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 Trump421
Joe Biden315
Jo Jorgensen196
Howie Hawkins43
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders245
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul43
Ted Cruz31
TOTAL:1544

The winner is Donald Trump with 27.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump549
Joe Biden563
Jo Jorgensen451
Howie Hawkins257
Tulsi Gabbard396
Dan Crenshaw186
Justin Amash346
Amy Klobuchar250
Bernie Sanders627
Andrew Yang535
Elizabeth Warren451
John Kasich182
Jeb Bush166
Rand Paul418
Ted Cruz348
Ballots Cast:1544

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump369
Joe Biden154
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders294
Andrew Yang102
Elizabeth Warren77
John Kasich22
Jeb Bush13
Rand Paul66
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump370
Joe Biden154
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders295
Andrew Yang102
Elizabeth Warren77
John Kasich25
Rand Paul67
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump370
Joe Biden163
Jo Jorgensen176
Howie Hawkins59
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders298
Andrew Yang104
Elizabeth Warren81
John Kasich26
Rand Paul67
Ted Cruz48

John Kasich eliminated in this round.

Round 4:

Donald Trump371
Joe Biden167
Jo Jorgensen177
Howie Hawkins59
Tulsi Gabbard44
Dan Crenshaw28
Justin Amash87
Bernie Sanders300
Andrew Yang106
Elizabeth Warren84
Rand Paul71
Ted Cruz50

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump374
Joe Biden168
Jo Jorgensen181
Howie Hawkins59
Tulsi Gabbard50
Justin Amash88
Bernie Sanders300
Andrew Yang107
Elizabeth Warren85
Rand Paul75
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump377
Joe Biden174
Jo Jorgensen191
Howie Hawkins63
Justin Amash97
Bernie Sanders307
Andrew Yang113
Elizabeth Warren87
Rand Paul78
Ted Cruz57

Ted Cruz eliminated in this round.

Round 7:

Donald Trump404
Joe Biden176
Jo Jorgensen194
Howie Hawkins64
Justin Amash99
Bernie Sanders309
Andrew Yang115
Elizabeth Warren87
Rand Paul96

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump409
Joe Biden183
Jo Jorgensen199
Justin Amash99
Bernie Sanders349
Andrew Yang119
Elizabeth Warren90
Rand Paul96

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump409
Joe Biden201
Jo Jorgensen207
Justin Amash101
Bernie Sanders394
Andrew Yang136
Rand Paul96

Rand Paul eliminated in this round.

Round 10:

Donald Trump447
Joe Biden202
Jo Jorgensen223
Justin Amash129
Bernie Sanders396
Andrew Yang147

Justin Amash eliminated in this round.

Round 11:

Donald Trump458
Joe Biden206
Jo Jorgensen323
Bernie Sanders401
Andrew Yang156

Andrew Yang eliminated in this round.

Round 12:

Donald Trump470
Joe Biden238
Jo Jorgensen356
Bernie Sanders480

Joe Biden eliminated in this round.

Round 13:

Donald Trump490
Jo Jorgensen419
Bernie Sanders635

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump701
Bernie Sanders843

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 Trump0/14/0 729 to
814
552 to
991
703 to
840
605 to
939
660 to
884
577 to
967
710 to
834
701 to
843
632 to
912
743 to
801
693 to
851
692 to
852
552 to
992
654 to
890
Joe Biden5/9/0814 to
729
683 to
860
733 to
810
665 to
879
802 to
742
740 to
804
767 to
777
612 to
932
517 to
1027
688 to
856
788 to
756
800 to
744
757 to
787
821 to
723
Jo Jorgensen14/0/0991 to
552
860 to
683
943 to
600
855 to
689
1028 to
516
934 to
610
908 to
636
775 to
769
773 to
771
863 to
681
1040 to
504
1057 to
487
1006 to
538
1031 to
513
Howie Hawkins10/4/0840 to
703
810 to
733
600 to
943
698 to
846
878 to
666
822 to
722
851 to
693
683 to
861
639 to
905
839 to
705
886 to
658
889 to
655
840 to
704
872 to
672
Tulsi Gabbard13/1/0938 to
605
878 to
665
688 to
855
845 to
698
1040 to
504
954 to
590
1032 to
512
805 to
739
822 to
722
941 to
603
1104 to
440
1094 to
450
950 to
594
1006 to
538
Dan Crenshaw7/7/0883 to
660
741 to
802
515 to
1028
665 to
878
504 to
1040
713 to
831
809 to
735
692 to
852
665 to
879
809 to
735
874 to
670
897 to
647
780 to
764
911 to
633
Justin Amash9/5/0966 to
577
803 to
740
609 to
934
721 to
822
590 to
954
831 to
713
854 to
690
739 to
805
737 to
807
840 to
704
1034 to
510
1058 to
486
996 to
548
1036 to
508
Amy Klobuchar7/7/0833 to
710
776 to
767
635 to
908
692 to
851
512 to
1032
735 to
809
690 to
854
701 to
843
592 to
952
838 to
706
967 to
577
966 to
578
871 to
673
911 to
633
Bernie Sanders11/3/0842 to
701
931 to
612
768 to
775
860 to
683
739 to
805
852 to
692
805 to
739
843 to
701
762 to
782
940 to
604
953 to
591
954 to
590
903 to
641
907 to
637
Andrew Yang12/2/0911 to
632
1026 to
517
770 to
773
904 to
639
722 to
822
879 to
665
807 to
737
952 to
592
782 to
762
1019 to
525
1122 to
422
1102 to
442
974 to
570
992 to
552
Elizabeth Warren6/8/0800 to
743
855 to
688
680 to
863
704 to
839
603 to
941
735 to
809
704 to
840
706 to
838
604 to
940
525 to
1019
877 to
667
909 to
635
850 to
694
869 to
675
John Kasich4/10/0850 to
693
755 to
788
503 to
1040
657 to
886
440 to
1104
670 to
874
510 to
1034
577 to
967
591 to
953
422 to
1122
667 to
877
971 to
573
823 to
721
927 to
617
Jeb Bush2/12/0851 to
692
743 to
800
486 to
1057
654 to
889
450 to
1094
647 to
897
486 to
1058
578 to
966
590 to
954
442 to
1102
635 to
909
573 to
971
757 to
787
909 to
635
Rand Paul4/10/0991 to
552
786 to
757
537 to
1006
703 to
840
594 to
950
764 to
780
548 to
996
673 to
871
641 to
903
570 to
974
694 to
850
721 to
823
787 to
757
1068 to
476
Ted Cruz1/13/0889 to
654
722 to
821
512 to
1031
671 to
872
538 to
1006
633 to
911
508 to
1036
633 to
911
637 to
907
552 to
992
675 to
869
617 to
927
635 to
909
476 to
1068

And the Condorcet winner is: Jo Jorgensen.

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 Trump5452 3.5
Joe Biden5183 3.4
Jo Jorgensen5755 3.7
Howie Hawkins4131 2.7
Tulsi Gabbard5330 3.5
Dan Crenshaw3814 2.5
Justin Amash5086 3.3
Amy Klobuchar4159 2.7
Bernie Sanders6690 4.3
Andrew Yang6415 4.2
Elizabeth Warren5266 3.4
John Kasich3649 2.4
Jeb Bush3583 2.3
Rand Paul5283 3.4
Ted Cruz4410 2.9

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 Trump5452
Joe Biden5183
Jo Jorgensen5755
Howie Hawkins4131
Tulsi Gabbard5330
Dan Crenshaw3814
Justin Amash5086
Amy Klobuchar4159
Bernie Sanders6690
Andrew Yang6415
Elizabeth Warren5266
John Kasich3649
Jeb Bush3583
Rand Paul5283
Ted Cruz4410

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 Sanders1009
Andrew Yang984

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 Trump7/7/0 652 to
713
522 to
777
669 to
589
558 to
695
585 to
448
549 to
685
666 to
633
639 to
766
582 to
813
689 to
666
652 to
533
635 to
518
480 to
617
531 to
377
Joe Biden10/4/0713 to
652
645 to
630
651 to
490
594 to
690
743 to
495
670 to
558
612 to
379
371 to
681
394 to
766
468 to
527
700 to
423
729 to
439
709 to
645
752 to
571
Jo Jorgensen11/3/0777 to
522
630 to
645
632 to
342
550 to
508
715 to
313
507 to
389
618 to
468
548 to
731
466 to
685
609 to
590
681 to
370
707 to
377
626 to
423
764 to
399
Howie Hawkins3/11/0589 to
669
490 to
651
342 to
632
336 to
653
493 to
451
392 to
551
428 to
481
297 to
739
282 to
773
416 to
531
476 to
456
500 to
499
464 to
620
554 to
586
Tulsi Gabbard11/3/0695 to
558
690 to
594
508 to
550
653 to
336
669 to
315
534 to
457
654 to
392
542 to
696
470 to
646
613 to
535
677 to
311
703 to
354
560 to
490
695 to
451
Dan Crenshaw0/14/0448 to
585
495 to
743
313 to
715
451 to
493
315 to
669
299 to
570
431 to
555
446 to
794
356 to
798
482 to
634
416 to
444
435 to
472
309 to
583
417 to
461
Justin Amash8/6/0685 to
549
558 to
670
389 to
507
551 to
392
457 to
534
570 to
299
505 to
489
497 to
732
414 to
699
522 to
606
553 to
357
599 to
377
521 to
412
657 to
418
Amy Klobuchar5/9/0633 to
666
379 to
612
468 to
618
481 to
428
392 to
654
555 to
431
489 to
505
323 to
743
253 to
783
351 to
540
510 to
361
553 to
419
523 to
613
605 to
565
Bernie Sanders14/0/0766 to
639
681 to
371
731 to
548
739 to
297
696 to
542
794 to
446
732 to
497
743 to
323
560 to
535
650 to
280
765 to
379
779 to
411
739 to
578
779 to
546
Andrew Yang13/1/0813 to
582
766 to
394
685 to
466
773 to
282
646 to
470
798 to
356
699 to
414
783 to
253
535 to
560
668 to
372
817 to
275
828 to
322
709 to
491
798 to
485
Elizabeth Warren9/5/0666 to
689
527 to
468
590 to
609
531 to
416
535 to
613
634 to
482
606 to
522
540 to
351
280 to
650
372 to
668
607 to
386
627 to
456
624 to
618
667 to
596
John Kasich2/12/0533 to
652
423 to
700
370 to
681
456 to
476
311 to
677
444 to
416
357 to
553
361 to
510
379 to
765
275 to
817
386 to
607
400 to
338
397 to
570
497 to
520
Jeb Bush1/13/0518 to
635
439 to
729
377 to
707
499 to
500
354 to
703
472 to
435
377 to
599
419 to
553
411 to
779
322 to
828
456 to
627
338 to
400
363 to
568
458 to
493
Rand Paul7/7/0617 to
480
645 to
709
423 to
626
620 to
464
490 to
560
583 to
309
412 to
521
613 to
523
578 to
739
491 to
709
618 to
624
570 to
397
568 to
363
586 to
306
Ted Cruz4/10/0377 to
531
571 to
752
399 to
764
586 to
554
451 to
695
461 to
417
418 to
657
565 to
605
546 to
779
485 to
798
596 to
667
520 to
497
493 to
458
306 to
586

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
0819135.37%
118517.99%
217057.36%
318978.19%
416437.09%
520348.78%
612655.46%
712535.41%
811104.79%
98393.62%
1013725.92%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump693587273617864777360235
Joe Biden51712195117129121111129814776
Jo Jorgensen42813312514512315463766869160
Howie Hawkins6121521181341001467556553165
Tulsi Gabbard424105117156152193124113694744
Dan Crenshaw638145130151911386769503332
Justin Amash53112511913410915363546664126
Amy Klobuchar57112411817211615911083541918
Bernie Sanders474899788828961100110116238
Andrew Yang36510310512212616312312212183111
Elizabeth Warren559119114841029394871039396
John Kasich6251331301551341688354351116
Jeb Bush5941681511691321397251341816
Rand Paul5091371131179012889971047684
Ted Cruz65113910180961126685877255

Number of bullet votes: 47 (3.04%).
Number of "approval" votes: 20 (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.