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 Trump424
Joe Biden316
Jo Jorgensen196
Howie Hawkins43
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders246
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul46
Ted Cruz31
TOTAL:1552

The winner is Donald Trump with 27.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump554
Joe Biden565
Jo Jorgensen451
Howie Hawkins259
Tulsi Gabbard399
Dan Crenshaw186
Justin Amash347
Amy Klobuchar250
Bernie Sanders630
Andrew Yang535
Elizabeth Warren451
John Kasich182
Jeb Bush167
Rand Paul421
Ted Cruz351
Ballots Cast:1552

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump372
Joe Biden154
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders295
Andrew Yang102
Elizabeth Warren77
John Kasich23
Jeb Bush13
Rand Paul69
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump373
Joe Biden154
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders296
Andrew Yang102
Elizabeth Warren77
John Kasich26
Rand Paul70
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump373
Joe Biden163
Jo Jorgensen176
Howie Hawkins59
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders299
Andrew Yang104
Elizabeth Warren81
John Kasich27
Rand Paul70
Ted Cruz48

Eliminated in this round:

Round 4:

Donald Trump377
Joe Biden169
Jo Jorgensen181
Howie Hawkins59
Tulsi Gabbard50
Justin Amash88
Bernie Sanders301
Andrew Yang107
Elizabeth Warren85
Rand Paul78
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump380
Joe Biden175
Jo Jorgensen191
Howie Hawkins63
Justin Amash97
Bernie Sanders308
Andrew Yang113
Elizabeth Warren87
Rand Paul81
Ted Cruz57

Ted Cruz eliminated in this round.

Round 6:

Donald Trump407
Joe Biden177
Jo Jorgensen194
Howie Hawkins64
Justin Amash99
Bernie Sanders310
Andrew Yang115
Elizabeth Warren87
Rand Paul99

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump412
Joe Biden184
Jo Jorgensen199
Justin Amash99
Bernie Sanders350
Andrew Yang119
Elizabeth Warren90
Rand Paul99

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump412
Joe Biden202
Jo Jorgensen207
Justin Amash101
Bernie Sanders395
Andrew Yang136
Rand Paul99

Rand Paul eliminated in this round.

Round 9:

Donald Trump450
Joe Biden204
Jo Jorgensen224
Justin Amash130
Bernie Sanders397
Andrew Yang147

Justin Amash eliminated in this round.

Round 10:

Donald Trump461
Joe Biden208
Jo Jorgensen325
Bernie Sanders402
Andrew Yang156

Andrew Yang eliminated in this round.

Round 11:

Donald Trump473
Joe Biden240
Jo Jorgensen358
Bernie Sanders481

Joe Biden eliminated in this round.

Round 12:

Donald Trump494
Jo Jorgensen422
Bernie Sanders636

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump708
Bernie Sanders844

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 Trump0/14/0 734 to
817
556 to
995
709 to
842
610 to
942
666 to
886
583 to
969
716 to
836
708 to
844
639 to
913
749 to
803
698 to
854
697 to
855
556 to
996
658 to
894
Joe Biden5/9/0817 to
734
686 to
865
736 to
815
668 to
884
806 to
746
744 to
808
771 to
781
618 to
934
521 to
1031
692 to
860
791 to
761
803 to
749
760 to
792
824 to
728
Jo Jorgensen14/0/0995 to
556
865 to
686
948 to
603
858 to
694
1035 to
517
939 to
613
914 to
638
781 to
771
780 to
772
870 to
682
1045 to
507
1062 to
490
1010 to
542
1034 to
518
Howie Hawkins10/4/0842 to
709
815 to
736
603 to
948
701 to
851
886 to
666
829 to
723
859 to
693
689 to
863
646 to
906
846 to
706
892 to
660
894 to
658
844 to
708
874 to
678
Tulsi Gabbard13/1/0941 to
610
883 to
668
693 to
858
850 to
701
1047 to
505
960 to
592
1039 to
513
811 to
741
829 to
723
948 to
604
1110 to
442
1099 to
453
954 to
598
1010 to
542
Dan Crenshaw7/7/0885 to
666
745 to
806
516 to
1035
665 to
886
505 to
1047
717 to
835
814 to
738
697 to
855
669 to
883
814 to
738
876 to
676
899 to
653
782 to
770
912 to
640
Justin Amash9/5/0968 to
583
807 to
744
612 to
939
722 to
829
592 to
960
835 to
717
859 to
693
744 to
808
743 to
809
846 to
706
1038 to
514
1062 to
490
999 to
553
1038 to
514
Amy Klobuchar7/7/0835 to
716
780 to
771
637 to
914
692 to
859
513 to
1039
738 to
814
693 to
859
707 to
845
598 to
954
843 to
709
970 to
582
970 to
582
874 to
678
913 to
639
Bernie Sanders11/3/0843 to
708
933 to
618
770 to
781
862 to
689
741 to
811
855 to
697
808 to
744
845 to
707
765 to
787
945 to
607
956 to
596
956 to
596
906 to
646
909 to
643
Andrew Yang12/2/0912 to
639
1030 to
521
771 to
780
905 to
646
723 to
829
883 to
669
809 to
743
954 to
598
787 to
765
1024 to
528
1126 to
426
1107 to
445
977 to
575
994 to
558
Elizabeth Warren6/8/0802 to
749
859 to
692
681 to
870
705 to
846
604 to
948
738 to
814
706 to
846
709 to
843
607 to
945
528 to
1024
880 to
672
911 to
641
853 to
699
870 to
682
John Kasich4/10/0853 to
698
760 to
791
506 to
1045
659 to
892
442 to
1110
676 to
876
514 to
1038
582 to
970
596 to
956
426 to
1126
672 to
880
975 to
577
828 to
724
930 to
622
Jeb Bush2/12/0854 to
697
748 to
803
489 to
1062
657 to
894
453 to
1099
653 to
899
490 to
1062
582 to
970
596 to
956
445 to
1107
641 to
911
577 to
975
761 to
791
911 to
641
Rand Paul4/10/0995 to
556
791 to
760
541 to
1010
707 to
844
598 to
954
770 to
782
553 to
999
678 to
874
646 to
906
575 to
977
699 to
853
724 to
828
791 to
761
1072 to
480
Ted Cruz1/13/0893 to
658
727 to
824
517 to
1034
677 to
874
542 to
1010
640 to
912
514 to
1038
639 to
913
643 to
909
558 to
994
682 to
870
622 to
930
641 to
911
480 to
1072

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 Trump5485 3.5
Joe Biden5202 3.4
Jo Jorgensen5779 3.7
Howie Hawkins4155 2.7
Tulsi Gabbard5361 3.5
Dan Crenshaw3832 2.5
Justin Amash5119 3.3
Amy Klobuchar4183 2.7
Bernie Sanders6717 4.3
Andrew Yang6439 4.1
Elizabeth Warren5283 3.4
John Kasich3670 2.4
Jeb Bush3602 2.3
Rand Paul5325 3.4
Ted Cruz4441 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 Trump5485
Joe Biden5202
Jo Jorgensen5779
Howie Hawkins4155
Tulsi Gabbard5361
Dan Crenshaw3832
Justin Amash5119
Amy Klobuchar4183
Bernie Sanders6717
Andrew Yang6439
Elizabeth Warren5283
John Kasich3670
Jeb Bush3602
Rand Paul5325
Ted Cruz4441

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 Sanders1015
Andrew Yang989

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 Trump7/7/0 656 to
715
526 to
779
674 to
590
561 to
699
589 to
449
552 to
688
670 to
635
643 to
768
586 to
815
693 to
668
656 to
535
640 to
520
484 to
620
535 to
380
Joe Biden10/4/0715 to
656
647 to
634
653 to
494
596 to
695
746 to
497
671 to
562
614 to
382
372 to
683
395 to
769
470 to
529
702 to
427
732 to
443
712 to
650
755 to
576
Jo Jorgensen11/3/0779 to
526
634 to
647
634 to
344
551 to
512
718 to
315
508 to
393
620 to
470
551 to
734
468 to
687
612 to
591
685 to
372
711 to
380
630 to
427
766 to
403
Howie Hawkins3/11/0590 to
674
494 to
653
344 to
634
337 to
658
495 to
453
392 to
554
430 to
483
300 to
742
284 to
775
419 to
532
478 to
459
503 to
502
467 to
624
556 to
591
Tulsi Gabbard11/3/0699 to
561
695 to
596
512 to
551
658 to
337
673 to
316
536 to
460
657 to
394
546 to
699
473 to
649
618 to
537
681 to
313
707 to
356
564 to
494
697 to
453
Dan Crenshaw0/14/0449 to
589
497 to
746
315 to
718
453 to
495
316 to
673
299 to
573
432 to
557
448 to
797
356 to
801
484 to
636
417 to
447
436 to
475
311 to
587
418 to
466
Justin Amash8/6/0688 to
552
562 to
671
393 to
508
554 to
392
460 to
536
573 to
299
508 to
490
500 to
735
416 to
700
526 to
606
556 to
359
602 to
380
524 to
416
660 to
422
Amy Klobuchar5/9/0635 to
670
382 to
614
470 to
620
483 to
430
394 to
657
557 to
432
490 to
508
325 to
746
254 to
784
354 to
541
512 to
362
555 to
421
526 to
616
606 to
570
Bernie Sanders14/0/0768 to
643
683 to
372
734 to
551
742 to
300
699 to
546
797 to
448
735 to
500
746 to
325
563 to
537
654 to
281
768 to
382
782 to
415
742 to
583
782 to
551
Andrew Yang13/1/0815 to
586
769 to
395
687 to
468
775 to
284
649 to
473
801 to
356
700 to
416
784 to
254
537 to
563
670 to
372
819 to
276
830 to
324
712 to
494
800 to
490
Elizabeth Warren9/5/0668 to
693
529 to
470
591 to
612
532 to
419
537 to
618
636 to
484
606 to
526
541 to
354
281 to
654
372 to
670
609 to
389
629 to
460
626 to
623
669 to
602
John Kasich2/12/0535 to
656
427 to
702
372 to
685
459 to
478
313 to
681
447 to
417
359 to
556
362 to
512
382 to
768
276 to
819
389 to
609
402 to
340
400 to
573
498 to
526
Jeb Bush1/13/0520 to
640
443 to
732
380 to
711
502 to
503
356 to
707
475 to
436
380 to
602
421 to
555
415 to
782
324 to
830
460 to
629
340 to
402
364 to
571
458 to
498
Rand Paul7/7/0620 to
484
650 to
712
427 to
630
624 to
467
494 to
564
587 to
311
416 to
524
616 to
526
583 to
742
494 to
712
623 to
626
573 to
400
571 to
364
589 to
310
Ted Cruz4/10/0380 to
535
576 to
755
403 to
766
591 to
556
453 to
697
466 to
418
422 to
660
570 to
606
551 to
782
490 to
800
602 to
669
526 to
498
498 to
458
310 to
589

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
0821035.27%
118728.04%
217237.40%
319078.19%
416567.11%
520518.81%
612725.46%
712605.41%
811144.79%
98393.60%
1013765.91%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump695597273627866777560235
Joe Biden51912397117129121112130814776
Jo Jorgensen42913412614612515663766869160
Howie Hawkins6131531201351011477557553165
Tulsi Gabbard425105117159152196124114694744
Dan Crenshaw640147131152911396869503332
Justin Amash53212612013510915463566764126
Amy Klobuchar57212611917211716111183541918
Bernie Sanders476929788828962100111116239
Andrew Yang36610510612212816412312312183111
Elizabeth Warren561121116841039394881039396
John Kasich6251361311561361698354351116
Jeb Bush5951691541701331407251341816
Rand Paul5101371151179212889971047687
Ted Cruz65213910281961166785877255

Number of bullet votes: 47 (3.03%).
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.