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 Trump419
Joe Biden313
Jo Jorgensen196
Howie Hawkins43
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders245
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul42
Ted Cruz31
TOTAL:1539

The winner is Donald Trump with 27.2% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump546
Joe Biden561
Jo Jorgensen449
Howie Hawkins257
Tulsi Gabbard394
Dan Crenshaw186
Justin Amash344
Amy Klobuchar250
Bernie Sanders626
Andrew Yang535
Elizabeth Warren450
John Kasich181
Jeb Bush165
Rand Paul416
Ted Cruz346
Ballots Cast:1539

The winner is Bernie Sanders with 40.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump368
Joe Biden152
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders294
Andrew Yang102
Elizabeth Warren77
John Kasich22
Jeb Bush13
Rand Paul64
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump369
Joe Biden152
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders295
Andrew Yang102
Elizabeth Warren77
John Kasich25
Rand Paul65
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump369
Joe Biden161
Jo Jorgensen176
Howie Hawkins59
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders298
Andrew Yang104
Elizabeth Warren81
John Kasich26
Rand Paul65
Ted Cruz48

John Kasich eliminated in this round.

Round 4:

Donald Trump370
Joe Biden165
Jo Jorgensen177
Howie Hawkins59
Tulsi Gabbard44
Dan Crenshaw28
Justin Amash87
Bernie Sanders300
Andrew Yang106
Elizabeth Warren84
Rand Paul69
Ted Cruz50

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump373
Joe Biden166
Jo Jorgensen181
Howie Hawkins59
Tulsi Gabbard50
Justin Amash88
Bernie Sanders300
Andrew Yang107
Elizabeth Warren85
Rand Paul73
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump376
Joe Biden172
Jo Jorgensen191
Howie Hawkins63
Justin Amash97
Bernie Sanders307
Andrew Yang113
Elizabeth Warren87
Rand Paul76
Ted Cruz57

Ted Cruz eliminated in this round.

Round 7:

Donald Trump403
Joe Biden174
Jo Jorgensen194
Howie Hawkins64
Justin Amash99
Bernie Sanders309
Andrew Yang115
Elizabeth Warren87
Rand Paul94

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump408
Joe Biden181
Jo Jorgensen199
Justin Amash99
Bernie Sanders349
Andrew Yang119
Elizabeth Warren90
Rand Paul94

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump408
Joe Biden199
Jo Jorgensen207
Justin Amash101
Bernie Sanders394
Andrew Yang136
Rand Paul94

Rand Paul eliminated in this round.

Round 10:

Donald Trump446
Joe Biden200
Jo Jorgensen223
Justin Amash127
Bernie Sanders396
Andrew Yang147

Justin Amash eliminated in this round.

Round 11:

Donald Trump457
Joe Biden204
Jo Jorgensen321
Bernie Sanders401
Andrew Yang156

Andrew Yang eliminated in this round.

Round 12:

Donald Trump469
Joe Biden236
Jo Jorgensen354
Bernie Sanders480

Joe Biden eliminated in this round.

Round 13:

Donald Trump489
Jo Jorgensen417
Bernie Sanders633

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump698
Bernie Sanders841

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 Trump0/14/0 726 to
812
551 to
987
700 to
838
603 to
936
658 to
881
576 to
963
707 to
832
698 to
841
630 to
909
740 to
799
691 to
848
690 to
849
551 to
988
653 to
886
Joe Biden5/9/0812 to
726
681 to
857
729 to
809
663 to
876
800 to
739
738 to
801
764 to
775
608 to
931
514 to
1025
683 to
856
786 to
753
797 to
742
755 to
784
819 to
720
Jo Jorgensen13/1/0987 to
551
857 to
681
938 to
600
851 to
688
1023 to
516
931 to
608
903 to
636
772 to
767
768 to
771
859 to
680
1035 to
504
1053 to
486
1004 to
535
1028 to
511
Howie Hawkins10/4/0838 to
700
809 to
729
600 to
938
696 to
843
876 to
663
820 to
719
849 to
690
683 to
856
637 to
902
838 to
701
884 to
655
887 to
652
838 to
701
870 to
669
Tulsi Gabbard13/1/0935 to
603
875 to
663
687 to
851
842 to
696
1037 to
502
952 to
587
1028 to
511
802 to
737
819 to
720
938 to
601
1100 to
439
1091 to
448
948 to
591
1004 to
535
Dan Crenshaw7/7/0880 to
658
738 to
800
515 to
1023
662 to
876
502 to
1037
711 to
828
805 to
734
689 to
850
662 to
877
806 to
733
870 to
669
895 to
644
778 to
761
909 to
630
Justin Amash9/5/0962 to
576
800 to
738
607 to
931
718 to
820
587 to
952
828 to
711
850 to
689
736 to
803
733 to
806
837 to
702
1029 to
510
1054 to
485
994 to
545
1033 to
506
Amy Klobuchar7/7/0831 to
707
774 to
764
635 to
903
689 to
849
511 to
1028
734 to
805
689 to
850
699 to
840
590 to
949
835 to
704
964 to
575
964 to
575
869 to
670
909 to
630
Bernie Sanders11/3/0840 to
698
930 to
608
766 to
772
855 to
683
737 to
802
850 to
689
803 to
736
840 to
699
759 to
780
937 to
602
950 to
589
951 to
588
901 to
638
905 to
634
Andrew Yang13/1/0908 to
630
1024 to
514
770 to
768
901 to
637
720 to
819
877 to
662
806 to
733
949 to
590
780 to
759
1017 to
522
1118 to
421
1100 to
439
972 to
567
990 to
549
Elizabeth Warren6/8/0798 to
740
855 to
683
679 to
859
700 to
838
601 to
938
733 to
806
702 to
837
704 to
835
602 to
937
522 to
1017
875 to
664
906 to
633
848 to
691
867 to
672
John Kasich4/10/0847 to
691
752 to
786
503 to
1035
654 to
884
439 to
1100
669 to
870
510 to
1029
575 to
964
589 to
950
421 to
1118
664 to
875
969 to
570
821 to
718
926 to
613
Jeb Bush2/12/0848 to
690
741 to
797
485 to
1053
651 to
887
448 to
1091
644 to
895
485 to
1054
575 to
964
588 to
951
439 to
1100
633 to
906
570 to
969
755 to
784
908 to
631
Rand Paul4/10/0987 to
551
783 to
755
534 to
1004
700 to
838
591 to
948
761 to
778
545 to
994
670 to
869
638 to
901
567 to
972
691 to
848
718 to
821
784 to
755
1064 to
475
Ted Cruz1/13/0885 to
653
719 to
819
510 to
1028
668 to
870
535 to
1004
630 to
909
506 to
1033
630 to
909
634 to
905
549 to
990
672 to
867
613 to
926
631 to
908
475 to
1064

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 Trump5432 3.5
Joe Biden5166 3.4
Jo Jorgensen5741 3.7
Howie Hawkins4123 2.7
Tulsi Gabbard5313 3.5
Dan Crenshaw3802 2.5
Justin Amash5063 3.3
Amy Klobuchar4149 2.7
Bernie Sanders6673 4.3
Andrew Yang6402 4.2
Elizabeth Warren5253 3.4
John Kasich3641 2.4
Jeb Bush3574 2.3
Rand Paul5260 3.4
Ted Cruz4388 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 Trump5432
Joe Biden5166
Jo Jorgensen5741
Howie Hawkins4123
Tulsi Gabbard5313
Dan Crenshaw3802
Justin Amash5063
Amy Klobuchar4149
Bernie Sanders6673
Andrew Yang6402
Elizabeth Warren5253
John Kasich3641
Jeb Bush3574
Rand Paul5260
Ted Cruz4388

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 Sanders1005
Andrew Yang981

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 Trump7/7/0 649 to
711
520 to
775
666 to
588
557 to
693
583 to
446
548 to
682
663 to
632
636 to
764
580 to
811
686 to
664
650 to
531
633 to
516
479 to
614
530 to
374
Joe Biden10/4/0711 to
649
643 to
628
650 to
489
592 to
688
741 to
493
668 to
556
610 to
377
370 to
679
392 to
764
467 to
527
698 to
422
727 to
438
707 to
643
750 to
569
Jo Jorgensen11/3/0775 to
520
628 to
643
631 to
341
549 to
507
713 to
312
506 to
387
617 to
467
546 to
729
465 to
684
607 to
588
679 to
369
705 to
376
625 to
421
764 to
397
Howie Hawkins3/11/0588 to
666
489 to
650
341 to
631
335 to
651
492 to
449
391 to
549
427 to
480
296 to
736
281 to
771
415 to
530
475 to
455
499 to
498
463 to
618
553 to
584
Tulsi Gabbard11/3/0693 to
557
688 to
592
507 to
549
651 to
335
667 to
314
533 to
455
652 to
391
540 to
694
469 to
645
611 to
533
675 to
311
701 to
353
559 to
488
695 to
449
Dan Crenshaw0/14/0446 to
583
493 to
741
312 to
713
449 to
492
314 to
667
299 to
568
430 to
554
444 to
792
355 to
797
480 to
632
414 to
444
434 to
472
309 to
581
417 to
458
Justin Amash8/6/0682 to
548
556 to
668
387 to
506
549 to
391
455 to
533
568 to
299
503 to
488
495 to
730
412 to
698
520 to
604
551 to
357
597 to
377
521 to
412
655 to
417
Amy Klobuchar5/9/0632 to
663
377 to
610
467 to
617
480 to
427
391 to
652
554 to
430
488 to
503
321 to
741
251 to
782
349 to
538
508 to
360
551 to
418
522 to
611
604 to
563
Bernie Sanders14/0/0764 to
636
679 to
370
729 to
546
736 to
296
694 to
540
792 to
444
730 to
495
741 to
321
558 to
534
648 to
280
762 to
378
776 to
410
737 to
576
777 to
544
Andrew Yang13/1/0811 to
580
764 to
392
684 to
465
771 to
281
645 to
469
797 to
355
698 to
412
782 to
251
534 to
558
666 to
370
814 to
275
826 to
322
708 to
489
798 to
483
Elizabeth Warren9/5/0664 to
686
527 to
467
588 to
607
530 to
415
533 to
611
632 to
480
604 to
520
538 to
349
280 to
648
370 to
666
605 to
385
625 to
455
622 to
616
665 to
594
John Kasich2/12/0531 to
650
422 to
698
369 to
679
455 to
475
311 to
675
444 to
414
357 to
551
360 to
508
378 to
762
275 to
814
385 to
605
400 to
337
397 to
568
497 to
517
Jeb Bush1/13/0516 to
633
438 to
727
376 to
705
498 to
499
353 to
701
472 to
434
377 to
597
418 to
551
410 to
776
322 to
826
455 to
625
337 to
400
363 to
566
458 to
490
Rand Paul7/7/0614 to
479
643 to
707
421 to
625
618 to
463
488 to
559
581 to
309
412 to
521
611 to
522
576 to
737
489 to
708
616 to
622
568 to
397
566 to
363
584 to
305
Ted Cruz4/10/0374 to
530
569 to
750
397 to
764
584 to
553
449 to
695
458 to
417
417 to
655
563 to
604
544 to
777
483 to
798
594 to
665
517 to
497
490 to
458
305 to
584

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
0815635.33%
118488.01%
217037.38%
318908.19%
416427.11%
520288.78%
612595.45%
712485.41%
811084.80%
98363.62%
1013675.92%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump691587273607864767359235
Joe Biden51412195117129121111128814775
Jo Jorgensen42613212514512315363766769160
Howie Hawkins6091511181341001467555553165
Tulsi Gabbard422105117156152191124112694744
Dan Crenshaw636145130149911386669503332
Justin Amash52912511913310915363546664124
Amy Klobuchar56912311817111615910983541918
Bernie Sanders472899688828960100110115238
Andrew Yang36310310412212616212212212183111
Elizabeth Warren556119114841029393861039396
John Kasich6221331301541341678354351116
Jeb Bush5911681511681321397151341816
Rand Paul5071371131169012889971047682
Ted Cruz64913910180961116685867155

Number of bullet votes: 47 (3.05%).
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.