelectedcandidates=True):
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if listelectedcandidates:
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for candidate in a.electedcandidates:
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print(candidate.canid," is elected with stake ",a.cansupport[candidate.index], "and score ",a.canscore[candidate.index])
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print()
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if listvoters:
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for nom in a.voterlist:
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print(nom.voterid," has load ",a.voterload[nom.index], "and supported ")
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for edge in nom.edges:
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print(edge.canid," with stake ",a.edgeweight[edge.index], end=" ")
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print()
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print("Minimum support ",min([a.cansupport[candidate.index] for candidate in a.electedcandidates]))
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def equalise(a, nom, tolerance):
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# Attempts to redistribute the nominators budget between elected validators
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# Assumes that all elected validators have backedstake set correctly
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# returns the max difference in stakes between sup
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electededges=[edge for edge in nom.edges if a.canelected[edge.canindex]]
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if len(electededges)==0:
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return 0.0
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stakeused = sum([a.edgeweight[edge.index] for edge in electededges])
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backedstakes=[a.cansupport[edge.canindex] for edge in electededges]
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backingbackedstakes=[a.cansupport[edge.canindex] for edge in electededges if a.edgeweight[edge.index] > 0.0]
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if len(backingbackedstakes) > 0:
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difference = max(backingbackedstakes)-min(backedstakes)
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difference += nom.budget-stakeused
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if difference < tolerance:
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return difference
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else:
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difference = nom.budget
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#remove all backing
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for edge in nom.edges:
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a.setweight(edge, 0.0)
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electededges.sort(key=lambda x: a.cansupport[x.canindex])
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cumulativebackedstake=0
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lastcandidateindex=len(electededges)-1
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for i in range(len(electededges)):
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backedstake=a.cansupport[electededges[i].canindex]
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#print(nom.nomid,electededges[i].valiid,backedstake,cumulativebackedstake,i)
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if backedstake * i - cumulativebackedstake > nom.budget:
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lastcandidateindex=i-1
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break
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cumulativebackedstake +=backedstake
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laststake=a.cansupport[electededges[lastcandidateindex].canindex]
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waystosplit=lastcandidateindex+1
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excess = nom.budget + cumulativebackedstake - laststake*waystosplit
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for edge in electededges[0:waystosplit]:
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a.setweight(edge,excess / waystosplit + laststake - a.cansupport[edge.canindex])
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return difference
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import random
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def equaliseall(a,maxiterations,tolerance,debug=False):
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for i in range(maxiterations):
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for j in range(len(a.voterlist)):
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nom=random.choice(a.voterlist)
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equalise(a,nom,tolerance/10)
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maxdifference=0
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for nom in a.voterlist:
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difference=equalise(a,nom,tolerance/10)
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maxdifference=max(difference,maxdifference)
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if maxdifference < tolerance:
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if debug:
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print("max iterations ",maxiterations," actual iterations ",i+1)
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return
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if maxiterations > 1 or debug:
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print(" reached max iterations ",maxiterations)
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def seqPhragménwithpostprocessing(votelist,numtoelect, ratio=1):
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a = seqPhragmén(votelist,numtoelect)
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passes=math.floor(ratio*numtoelect)
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equaliseall(a,ratio*numtoelect,0.1, True)
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return a
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def factor3point15(votelist, numtoelect,tolerance=0.1):
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nomlist,candidates=setuplists(votelist)
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a=assignment(nomlist,candidates)
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for round in range(numtoelect):
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bestcandidate,score=calculateMaxScore(a)
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insertWithScore(a,bestcandidate, score)
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equaliseall(a,1000000,tolerance)
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return a
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def maybecandidate(a,newcandidate,shouldremoveworst, tolerance):
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assert(a.canelected[newcandidate.index]==False)
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currentvalue=min([a.cansupport[candidate.index] for candidate in a.electedcandidates])
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#To find a new assignment without losing our current one, we will need to copy the edges
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b=assignment(a.voterlist,a.candidates,a)
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if shouldremoveworst:
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worstcanidate =min(electedcandidates, key = lambda x: b.cansupport[x.index])
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b.unelect(worstcandidate)
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b.elect(newcandidate)
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equaliseall(b,100000000,tolerance)
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newvalue=min([b.cansupport[candidate.index] for candidate in b.electedcandidates])
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return b, newvalue
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def SFFB18(votelist, numtoelect,tolerance=0.1):
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nomlist,candidates=setuplists(votelist)
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a=assignment(nomlist,candidates)
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for round in range(numtoelect):
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if round == 0:
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newcandidate=max([(can,a.canapproval[can.index]) for can in a.candidates],key = lambda x : x[1])[0]
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a.elect(newcandidate)
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equaliseall(a,1,tolerance)
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else:
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bestvalue=0
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for can in a.candidates:
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if not a.canelected[can.index] and a.canapproval[can.index] > bestvalue:
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b,newvalue = maybecandidate(a,can, False, tolerance)
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if newvalue > bestvalue:
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bestassignment=b
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bestvalue=newvalue
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if bestvalue > 0:
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a=bestassignment
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return a
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def binarysearchfeasible(votelist,numtoelect,tolerance=0.1):
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nomlist,candidates=setuplists(votelist)
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a=assignment(nomlist,candidates)
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#First do factor 3.15
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#but keep track of the order we elect people and the value then
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orderelectedwithvalue=[]
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for round in range(numtoelect):
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bestcandidate,score=calculateMaxScore(a)
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insertWithScore(a,bestcandidate, score)
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equaliseall(a,1000000,tolerance/numtoelect)
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currentvalue=min([a.cansupport[candidate.index] for candidate in a.electedcandidates])
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orderelectedwithvalue.append((bestcandidate,currentvalue))
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if len(a.candidates)==numtoelect:
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return a
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bestknownvalue=currentvalue
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bestassignment=assignment(a.voterlist,a.candidates,a)
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bestorderelected=orderelectedwithvalue.copy()
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maxunelectedapproval = max([a.canapproval[i] for i in range(len(a.candidates)) if not a.canelected[i]])
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totalvotes=sum([nom.budget for nom in a.voterlist])
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maxvalue=min(3.15*currentvalue, max(currentvalue,maxunelectedapproval), totalvotes/numtoelect)
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while(maxvalue - bestknownvalue > tolerance):
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targetvalue=math.sqrt(maxvalue*bestknownvalue)
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lastgoodindex=len([x for x in orderelectedwithvalue if x[1] >= targetvalue])-1
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#print(orderelectedwithvalue, targetvalue,lastgoodindex, maxvalue,bestknownvalue,currentvalue,targetvalue)
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assert(lastgoodindex >= 0)
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assert(orderelectedwithvalue[lastgoodindex][1] >= targetvalue)
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for x in orderelectedwithvalue[lastgoodindex+1:]:
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a.unelect(x[0])
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del orderelectedwithvalue[lastgoodindex+1:]
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for nom in a.voterlist:
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for edge in nom.edges:
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if not a.canelected[edge.canindex]:
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a.setweight(edge,0)
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equaliseall(a,1000000,tolerance/numtoelect)
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currentvalue=min([a.cansupport[candidate.index] for candidate in a.electedcandidates])
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if currentvalue < targetvalue:
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if targetvalue >= sqrt(currentvalue, maxvalue):
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#At this point we are getting so much error from tolerance in equaliseall
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#that we should give up
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print("Giving up with error at most ",maxvalue-bestknownvalue)
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return
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else:
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targetvalue=currentvalue
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#print(targetvalue,lastgoodindex, maxvalue,bestknownvalue,currentvalue)
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for round in range(lastgoodindex+1,numtoelect):
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# First try maxscore candidate, which will help with PJR
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bestcandidate,score=calculateMaxScore(a)
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if score >= targetvalue:
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insertWithScore(a,bestcandidate, score)
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equaliseall(a,1000000,tolerance/numtoelect)
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currentvalue=min([a.cansupport[candidate.index] for candidate in a.electedcandidates])
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assert(currentvalue >= targetvalue)
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orderelectedwithvalue.append((bestcandidate,currentvalue))
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continue
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else:
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b,newvalue = maybecandidate(a,bestcandidate, False, tolerance)
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if newvalue >= targetvalue:
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a=b
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orderelectedwithvalue.append((bestcandidate,newvalue))
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currentvalue=newvalue
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continue
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#Then try some candidates in which we are guaranteed that one is feasible if threshold >= d*/2
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calculateScores(a,targetvalue/2)
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scores=[(can, a.canscore[can.index]) for can in a.candidates if not a.canelected[can.index] and a.canapproval[can.index] >= targetvalue and a.canscore[can.index] >= targetvalue/2]
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scores.sort(reverse=True,key=lambda x: x[1])
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for can,score in scores:
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b,newvalue = maybecandidate(a,can, False, tolerance)
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if newvalue >= targetvalue:
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a=b
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orderelectedwithvalue.append((can,newvalue))
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currentvalue=newvalue
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break
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else:
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break
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# print("here",currentvalue,targetvalue)
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if len(a.electedcandidates) < numtoelect:
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maxvalue = targetvalue
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a=bestassignment
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orderelectedwithvalue=bestorderelected
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else:
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bestknownvalue=currentvalue
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bestassignment=assignment(a.voterlist,a.candidates,a)
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bestorderelected=orderelectedwithvalue.copy()
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return a
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import unittest
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class electiontests(unittest.TestCase):
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def testexample1Phragmén(self):
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votelist=[("A",10.0,["X","Y"]),("B",20.0,["X","Z"]),("C",30.0,["Y","Z"])]
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a = seqPhragmén(votelist,2)
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self.assertEqual({can.canid for can in a.electedcandidates},{"Y","Z"})
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self.assertAlmostEqual(a.canscore[2],0.02)
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self.assertAlmostEqual(a.canscore[1],0.04)
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def testexample1approval(self):
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votelist=[("A",10.0,["X","Y"]),("B",20.0,["X","Z"]),("C",30.0,["Y","Z"])]
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a = approvalvoting(votelist,2)
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self.assertEqual({can.canid for can in a.electedcandidates},{"Y","Z"})
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self.assertAlmostEqual(a.canapproval[2],50.0)
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self.assertAlmostEqual(a.canapproval[1],40.0)
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def dotests():
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unittest.main()
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import time
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def doall(votelist, numtoelect, listvoters=True, listcans=True):
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if listvoters:
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print("Votes ",votelist)
|
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alglist=[(approvalvoting,"Approval voting"), (seqPhragmén, "Sequential Phragmén"),
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(seqPhragménwithpostprocessing, "Sequential Phragmén with post processing"),
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(factor3point15, "The factor 3.15 thing"), (binarysearchfeasible,"Factor 2 by binary search"), (SFFB18, "SFFB18")]
|
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for alg,name in alglist:
|
|
st=time.perf_counter()
|
|
a = alg(votelist,numtoelect)
|
|
et=time.perf_counter()
|
|
print(name, " gives")
|
|
printresult(a,listvoters,listcans)
|
|
print(" in ",et-st," seconds.")
|
|
print()
|
|
|
|
|
|
def example1():
|
|
votelist=[("A",10.0,["X","Y"]),("B",20.0,["X","Z"]),("C",30.0,["Y","Z"])]
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|
doall(votelist,2)
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|
|
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|
|
def example2():
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|
# Approval voting does not do so well for this kind of thing.
|
|
votelist=[("A",30.0,["T", "U","V","W"]),("B",20.0,["X"]),("C",20.0,["Y"]),("D",20.0,["Z"])]
|
|
doall(votelist,4)
|
|
|
|
def example3():
|
|
#Proportional representation test.
|
|
#Red should has 50% more votes than blue. So under PR, it would get 12/20 seats
|
|
redparty=["Red"+str(i) for i in range(20)]
|
|
blueparty=["Blue"+str(i) for i in range(20)]
|
|
redvoters = [("RedV"+str(i),20.0,redparty) for i in range(30)]
|
|
bluevoters = [("BlueV"+str(i),20.0,blueparty) for i in range(20)]
|
|
votelist= redvoters+bluevoters
|
|
doall(votelist, 20, False)
|
|
|
|
|
|
def example4():
|
|
#Now we want an example where seq Phragmén is not so good.
|
|
votelist=[("A",30.0,["V","W"]),("B",20.0,["V","Y"]),("C",20.0,["W","Z"]),("D",20.0,["Z"])]
|
|
print("Votes ",votelist)
|
|
doall(votelist,4)
|
|
|
|
def example5():
|
|
votelist = [
|
|
("10", 1000, ["10"]),
|
|
("20", 1000, ["20"]),
|
|
("30", 1000, ["30"]),
|
|
("40", 1000, ["40"]),
|
|
('2', 500, ['10', '20', '30']),
|
|
('4', 500, ['10', '20', '40'])
|
|
]
|
|
print("Votes ",votelist)
|
|
doall(votelist,4)
|
|
|
|
def example6():
|
|
#Now we want an example where seq Phragmén is not so good.
|
|
votelist=[("A",100.0,["V","W","X","Y","Z"]),("B",100.0,["W","X","Y","Z"]),
|
|
("C",100.0,["X","Y","Z"]),("D",100.0,["Y","Z"]), ("E",100.0,["Z"]),
|
|
("M",50.0, ["M"])]
|
|
print("Votes ",votelist)
|
|
doall(votelist,5)
|
|
|
|
def exampleLine():
|
|
votelist = [
|
|
("a", 2000, ["A"]),
|
|
("b", 1000, ["A","B"]),
|
|
("c", 1000, ["B","C"]),
|
|
("d", 1000, ["C","D"]),
|
|
("e", 1000, ["D","E"]),
|
|
("f", 1000, ["E","F"]),
|
|
("g", 1000, ["F","G"])
|
|
]
|
|
doall(votelist,7)
|
|
|
|
def ri(vals=20,noms=2000, votesize=10):
|
|
#Let's try a random instance
|
|
candidates=["Val"+str(i) for i in range(vals)]
|
|
votelist=[("Nom"+str(i), 100, random.sample(candidates,votesize)) for i in range(noms)]
|
|
doall(votelist, vals // 2, False, False)
|
|
|
|
def ripartylist(vals=200,noms=2000, votesize=10,seed=1):
|
|
#Half the validators are in a party which 1/4 of the nominators vote for.
|
|
# Approval voting does worse now
|
|
# and this is probably more realistic than the pure random instance.
|
|
random.seed(seed)
|
|
candidates=["Val"+str(i) for i in range(vals//2)]
|
|
partycandidates=["PartyVal"+str(i) for i in range(vals- vals // 2)]
|
|
partynoms = noms // 4
|
|
votelist=[("Nom"+str(i), 100, random.sample(candidates,votesize)) for i in range(noms - partynoms)]
|
|
votelist += [("Nom"+str(i), 100, partycandidates) for i in range(partynoms)]
|
|
return votelist
|
|
|
|
|
|
def riparty(vals=200,noms=2000, votesize=10,seed=1):
|
|
#Half the validators are in a party which 1/4 of the nominators vote for.
|
|
# Approval voting does worse now
|
|
# and this is probably more realistic than the pure random instance.
|
|
votelist=ripartylist(vals,noms,seed)
|
|
doall(votelist, vals // 4, False, False)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
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|
|
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|
|
|
|
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|