Presidential Election 2020: Extended Count

Tally for votes by US Citizens.

This page includes not only the basic tallies for each voting system, as if each respective system were in use, it also includes some extra stats:

  1. The Condorcet winner for the Ranked Choice ballots -- if there is one. For Condorcet we look at each pair of candidates and determine who would win if only those two candidates were in the race, determining how voters voted using the relative ranks in the Ranked Choice ballots. If one candidate beats all the others in these pairwise contests, then we have a Condorcet winner. (Such a winner is not guaranteed! Ranked Choice ballots can lead to circularity: Candidate A beats Candidate B, B beats C, and yet C beats A.
  2. The winnier for the Range ballots if we did Range with Runoff (similar to Star Voting but with more stars).
  3. The Condorcet winner for the Range Votes -- if there is one. Here we look at the scores of candidates pairwise to determine voter preference. If a voter gives each candidate the same score, we treat the ballot as an abstention for that pairwise contest.
  4. A histogram of the scores for the Range Votes. Did the voters "bullet vote" giving their favorite candidate a ten and the rest nothing? Or did they grant intermediate values for intermediate candidates?

Plurality Vote Count

Plurality vote totals:

CandidateNumber of Votes
Donald Trump362
Joe Biden302
Jo Jorgensen195
Howie Hawkins37
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders233
Andrew Yang56
Elizabeth Warren38
John Kasich17
Jeb Bush8
Rand Paul39
Ted Cruz29
TOTAL:1437

The winner is Donald Trump with 25.2% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump485
Joe Biden537
Jo Jorgensen443
Howie Hawkins243
Tulsi Gabbard383
Dan Crenshaw178
Justin Amash337
Amy Klobuchar230
Bernie Sanders601
Andrew Yang522
Elizabeth Warren428
John Kasich176
Jeb Bush153
Rand Paul402
Ted Cruz313
Ballots Cast:1437

The winner is Bernie Sanders with 41.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump319
Joe Biden141
Jo Jorgensen172
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash83
Amy Klobuchar20
Bernie Sanders281
Andrew Yang98
Elizabeth Warren74
John Kasich22
Jeb Bush10
Rand Paul62
Ted Cruz41

Jeb Bush eliminated in this round.

Round 2:

Donald Trump320
Joe Biden141
Jo Jorgensen172
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Amy Klobuchar20
Bernie Sanders282
Andrew Yang98
Elizabeth Warren74
John Kasich25
Rand Paul62
Ted Cruz45

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump320
Joe Biden149
Jo Jorgensen174
Howie Hawkins53
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Bernie Sanders285
Andrew Yang99
Elizabeth Warren77
John Kasich26
Rand Paul62
Ted Cruz45

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump322
Joe Biden150
Jo Jorgensen178
Howie Hawkins53
Tulsi Gabbard44
Justin Amash85
Bernie Sanders285
Andrew Yang100
Elizabeth Warren77
John Kasich28
Rand Paul65
Ted Cruz50

John Kasich eliminated in this round.

Round 5:

Donald Trump323
Joe Biden154
Jo Jorgensen179
Howie Hawkins53
Tulsi Gabbard49
Justin Amash87
Bernie Sanders287
Andrew Yang102
Elizabeth Warren80
Rand Paul70
Ted Cruz53

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump326
Joe Biden160
Jo Jorgensen189
Howie Hawkins56
Justin Amash96
Bernie Sanders294
Andrew Yang108
Elizabeth Warren82
Rand Paul73
Ted Cruz53

Ted Cruz eliminated in this round.

Round 7:

Donald Trump351
Joe Biden162
Jo Jorgensen192
Howie Hawkins57
Justin Amash97
Bernie Sanders296
Andrew Yang110
Elizabeth Warren82
Rand Paul90

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump354
Joe Biden168
Jo Jorgensen194
Justin Amash97
Bernie Sanders336
Andrew Yang113
Elizabeth Warren85
Rand Paul90

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump354
Joe Biden186
Jo Jorgensen201
Justin Amash98
Bernie Sanders381
Andrew Yang127
Rand Paul90

Rand Paul eliminated in this round.

Round 10:

Donald Trump390
Joe Biden187
Jo Jorgensen217
Justin Amash124
Bernie Sanders382
Andrew Yang137

Justin Amash eliminated in this round.

Round 11:

Donald Trump400
Joe Biden191
Jo Jorgensen314
Bernie Sanders386
Andrew Yang146

Andrew Yang eliminated in this round.

Round 12:

Donald Trump411
Joe Biden220
Jo Jorgensen346
Bernie Sanders460

Joe Biden eliminated in this round.

Round 13:

Donald Trump429
Jo Jorgensen406
Bernie Sanders602

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump634
Bernie Sanders803

And the winner is: Bernie Sanders

Condorcet Count of Ranked Choice Ballots

CandidateW/L/Tvs.
Trump
vs.
Biden
vs.
Jorgensen
vs.
Hawkins
vs.
Gabbard
vs.
Crenshaw
vs.
Amash
vs.
Klobuchar
vs.
Sanders
vs.
Yang
vs.
Warren
vs.
Kasich
vs.
Bush
vs.
Paul
vs.
Cruz
Donald Trump0/14/0 660 to
777
485 to
952
635 to
802
538 to
899
594 to
843
510 to
927
638 to
799
634 to
803
566 to
871
672 to
765
625 to
812
623 to
814
487 to
950
586 to
851
Joe Biden6/8/0777 to
660
641 to
796
694 to
743
622 to
815
757 to
680
695 to
742
727 to
710
574 to
863
480 to
957
641 to
796
744 to
693
757 to
680
712 to
725
774 to
663
Jo Jorgensen13/1/0952 to
485
796 to
641
886 to
551
796 to
641
972 to
465
875 to
562
848 to
589
719 to
718
715 to
722
803 to
634
970 to
467
996 to
441
947 to
490
980 to
457
Howie Hawkins10/4/0802 to
635
743 to
694
551 to
886
627 to
810
813 to
624
747 to
690
784 to
653
624 to
813
579 to
858
775 to
662
813 to
624
823 to
614
771 to
666
819 to
618
Tulsi Gabbard13/1/0899 to
538
815 to
622
641 to
796
810 to
627
979 to
458
883 to
554
965 to
472
739 to
698
756 to
681
871 to
566
1025 to
412
1027 to
410
882 to
555
949 to
488
Dan Crenshaw6/8/0843 to
594
680 to
757
465 to
972
624 to
813
458 to
979
645 to
792
742 to
695
625 to
812
600 to
837
743 to
694
802 to
635
827 to
610
709 to
728
852 to
585
Justin Amash9/5/0927 to
510
742 to
695
562 to
875
690 to
747
554 to
883
792 to
645
796 to
641
680 to
757
678 to
759
779 to
658
959 to
478
987 to
450
931 to
506
981 to
456
Amy Klobuchar6/8/0799 to
638
710 to
727
589 to
848
653 to
784
472 to
965
695 to
742
641 to
796
634 to
803
528 to
909
768 to
669
890 to
547
895 to
542
802 to
635
853 to
584
Bernie Sanders11/3/0803 to
634
863 to
574
718 to
719
813 to
624
698 to
739
812 to
625
757 to
680
803 to
634
701 to
736
878 to
559
886 to
551
887 to
550
833 to
604
848 to
589
Andrew Yang13/1/0871 to
566
957 to
480
722 to
715
858 to
579
681 to
756
837 to
600
759 to
678
909 to
528
736 to
701
954 to
483
1043 to
394
1027 to
410
902 to
535
932 to
505
Elizabeth Warren6/8/0765 to
672
796 to
641
634 to
803
662 to
775
566 to
871
694 to
743
658 to
779
669 to
768
559 to
878
483 to
954
806 to
631
837 to
600
778 to
659
811 to
626
John Kasich4/10/0812 to
625
693 to
744
467 to
970
624 to
813
412 to
1025
635 to
802
478 to
959
547 to
890
551 to
886
394 to
1043
631 to
806
907 to
530
757 to
680
871 to
566
Jeb Bush2/12/0814 to
623
680 to
757
441 to
996
614 to
823
410 to
1027
610 to
827
450 to
987
542 to
895
550 to
887
410 to
1027
600 to
837
530 to
907
687 to
750
852 to
585
Rand Paul5/9/0950 to
487
725 to
712
490 to
947
666 to
771
555 to
882
728 to
709
506 to
931
635 to
802
604 to
833
535 to
902
659 to
778
680 to
757
750 to
687
1009 to
428
Ted Cruz1/13/0851 to
586
663 to
774
457 to
980
618 to
819
488 to
949
585 to
852
456 to
981
584 to
853
589 to
848
505 to
932
626 to
811
566 to
871
585 to
852
428 to
1009

We have a tie! No candidate won every head to head contest.

Range Count

Here is the straight up count using the Range ballots. Candidate with the highest number of total stars wins.

CandidateTotal StarsAverage Stars
Donald Trump4868 3.4
Joe Biden4861 3.4
Jo Jorgensen5497 3.8
Howie Hawkins3829 2.7
Tulsi Gabbard5055 3.5
Dan Crenshaw3535 2.5
Justin Amash4818 3.4
Amy Klobuchar3849 2.7
Bernie Sanders6310 4.4
Andrew Yang6067 4.2
Elizabeth Warren4927 3.4
John Kasich3388 2.4
Jeb Bush3313 2.3
Rand Paul4995 3.5
Ted Cruz4056 2.8

And the winner is: Bernie Sanders

Range with Runoff

Another possible way to use range ballots is to pick the top two candidates based on the number of stars and then do a runoff round using simple majority voting. (Or more than two if there is a tie for second place.) For the second round we count ballots where the top two candidates have the same number of stars as both being approved -- which has no impact except for a special case. ( If there are more than two candidates in the second round, 2 candidates might have more than the third making the tie meaningful.)

The idea behind Range with Runoff is to encourage people to express preferences between all candidates so that their vote counts in the second round. (Since this was not in the instructions for this simulation, doing a Range with Runoff count here is not a great test of the concept!)

Range with Runoff as per this experiment is similar to Star Voting, only with more possible stars.

First Round:

For the first round, we count just as in Range Voting, but we are interested in the top two candidates. If there is a tie for second place in this round, then we take the top candidate and all second place candidates to the second round.

CandidateNumber of Stars
Donald Trump4868
Joe Biden4861
Jo Jorgensen5497
Howie Hawkins3829
Tulsi Gabbard5055
Dan Crenshaw3535
Justin Amash4818
Amy Klobuchar3849
Bernie Sanders6310
Andrew Yang6067
Elizabeth Warren4927
John Kasich3388
Jeb Bush3313
Rand Paul4995
Ted Cruz4056

The following candidates make it to Round 2:

Second Round:

Here are the vote counts for the second round. A candidate gets a vote if he/she has the highest number of stars in the truncated ballot. If multiple candidates get the same, highest, star count, then multiple candidates get a vote. In this sense, the second round is somewhere between Plurality and Approval.

CandidateVotes
Bernie Sanders942
Andrew Yang906

And the winner is: Bernie Sanders

Range Condorcet Count

Did straight up Range counting produce the Condorcet winner? (That is, the winner if only two candidates were one the ballot and we were to do majority balloting based on the Range data.) Let's find out! For the table below I use the number of stars to determine preference between each pair of candidates for each voter. If a pair of candidates get the same number of stars, I treat the ballot as an abstention for that pairwise race.

CandidateW/L/Tvs.
Trump
vs.
Biden
vs.
Jorgensen
vs.
Hawkins
vs.
Gabbard
vs.
Crenshaw
vs.
Amash
vs.
Klobuchar
vs.
Sanders
vs.
Yang
vs.
Warren
vs.
Kasich
vs.
Bush
vs.
Paul
vs.
Cruz
Donald Trump5/9/0 586 to
687
454 to
752
603 to
560
492 to
674
520 to
426
481 to
662
600 to
606
578 to
730
519 to
780
624 to
638
587 to
509
574 to
496
419 to
593
473 to
363
Joe Biden10/4/0687 to
586
607 to
592
614 to
448
553 to
649
704 to
452
630 to
518
578 to
338
342 to
641
364 to
721
437 to
491
662 to
385
690 to
398
669 to
604
712 to
526
Jo Jorgensen11/3/0752 to
454
592 to
607
607 to
311
522 to
483
682 to
283
480 to
365
590 to
432
521 to
686
447 to
647
582 to
553
653 to
342
679 to
345
594 to
391
736 to
355
Howie Hawkins3/11/0560 to
603
448 to
614
311 to
607
303 to
630
460 to
425
364 to
523
402 to
452
272 to
699
263 to
733
386 to
497
443 to
433
472 to
471
429 to
592
522 to
544
Tulsi Gabbard11/3/0674 to
492
649 to
553
483 to
522
630 to
303
640 to
290
509 to
434
624 to
358
513 to
654
450 to
606
579 to
498
649 to
286
676 to
326
530 to
464
667 to
413
Dan Crenshaw0/14/0426 to
520
452 to
704
283 to
682
425 to
460
290 to
640
274 to
541
402 to
521
413 to
751
335 to
754
450 to
596
392 to
416
405 to
444
283 to
553
388 to
420
Justin Amash8/6/0662 to
481
518 to
630
365 to
480
523 to
364
434 to
509
541 to
274
479 to
457
470 to
690
394 to
659
495 to
568
526 to
331
572 to
350
492 to
389
629 to
377
Amy Klobuchar6/8/0606 to
600
338 to
578
432 to
590
452 to
402
358 to
624
521 to
402
457 to
479
293 to
706
231 to
743
319 to
515
478 to
336
522 to
390
490 to
582
573 to
524
Bernie Sanders14/0/0730 to
578
641 to
342
686 to
521
699 to
272
654 to
513
751 to
413
690 to
470
706 to
293
531 to
495
618 to
253
726 to
352
736 to
382
698 to
553
738 to
506
Andrew Yang13/1/0780 to
519
721 to
364
647 to
447
733 to
263
606 to
450
754 to
335
659 to
394
743 to
231
495 to
531
628 to
345
777 to
257
787 to
298
663 to
473
759 to
448
Elizabeth Warren9/5/0638 to
624
491 to
437
553 to
582
497 to
386
498 to
579
596 to
450
568 to
495
515 to
319
253 to
618
345 to
628
571 to
358
593 to
424
585 to
587
630 to
554
John Kasich2/12/0509 to
587
385 to
662
342 to
653
433 to
443
286 to
649
416 to
392
331 to
526
336 to
478
352 to
726
257 to
777
358 to
571
377 to
313
371 to
542
471 to
478
Jeb Bush1/13/0496 to
574
398 to
690
345 to
679
471 to
472
326 to
676
444 to
405
350 to
572
390 to
522
382 to
736
298 to
787
424 to
593
313 to
377
337 to
539
433 to
452
Rand Paul8/6/0593 to
419
604 to
669
391 to
594
592 to
429
464 to
530
553 to
283
389 to
492
582 to
490
553 to
698
473 to
663
587 to
585
542 to
371
539 to
337
558 to
270
Ted Cruz4/10/0363 to
473
526 to
712
355 to
736
544 to
522
413 to
667
420 to
388
377 to
629
524 to
573
506 to
738
448 to
759
554 to
630
478 to
471
452 to
433
270 to
558

And the Condorcet winner is: Bernie Sanders.

Range Histogram

Many people worry that with Range Voting people will game the system by Bullet Voting: giving their favorite candidate ten stars and everyone else a zero. (This is one justification for Range with Runoff: it gives more incentives to opine on all the viable candidates.)

Another possibility is that people could give 10s to multiple favorites and zeroes to the rest (min/max strategy). In this case Range degenerates to Approval.

So, will people Bullet Vote? Will they simply do an Approval Vote? To get an idea I have generated a histogram table of the number of ballots that include each of the number of stars. Note that it is possible to have more instances of a number of stars than there are ballots, as the total number of instances is the number of ballots times the number of candidates.

Percentages are percentages of possible instances.

Number of StarsNumber of InstancesPercent
0768135.63%
117187.97%
215097.00%
317288.02%
415307.10%
518748.69%
611955.54%
711745.45%
810444.84%
98023.72%
1013006.03%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump666566472577258696453206
Joe Biden47711283110124112108121764668
Jo Jorgensen39212210913610914362726568159
Howie Hawkins579143105117951337052523061
Tulsi Gabbard39094104140145180120109674642
Dan Crenshaw608132116132851266465463231
Justin Amash4951171011229914160526562123
Amy Klobuchar53911610615211015110279491716
Bernie Sanders44382847876785893103111231
Andrew Yang336939311311715011611411681108
Elizabeth Warren526111987895828880978894
John Kasich5891231161431221577850331115
Jeb Bush5571561391581241296546311616
Rand Paul472127101103841168595997679
Ted Cruz6121349074881046177816551

Number of bullet votes: 40 (2.78%).
Number of "approval" votes: 18 (1%).

Look at Other Results?

Use the form below to look at the results for other parties or to toggle the inclusion of test runs.