-
Notifications
You must be signed in to change notification settings - Fork 0
/
EPRv2.r
928 lines (913 loc) · 39.2 KB
/
EPRv2.r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
# 2/8/20 LSL removed printout of ordinals in Stage 1 as they are unnecessary
# 12/30/19 LSL descriptive updates for JPR article: Legislatures Elected by EPR: An Algorithm v3
# 7/18/19 LSL continue vote count until every voter's preferences are allotted to candidates
# 12/16/18 LSL copied code from 18-11-12-Anders-newAlgorithm.docx
# Init program: remove old data, set random seed
rm(list = ls())
set.seed(1)
setwd("/users/stevanleonard/dropbox/Documents/EPR Steve Bosworth/")
external.data.name <-
"epr-voter-data-v2.csv" # required name of input ballot data
sink(paste("EPRv2-", external.data.name, ".txt", sep="")) # send output to file
current.time <- format(Sys.time(), "%a %b %d %X %Y")
print("EPRv2")
cat(current.time,"\n")
print("Candidates are elected by voters grading all the candidates using the values: ")
print("6=Excellent, 5=Very Good, 4=Good, 3=Acceptable, 2=Poor, 1=Reject.")
print("The count is complete by the end of Stage 4.")
# NOTE: In addition to defining external.data.name above, these paramaters must be set
# to define the operation of the algorithm
cat("Parameters defined for this run of the algorithm\n")
cat("Ballot data file:", external.data.name, "\n")
positions <- 7 # number of open positions to fill with candidates
cat("Positions to fill with candidates:", positions, "\n")
limit.percent <-
20 # each candidate must transfer votes they receive beyond the limit
cat("Percentage of votes after which a candidate must transfer votes they receive:", limit.percent, "%\n")
# end of user defined parameters
# Initialize general values and read in voter data
grades <-
c("Reject", "Poor", "Acceptable", "Good", "Very good", "Excellent")
min.affirmed.evaluation <-
3 # The value of Acceptable is the minimum value a voter can give to help elect a candidate
Acceptable <- 3 # minimum grade to count
voter.mat <-
as.matrix(read.csv(
external.data.name,
strip.white = TRUE,
header = FALSE
))
voters <- nrow(voter.mat)
candidates <- ncol(voter.mat)
for (k in 1:voters) {
for (l in 1:candidates)
if ((is.na(voter.mat[k,l]))) {
cat("Error in input ballot data: unequal length at row", k, "\n")
stop("Program is terminating")
}
if ((min(voter.mat[k, ]) < 1) || (max(voter.mat[k, ] > 6))) {
cat("Error in input ballot data: Value less than 1 or greater than 6 in row", k, "\n")
stop("Program is terminating")
}
}
vote.limit <- round(voters * limit.percent / 100)
if (vote.limit < round(voters / positions)) {
vote.limit <- round(voters / positions)
print(
paste(
"* * * NOTE: vote.limit set to ",
vote.limit,
"to meet minimum set by voters/positions",
voters,
"/",
positions
)
)
}
# Initialize candidate and voter matrices
voter.mat.orig <- voter.mat # save: voter.mat is modified in Stage 1
names <- toupper(letters) # candidate names are A, B,..Z
candidate.names <- names[1:candidates]
voter.names <- paste("Voter", 1:voters, sep = " ")
voter.candidate <- 1:voters * NA
voter.round <- 1:voters * NA
voter.transfer <- 1:voters * NA
rownames(voter.mat) <-
voter.names # init row heading in first column
colnames(voter.mat) <- candidate.names
candidate.proxy.default <- 1:candidates * NA
# Initialize candidate computation matrices
candidate.vec1 <-
replicate(candidates, 0) # count of selectors by candidate for current round
candidate.evals.vec1 <-
replicate(candidates, 0) # sum of selectors by candidate for current round
council <- names[1:candidates] # list of winners so far
council.numbers <-
1:candidates # list of candidates (winners) exclusively yet provisionally receiving
# a number of votes (affirmed evaluations) during the current round
weights.stage1 <-
replicate(candidates, 0) # affirmed evaluations by candidate
selectors <- 6 # list of grades (affirmed evaluations) currently selecting on
selector.add <- 6 # current grade selecting on
winners_so_far <- 0 # count of winning candidates
# Stage 1: Each round calculates winners across all candidates by counting the
# most highly graded candidate by the largest number of voters
Stage <- 1
print("Begin Stage 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
cat("Perform an initial count of all the affirmed evaluations that must be ")
cat("provisionally yet exclusively counted for each of the candidates. ")
cat("This count is determined in multiple rounds. When more than one candidate ")
cat("receives the same grade from the same voter, the candidate who has ")
cat("the largest number of votes as a result of retaining that grade exclusively ")
cat("is selected. This is justified by the assumption that the candidate who has the ")
cat("largest number of same grades or higher is probably the one most qualified for office.\n")
# define a function for the loop that accumulates votes
more_voters <- TRUE
this_round <- 0
while (more_voters) {
this_round <- this_round + 1 # i corresponds to the round
print("*******************************************************")
print(paste("Stage 1, Round ", this_round, sep = ""))
print("*******************************************************")
print(paste("Ballots remaining to be counted (", nrow(voter.mat), "):\n", sep="") )
print(voter.mat)
print(paste("Selector: ", selectors, " (", grades[selectors], ")", sep =
""))
candidate.evals.vec1[1:candidates] <- 0 # init all to 0
candidate.vec1[1:candidates] <- 0 # init all to 0
for (j in 1:candidates) {
candidate.vec1[j] <- sum(voter.mat[, j] == selectors)
candidate.evals.vec1[j] <-
sum(voter.mat[, j][voter.mat[, j] == selectors])
}
print("Count of affirmed evaluations at selector level: ")
print(rbind(council, candidate.vec1))
if (sum(candidate.vec1) == 0) {
cat("No grades for selector", selectors, "(", grades[selectors], ").\n")
}
selection <-
candidate.vec1 == max(candidate.vec1)
if ((sum(selection) > 0) && (sum(candidate.vec1) > 0)) {
winner.names <- candidate.names[which(selection)]
# In case of tie in count of selectors (affirmed evaluations),
# first add grades using their ordinal values (Excellent=6..Acceptable=3) using candidate.evals.vec1
# If a tie exists with ordinal values, use sample() to randomly select a winner
# Note: Future version of algo will not first check the sum of ordinals as they will always be the same in Stage 1
topWinnersByEvals <-
which(max(candidate.evals.vec1[selection]) == candidate.evals.vec1)
# in case of tie in both count of selectors and sum of oridinal values, choose a winner randomly from top ordinal winners
# sample() returns random choice from equal winners
winner <-
sample(winner.names[which(winner.names == names[topWinnersByEvals])], size = 1)
winner_ties <-
winner.names[which(winner.names == names[topWinnersByEvals])]
if (length(winner_ties) > 1) {
cat("Tied winners to be determined by lot: ",
winner_ties,
"\n",
file = "",
sep = " ")
# cat(
# "Sum of each candidate's ordinal evaluations, counted numerically. Used first to break ties before one of the candidates with the same number of affirmed evaluations is chosen randomly.\n"
# )
# print(candidate.evals.vec1)
#print("Selection: ")
#print(selection)
}
winner.number <- which(winner == candidate.names)
if (weights.stage1[winner.number] == 0)
{
winners_so_far <- winners_so_far + 1
#council.numbers[winners_so_far] <- winner.number
}
weights.stage1[winner.number] <-
weights.stage1[winner.number] + candidate.vec1[winner.number]
#voter.ind<-which(voter.names %in% rownames(voter.mat[voter.mat[,winner.number] %in% selectors,]))
voter.ind <-
which(voter.names %in% rownames(voter.mat)[voter.mat[, winner.number] == selectors])
voter.candidate[voter.ind] <- winner
voter.round[voter.ind] <- this_round
voter.mat <-
voter.mat[!voter.mat[, winner.number] == selectors, ]
print(
paste(
"The winner of round ",
this_round,
" is: ",
winner,
", with ",
candidate.vec1[winner.number],
" affirmed evaluations.",
sep = ""
)
)
print(paste("Winner number (the candidate who received the largest number of affirmed evaluations in the current round): ", winner.number))
print(
paste(
"Provisional running totals of votes (affirmed evaluations) received by each candidate after round ",
this_round,
":",
sep = ""
)
)
print(rbind(council, weights.stage1))
print("Votes thus far: ")
print(cbind(voter.names, voter.candidate, voter.round))
}
# init for next round and check if all voters processed
if (nrow(voter.mat) == 0)
more_voters <- FALSE
else {
keep_selector <- FALSE
# look for this selector in remaining ballots and keep if found
for (k in 1:dim(voter.mat)[1]) {
if (selector.add == max(voter.mat[k, ])) {
keep_selector <- TRUE
}
}
if (keep_selector == FALSE)
{
# look for a selector in valid range, quit if not found
valid_selector <- FALSE
for (k in 1:dim(voter.mat)[1]) {
if (max(voter.mat[k, ]) >= min.affirmed.evaluation)
{
valid_selector <- TRUE
break
}
}
if (valid_selector)
{
selector.add <- selector.add - 1
selectors <-
selector.add # don't keep a list of selectors, only current
}
else
more_voters <- FALSE
}
}
}
if (more_voters) {
print(paste("Ballots remaining to be counted (", nrow(voter.mat), "):\n", sep="") )
print(voter.mat)
notremoved <- NULL
for (k in 1:dim(voter.mat)[1]) {
if (max(voter.mat[k,]) > (min.affirmed.evaluation - 1)) {
newchoice <- which(voter.mat[k,] == max(voter.mat[k,]))
weights.stage1[newchoice] <- weights.stage1[newchoice] + 1
print(
paste(
"The weight of ",
rownames(voter.mat)[k],
" goes to ",
names(newchoice),
". ",
"This selection is based on the voter's evaluation which is above min.affirmed.evaluation.",
sep = ""
)
)
voter.ind <- which(voter.names %in% rownames(voter.mat)[k])
voter.candidate[voter.ind] <- names(newchoice)
voter.round[voter.ind] <-
"Final above min.affirmed.evaluation"
} else
notremoved <- c(notremoved, k)
voter.mat <- voter.mat[notremoved,]
print("Ballots with no vote counted:")
print(voter.mat)
}
for (n in 1:dim(voter.mat)[1]) {
voter.ind <- which(voter.names %in% rownames(voter.mat)[n])
voter.candidate[voter.ind] <- "None"
voter.round[voter.ind] <- "Ballot not countable"
print(paste("Uncountable ballot for voter: ",
voter.ind))
}
}
for (m in 1:length(council)) {
print(paste(council[m], " has the following supporters: "))
print(voter.names[voter.candidate %in% council[m]])
}
print("End Stage 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
print("Vote apportionment after Stage 1: ")
print(cbind(voter.names, voter.candidate, voter.round))
print("Affirmed evaluations by candidate")
print(rbind(candidate.names[council.numbers], weights.stage1))
print("Begin Stage 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
Stage <- 2
# apply a percentabe limit, such as 20%, by candidate and transfer to a candidate
# with a remaining highest grade from the same voter. Voters are selected randomly.
weights.stage2 <- weights.stage1
print(
paste(
"To eliminate the possibility that any winner could receive enough affirmed evaluations ",
"(weighted votes) to dictate to the council, this election limits the number of votes a ",
"super-popular candidate can retain to ",
limit.percent,
"%, or ",
vote.limit,
" of the ",
voters,
" total voters.",
sep = ""
)
)
cat("During Stage 2, if some of the extra votes initially held by a super-popular candidate ")
cat("cannot be automatically transferred, the remaining votes that must be transferred ")
cat("become proxy votes that are transferred publicly during the last step in Stage 4 ")
cat(
"to any of the other eligible winners judged by the relevant super-popular winner to be most fit for office.\n"
)
cat("Note: A future version of the algorithm will make the candidate your vote went to in Stage 1 ")
cat("the owner of your proxy vote, if required.\n")
# repeat while super-popular candidates remain, sorted by candidate with most votes to transfer
# Note: A future version of the program will select the next super-popular candidate by lot as the order of
# candidates does not change the result
proxy.candidate <- NULL
xfer.loop <- 0
while ((max.weight <- max(weights.stage2)) > vote.limit) {
# find the candidate with the highest weight (largest number of affirmed evaluations)
# If more than one candidate with the same weight, select randomly
xfer.loop <- xfer.loop + 1
print("**********************")
cat("Stage 2 transfer loop ", xfer.loop, "\n")
print("**********************")
transfer.candidates <- NULL
for (i in 1:candidates) {
if (weights.stage2[i] == max.weight)
transfer.candidates <- c(transfer.candidates, i)
}
cat("Candidates currently holding more than ",
vote.limit,
"votes: ",
names[transfer.candidates],
"\n")
if (length(transfer.candidates) > 1)
transfer.candidate <- sample(transfer.candidates, size = 1)
else
transfer.candidate <- transfer.candidates
transfer.count <- max.weight - vote.limit
transfer.name <- names[transfer.candidate]
cat("Candidate with most votes: ",
transfer.name,
"(",
max.weight,
")\n")
print(paste(
"Transfer ",
transfer.count,
" votes from candidate ",
transfer.name,
sep = ""
))
# process transfers for transfer.candidate until complete
# note this might end with proxy votes for some voters if not enough voters
# marked other candidates or if the candidates they marked have too many votes
# Create the set of ballots from this candidate that have a remaining highest candidate marked
voters.to.transfer <- NULL
voter.candidate.to.transfer <- NULL
# select voters that match candidate to transfer and have not been marked for transfer
for (i in 1:voters) {
if (is.na(voter.candidate[i]))
next()
if ((voter.candidate[i] == transfer.name) &&
(is.na(voter.transfer[i])))
voters.to.transfer <- c(voters.to.transfer, i)
}
print("Select from the following voters' ballots that have a remaining highest grade for an eligible candidate:")
print(voters.to.transfer)
# select only those voters who voted for this candidate
voter.mat.stage2 <-
voter.mat.orig[voters.to.transfer,] # use only voters for this candidate
if (length(voters.to.transfer) == 1) {
# if only one voter force a multi-dim array by adding and then removing an empty row
voter.mat.stage2 <- rbind(voter.mat.stage2, NA)
voter.mat.stage2 <- na.omit(voter.mat.stage2)
}
# set grade for this candidate to 0 to remove from selection
voter.mat.stage2[, transfer.candidate] <- 0
# pick the remaining highest candidate for each voter
voter.count.stage2 <- length(voters.to.transfer)
candidates.stage2 <-
replicate(candidates, 0) # count of candidates
# sum the count of candidates that have the highest grade across voters
voters.stage2 <- NULL
voters.next.highest.graded <- NULL
print("Next highest graded candidate by voter:")
for (i in 1:voter.count.stage2) {
selector.max <- max(voter.mat.stage2[i, ]) # highest selector
if (selector.max >= Acceptable) {
candidates.equal.stage2 <- NULL
for (k in 1:candidates) {
if (voter.mat.stage2[i, k] == selector.max)
candidates.equal.stage2 <- c(candidates.equal.stage2, k)
}
if (length(candidates.equal.stage2) > 1)
# select one of multiple candidates with same grade
candidate.stage2 <-
sample(candidates.equal.stage2, size = 1)
else
candidate.stage2 <- candidates.equal.stage2
voter.candidate.to.transfer <-
c(voter.candidate.to.transfer, candidate.stage2) # list of highest graded remaining candidates
voters.next.highest.graded <-
c(voters.next.highest.graded, voters.to.transfer[i]) # list of corresponding voters
print(paste("voter ",
voters.to.transfer[i],
" candidate ",
names[candidate.stage2],
sep =
""))
if (length(candidates.equal.stage2) > 1) {
cat(" candidate ties: ", names[candidates.equal.stage2], "\n")
}
candidates.stage2[candidate.stage2] <-
candidates.stage2[candidate.stage2] + 1
}
} # end of loop that builds list of highest graded remaining candidates and corresponding voters
# for super-popular candidates
candidates.to.ignore <- which(weights.stage2 >= vote.limit)
candidates.stage2[candidates.to.ignore] <- 0
cat("Candidates and their current affirmed evaluations that may receive Stage 2 transfers from the voters listed above: \n")
print(rbind(council, candidates.stage2))
proxy.required <-
FALSE # must transfer proxy votes if not enough graded votes to transfer
# loop until all votes from this super-popular candidate are transferred or determined to be proxy votes
while (transfer.count > 0) {
# make sure there are votes to transfer
if (max(candidates.stage2) == 0) {
proxy.required <- TRUE
break
}
# select up to transfer.count votes to transfer
candidate.to.transfer.to <-
which(candidates.stage2 == max(candidates.stage2))
if (length(candidate.to.transfer.to) > 1) {
cat("multiple candidates with max: ",
candidate.to.transfer.to,
"\n")
candidate.to.transfer.to <-
sample(candidate.to.transfer.to, size = 1)
}
xfer.count <-
min(candidates.stage2[candidate.to.transfer.to], transfer.count)
if ((weights.stage2[candidate.to.transfer.to] + xfer.count) > vote.limit) {
# transfer limited to reaching vote limit
xfer.count <-
vote.limit - weights.stage2[candidate.to.transfer.to]
cat("* * * Transfer to candidate ",
names[candidate.to.transfer.to],
"limited to ",
xfer.count,
" votes\n")
}
cat(
"Candidate",
names[candidate.to.transfer.to],
"automatically selected by lot to receive up to",
xfer.count,
"votes from",
transfer.name,
"\n"
)
# update the current votes to show which voters had their vote transferred and to whom
voters.to.transfer.candidate <-
which(voter.candidate.to.transfer == candidate.to.transfer.to)
voters.transferred <-
sort(sample(voters.next.highest.graded[voters.to.transfer.candidate], size = xfer.count))
cat(
"Voters' ballots selected automatically by lot to transfer: ",
voters.transferred,
"\n"
)
voter.candidate[voters.transferred] <-
names[candidate.to.transfer.to]
voter.transfer[voters.transferred] <-
paste("From ", transfer.name, " to ", names[candidate.to.transfer.to], sep =
"")
weights.stage2[transfer.candidate] <-
weights.stage2[transfer.candidate] - xfer.count
weights.stage2[candidate.to.transfer.to] <-
weights.stage2[candidate.to.transfer.to] + xfer.count
transfer.count <- transfer.count - xfer.count
candidates.stage2[candidate.to.transfer.to] <-
0 # clear: no longer open for transfer
cat("Affirmed evaluations by voter for candidate for loop", xfer.loop, "of Stage 2\n")
print(rbind(candidate.names[council.numbers], weights.stage2))
}
if (proxy.required) {
cat(
"* * * Proxy votes (",
transfer.count,
") required for transfer from candidate ",
transfer.name,
"\n"
)
voters.to.transfer <- NULL
# select voters that match candidate to transfer and have not been marked for transfer
for (i in 1:voters) {
if (is.na(voter.candidate[i]))
next()
if ((voter.candidate[i] == transfer.name) &&
(is.na(voter.transfer[i])))
voters.to.transfer <- c(voters.to.transfer, i)
}
cat("Voters available to transfer ", voters.to.transfer, "\n")
xfer.proxy.count <-
min(length(voters.to.transfer), transfer.count)
voters.transferred <-
sample(voters.to.transfer, size = xfer.proxy.count)
cat(
"Transfer ",
xfer.proxy.count,
" proxy votes for candidate ",
transfer.name,
" to these voters:\n"
)
print(voters.transferred)
if (xfer.proxy.count < transfer.count) {
# in Stage 2, this should never happen as each candidate can assign any number
# of their voters as proxy votes. See Stage 4 for implementation of proxy votes
stop("* * * ERROR: candidate does not have enough voters to handle proxy votes")
# save the default proxy votes for this candidate that could not be transferred
candidate.proxy.default[transfer.candidate] <-
transfer.count - xfer.proxy.count
}
# update voter array
voter.transfer[voters.transferred] <-
paste("Proxy vote Stage 2 from ", transfer.name, sep = "")
# proxy votes end the transfer phase for this candidate
# update weights to reflect proxy votes that will occur later
weights.stage2[transfer.candidate] <-
weights.stage2[transfer.candidate] - transfer.count
print("Affirmed evaluations by candidate")
print(rbind(candidate.names[council.numbers], weights.stage2))
transfer.count <- 0 # done with this candidate
}
}
print("End Stage 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
print("Vote apportionment after Stage 2: ")
print(cbind(voter.names, voter.candidate, voter.round, voter.transfer))
print("Affirmed evaluations by candidate")
print(rbind(candidate.names[council.numbers], weights.stage2))
print("Begin Stage 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
Stage <- 3
weights.stage3 <- weights.stage2
candidate.count <- length(which(weights.stage3 != 0))
cat("Step 1: Determine the elected candidates, who are the candidates that received the largest number ")
cat("of affirmed evaluations by the end of Stage 2.\n")
cat(
"Note: A future version of the algorithm will sum each candidate's ordinal evaluations, counted numerically, and will use this value first to break ties before one of the candidates with the same number of affirmed evaluations is chosen randomly.\n"
)
cat(
"Step 2: Transfer votes from unelected candidates to those selected as winning candidates as follows:\n"
)
cat(
"Start with the unelected candidate currently holding the largest number of affirmed evaluations, resolving any ties randomly. ")
cat(
"Transfer all votes that can be transferred automatically by the algorithm to any of the eligible winners. ")
cat("These are ballots that identify an eligible winner with a grade of at least Acceptable. ")
cat("Ballots that connot be transferred automatically become proxy votes of that unelected candidate and are handled in Stage 4.\n")
cat("Note: A future version of the algorithm will make the candidate your vote went to in Stage 1 ")
cat("the owner of your proxy vote, if required.\n")
# NOTE: As the results will be the same, a future version of the algorithm will require the order of these transfers to be determined by lot.
if (candidate.count < positions) {
# Contingency 1: fewer candidates than positions to fill
print(
paste(
"Contingency 1: Fewer candates with votes",
candidate.count,
" than positions to fill",
positions
)
)
cat("The number of winners that received affirmed evaluations by this stage in the count ")
cat("is fewer than the number of candidates to be elected. ")
cat(
"In this case, these fewer candidates are elected, and they will ensure that each voter ")
cat("is as fully represented as possible in the legislature "
)
cat("by the candidate they gave their highest grade. ")
cat(
"However, if a city or state wishes to require the target number of candidates to be elected "
)
cat(
"even when the target number has not been elected by the above steps, the algorithm can be modified to achieve this result. "
)
cat(
"At the same time, note that such a modification could also have the undesirable effect of partially wasting some citizens votes qualitatively.\n"
)
cat("The algorithm can be modified as follows:\n")
cat(
"Starting with the winning candidate who has the largest number of affirmed evaluations, automatically transfer one ballot chosen by lot to one of the candidates "
)
cat(
"who has not yet received any votes. Do the same with such a ballot currently held by the winner with the second highest number of affirmed evaluations, "
)
cat(
"then the third, etc. If necessary, repeat this action of one at a time transfers until each of the target number of winners has received at least one vote.\n"
)
stop("* * * ERROR: This contingency is not yet implemented.\n")
}
# select the elected candidates
candidates.sorted <-
sort(weights.stage3[which(weights.stage3 != 0)],
decreasing = TRUE) # sort the candidates by larget weight (affirmed evaluations)
candidates.sorted.index <-
order(weights.stage3[which(weights.stage3 != 0)],
decreasing = TRUE) # compute the sorted candidates' index (position) within the original weights
cat("\nStage 3, Step 1: Select the",
positions,
"candidates to be elected.\n")
print("Candidates' affirmed evaluations in descending order and corresponding candidate as received from Stage 2")
print (rbind(names[candidates.sorted.index], candidates.sorted))
if (candidate.count > positions) {
# determine winning candidates
if (candidates.sorted[positions] == candidates.sorted[positions + 1]) {
# decide randomly which of the candidates with equal votes at lowest position to select as winner
candidates.to.narrow <- candidates.sorted[positions:candidates]
candidate.lowest <-
sample(which(candidates.to.narrow == max(candidates.to.narrow)), size =
1)
cat(
"From tie of lowest candidates,",
"the algorithm randomly selected candidate",
names[positions + candidate.lowest - 1],
"\n"
)
# must relate this selection back to candidate in index, which points to position in original weights
# for example, if candidate.lowest is 2, then the candidate that corresponds
# to the index for second candidate relative to positions
candidate.lowest.index <-
candidates.sorted.index[positions + candidate.lowest - 1]
# swap the two index positions (they might be the same)
candidate.index.orig <-
candidates.sorted.index[positions + candidate.lowest - 1]
candidates.sorted.index[positions + candidate.lowest - 1] =
candidates.sorted.index[positions]
candidates.sorted.index[positions] =
candidate.index.orig
}
}
print("Affirmed evaluations for winning candidates after Step 1 of Stage 3")
print (rbind(names[candidates.sorted.index[1:positions]], candidates.sorted[1:positions]))
cat("\nStage 3, Step 2: Transfer votes from unelected candidates to elected candidates.\n")
cat("Start with the unelected candidate with the largest number of votes to transfer. ")
cat("For ballots that have a remaining highest grade of at least Acceptable for an eligible candidate, ")
cat("transfer these votes to eligible winners.\n")
if (candidate.count > positions) {
# transfer votes from highest weighted unelected candidates until all their votes are transferred
# repeat until all unelected candidates' votes are transferred
proxy.candidate <- NULL
weights.stage3.transfer <-
weights.stage3 # use this to track the remaining unelected candidates
# zero weights of elected candidates to do transfer of votes from unelected candidates
weights.stage3.transfer[candidates.sorted.index[1:positions]] <- 0
xfer.loop <- 0
while ((max.weight <- max(weights.stage3.transfer)) > 0) {
# find the candidate with most votes to transfer, ties broken by random selection
# Note: A future version of the program will select the next super-popular candidate by lot as the order of
# candidates does not change the result
xfer.loop <- xfer.loop + 1
print("**********************")
cat("Stage 3, Step 2 transfer loop ", xfer.loop, "\n")
print("**********************")
transfer.candidates <- NULL
for (i in 1:candidates) {
if (weights.stage3.transfer[i] == max.weight)
transfer.candidates <- c(transfer.candidates, i)
}
if (length(transfer.candidates) > 1)
transfer.candidate <- sample(transfer.candidates, size = 1)
else
transfer.candidate <- transfer.candidates
transfer.count <- max.weight
transfer.name <- names[transfer.candidate]
print(
paste(
"Transfer ",
transfer.count,
" votes (remaining highest affirmed evaluations) from unelected candidate ",
transfer.name,
sep = ""
)
)
# process transfers for transfer.candidate until the number required are transferred
# note this automated transfer might end with proxy votes from some voters if not enough voters
# marked other eligible candidates
# Create the set of ballots from this candidate that have a remaining highest grade of at least Acceptable
# for an eligible candidate
voters.to.transfer <- NULL
voter.candidate.to.transfer <- NULL
# select voters that match candidate to transfer and have not been marked for transfer
for (i in 1:voters) {
if (is.na(voter.candidate[i]))
next()
if ((voter.candidate[i] == transfer.name) &&
(is.na(voter.transfer[i])))
voters.to.transfer <- c(voters.to.transfer, i)
}
cat("Voters' ballots to select from:", voters.to.transfer, "\n")
# select only those voters who voted for this candidate
voter.mat.stage3 <-
voter.mat.orig[voters.to.transfer,] # use only voters for this candidate
if (length(voters.to.transfer) == 1) {
# if only one voter force a multi-dim array by adding and then removing an empty row
voter.mat.stage3 <- rbind(voter.mat.stage3, NA)
voter.mat.stage3 <- na.omit(voter.mat.stage3)
}
# set grade for unelected candidates to 0 to remove from selection
voter.count.stage3 <- length(voters.to.transfer)
for (i in 1:voter.count.stage3)
for (k in 1:candidates)
if (! (k %in% candidates.sorted.index[1:positions]))
voter.mat.stage3[i, k] <- 0
# for each voter, pick the remaining candidate with highest grade
candidates.stage3 <-
replicate(candidates, 0) # count of candidates
# sum the count of candidates that have the highest grade across voters
voters.stage3 <- NULL
voters.next.highest.graded <- NULL
print("Remaining highest graded candidate by voter:")
for (i in 1:voter.count.stage3) {
selector.max <- max(voter.mat.stage3[i, ]) # highest selector
if (selector.max >= Acceptable) {
candidates.equal.stage3 <- NULL
for (k in 1:candidates) {
if (voter.mat.stage3[i, k] == selector.max)
candidates.equal.stage3 <- c(candidates.equal.stage3, k)
}
if (length(candidates.equal.stage3) > 1)
# select one of multiple candidates with same grade
candidate.stage3 <-
sample(candidates.equal.stage3, size = 1)
else
candidate.stage3 <- candidates.equal.stage3
voter.candidate.to.transfer <-
c(voter.candidate.to.transfer, candidate.stage3) # list of highest graded remaining candidates
voters.next.highest.graded <-
c(voters.next.highest.graded, voters.to.transfer[i]) # list of corresponding voters
print(paste(
"voter ",
voters.to.transfer[i],
" candidate ",
names[candidate.stage3],
sep =
""
))
if (length(candidates.equal.stage3) > 1) {
cat(" candidate ties: ", names[candidates.equal.stage3], "\n")
}
candidates.stage3[candidate.stage3] <-
candidates.stage3[candidate.stage3] + 1
}
} # end for loop to transfer candidate votes (weights) from unelected candidates
candidates.to.ignore <- which(weights.stage3 >= vote.limit)
if (exists("candidates.to.ignore"))
candidates.stage3[candidates.to.ignore] <- 0
cat("Candidates eligible to receive Stage 3 transfers from candidate", transfer.name, "\n")
print(rbind(council, candidates.stage3))
proxy.required <-
FALSE # must transfer proxy votes if not enough graded votes were found to automatically transfer
# loop until all votes from this unelected candidate are transferred or assigned to be proxy votes
while (transfer.count > 0) {
# make sure there are votes to transfer
if (max(candidates.stage3) == 0) {
proxy.required <- TRUE
break
}
# select up to transfer.count votes to transfer
candidate.to.transfer.to <-
which(candidates.stage3 == max(candidates.stage3))
if (length(candidate.to.transfer.to) > 1) {
cat("multiple candidates with max: ",
candidate.to.transfer.to,
"\n")
candidate.to.transfer.to <-
sample(candidate.to.transfer.to, size = 1)
}
xfer.count <-
min(candidates.stage3[candidate.to.transfer.to], transfer.count)
if ((weights.stage3[candidate.to.transfer.to] + xfer.count) > vote.limit) {
# transfer limited to reaching vote limit
xfer.count <-
vote.limit - weights.stage3[candidate.to.transfer.to]
cat("* * * Transfer to candidate ",
names[candidate.to.transfer.to],
"limited to ",
xfer.count,
" votes\n")
}
cat(
"Transfer ",
xfer.count,
" votes from candidate ",
transfer.name,
"to ",
names[candidate.to.transfer.to],
"\n"
)
# update the current votes to show which voters had their vote transferred and to whom
voters.to.transfer.candidate <-
which(voter.candidate.to.transfer == candidate.to.transfer.to)
voters.transferred <-
sort(sample(voters.next.highest.graded[voters.to.transfer.candidate], size = xfer.count))
cat("Voters' ballots to transfer: ", voters.transferred, "\n")
voter.candidate[voters.transferred] <-
names[candidate.to.transfer.to]
voter.transfer[voters.transferred] <-
paste("From ", transfer.name, " to ", names[candidate.to.transfer.to], sep =
"")
weights.stage3[transfer.candidate] <-
weights.stage3[transfer.candidate] - xfer.count
# also update transfer weights used to track unelected candidates
weights.stage3.transfer[transfer.candidate] <-
weights.stage3.transfer[transfer.candidate] - xfer.count
weights.stage3[candidate.to.transfer.to] <-
weights.stage3[candidate.to.transfer.to] + xfer.count
transfer.count <- transfer.count - xfer.count
candidates.stage3[candidate.to.transfer.to] <-
0 # clear: no longer open for transfer
print("Remaining weights held by unelected candidates:")
print(rbind(council, weights.stage3.transfer))
print("Affirmed evaluations by candidate")
print(rbind(council, weights.stage3))
}
if (proxy.required) {
cat(
"* * * No more automatic transfer of votes available from candidate ", transfer.name, ". Therefore, ",
transfer.count,
" proxy vote(s) must be transferred by candidate ",
transfer.name,
" in Stage 4.\n", sep=""
)
voters.to.transfer <- NULL
# select voters that match candidate to transfer and have not been marked for transfer
for (i in 1:voters) {
if (is.na(voter.candidate[i]))
next()
if ((voter.candidate[i] == transfer.name) &&
(is.na(voter.transfer[i])))
voters.to.transfer <- c(voters.to.transfer, i)
}
cat("Voters' ballots available to transfer:",
voters.to.transfer,
"\n")
xfer.proxy.count <-
min(length(voters.to.transfer), transfer.count)
voters.transferred <-
sample(voters.to.transfer, size = xfer.proxy.count)
cat(
"Transfer ",
xfer.proxy.count,
"proxy vote(s) from candidate ",
transfer.name,
"from these voters' ballots:",
sort(voters.transferred),
"\n"
)
if (xfer.proxy.count < transfer.count) {
# in Stage 3, this should never happen as each candidate can assign any number
# of their voters as proxy votes.
stop("* * * ERROR: candidate does not have enough voters to handle proxy votes")
# save the proxy votes for this candidate that could not be transferred
candidate.proxy.default[transfer.candidate] <-
transfer.count - xfer.proxy.count
#print("Proxy votes that could not be transferred automatically: ", transfer.count-xfer.proxy.count)
}
# update voter array
voter.transfer[voters.transferred] <-
paste("Proxy vote Stage 3 from ", transfer.name, sep = "")
# proxy votes end the transfer phase for this candidate
# update weights to reflect proxy votes that will occur later
weights.stage3[transfer.candidate] <-
weights.stage3[transfer.candidate] - transfer.count
# also update transfer weights used to track unelected candidates
weights.stage3.transfer[transfer.candidate] <-
weights.stage3.transfer[transfer.candidate] - transfer.count
print("Affirmed evaluations by candidate")
print(rbind(council, weights.stage3))
print("Remaining weights held by unelected candidates:")
print(rbind(council, weights.stage3.transfer))
transfer.count <- 0 # done with this candidate
}
}
}
print("End Stage 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
print("Vote apportionment after Stage 3: ")
print(cbind(voter.names, voter.candidate, voter.round, voter.transfer))
print("Affirmed evaluations for winning candidates")
print(rbind(candidate.names[council.numbers], weights.stage3))
cat("\n")
print("Begin Stage 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
cat("Stage 4, though not carried out by the algorithm, identifies the proxy votes ")
cat("determined in Stages 2 and 3 that must be publicly transferred.\n")
cat("Finalize the weighted votes of each winner as follows:\n")
cat("The candidate with the largest number of affirmed evaluations (ties resolved by lot) ")
cat("publicly transfers their proxy votes to any of the eligible winners they find most suitable for office. "
)
cat("Continue the same transfer process with the candidate with the next most affirmed evaluations ")
cat("until all proxy votes are transferred.\n")
# accumulate the voters with proxy votes to be transferred
voter.names.stage4 <- NULL
voter.candidate.stage4 <- NULL
voter.transfer.stage4 <- NULL
for (i in 1:voters) {
if (is.na(voter.transfer[i]))
next()
first.char <- substr(voter.transfer[i], 1, 1)
if (first.char == "P") {
voter.names.stage4 <- c(voter.names.stage4, voter.names[i])
voter.transfer.stage4 <-
c(voter.transfer.stage4, voter.transfer[i])
}
}
if (is.null(voter.names.stage4)) {
print("No proxy votes to transfer")
} else {
cat("Voter ballots with proxy votes to transfer:\n")
print(cbind(voter.names.stage4, voter.transfer.stage4))
}
print("End Stage 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
cat("\n")
print("******** End of EPR output **********")