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 Trump431
Joe Biden321
Jo Jorgensen197
Howie Hawkins43
Tulsi Gabbard37
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders248
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul46
Ted Cruz31
TOTAL:1568

The winner is Donald Trump with 27.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump562
Joe Biden571
Jo Jorgensen452
Howie Hawkins262
Tulsi Gabbard400
Dan Crenshaw187
Justin Amash347
Amy Klobuchar253
Bernie Sanders634
Andrew Yang536
Elizabeth Warren453
John Kasich183
Jeb Bush169
Rand Paul423
Ted Cruz357
Ballots Cast:1568

The winner is Bernie Sanders with 40.4% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump379
Joe Biden158
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders298
Andrew Yang102
Elizabeth Warren77
John Kasich23
Jeb Bush13
Rand Paul69
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump380
Joe Biden158
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard41
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders299
Andrew Yang102
Elizabeth Warren77
John Kasich26
Rand Paul70
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump380
Joe Biden167
Jo Jorgensen177
Howie Hawkins59
Tulsi Gabbard41
Dan Crenshaw27
Justin Amash85
Bernie Sanders302
Andrew Yang104
Elizabeth Warren81
John Kasich27
Rand Paul70
Ted Cruz48

Eliminated in this round:

Round 4:

Donald Trump384
Joe Biden173
Jo Jorgensen182
Howie Hawkins59
Tulsi Gabbard51
Justin Amash88
Bernie Sanders304
Andrew Yang107
Elizabeth Warren85
Rand Paul78
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump387
Joe Biden179
Jo Jorgensen192
Howie Hawkins63
Justin Amash97
Bernie Sanders311
Andrew Yang113
Elizabeth Warren87
Rand Paul81
Ted Cruz58

Ted Cruz eliminated in this round.

Round 6:

Donald Trump414
Joe Biden181
Jo Jorgensen196
Howie Hawkins64
Justin Amash99
Bernie Sanders313
Andrew Yang115
Elizabeth Warren87
Rand Paul99

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump419
Joe Biden188
Jo Jorgensen201
Justin Amash99
Bernie Sanders353
Andrew Yang119
Elizabeth Warren90
Rand Paul99

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump419
Joe Biden206
Jo Jorgensen209
Justin Amash101
Bernie Sanders398
Andrew Yang136
Rand Paul99

Rand Paul eliminated in this round.

Round 9:

Donald Trump457
Joe Biden208
Jo Jorgensen226
Justin Amash130
Bernie Sanders400
Andrew Yang147

Justin Amash eliminated in this round.

Round 10:

Donald Trump468
Joe Biden212
Jo Jorgensen327
Bernie Sanders405
Andrew Yang156

Andrew Yang eliminated in this round.

Round 11:

Donald Trump480
Joe Biden244
Jo Jorgensen360
Bernie Sanders484

Joe Biden eliminated in this round.

Round 12:

Donald Trump503
Jo Jorgensen425
Bernie Sanders640

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump719
Bernie Sanders849

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 Trump0/14/0 744 to
823
566 to
1001
719 to
848
620 to
948
677 to
891
593 to
975
727 to
841
719 to
849
651 to
917
761 to
807
710 to
858
710 to
858
567 to
1001
670 to
898
Joe Biden5/9/0823 to
744
693 to
874
741 to
826
675 to
893
815 to
753
752 to
816
780 to
788
626 to
942
531 to
1037
702 to
866
802 to
766
812 to
756
769 to
799
833 to
735
Jo Jorgensen14/0/01001 to
566
874 to
693
955 to
612
866 to
702
1045 to
523
949 to
619
923 to
645
789 to
779
790 to
778
879 to
689
1055 to
513
1072 to
496
1019 to
549
1043 to
525
Howie Hawkins10/4/0848 to
719
826 to
741
612 to
955
710 to
858
896 to
672
839 to
729
869 to
699
698 to
870
657 to
911
858 to
710
902 to
666
903 to
665
853 to
715
882 to
686
Tulsi Gabbard13/1/0947 to
620
892 to
675
701 to
866
857 to
710
1057 to
511
971 to
597
1049 to
519
819 to
749
840 to
728
959 to
609
1121 to
447
1108 to
460
962 to
606
1018 to
550
Dan Crenshaw7/7/0890 to
677
752 to
815
522 to
1045
671 to
896
511 to
1057
727 to
841
824 to
744
706 to
862
678 to
890
824 to
744
886 to
682
906 to
662
790 to
778
920 to
648
Justin Amash9/5/0974 to
593
815 to
752
618 to
949
728 to
839
597 to
971
841 to
727
867 to
701
752 to
816
751 to
817
856 to
712
1048 to
520
1072 to
496
1007 to
561
1046 to
522
Amy Klobuchar7/7/0840 to
727
787 to
780
644 to
923
698 to
869
519 to
1049
744 to
824
701 to
867
712 to
856
606 to
962
851 to
717
979 to
589
979 to
589
882 to
686
922 to
646
Bernie Sanders11/3/0848 to
719
941 to
626
778 to
789
869 to
698
749 to
819
862 to
706
816 to
752
856 to
712
775 to
793
957 to
611
966 to
602
964 to
604
915 to
653
917 to
651
Andrew Yang12/2/0916 to
651
1036 to
531
777 to
790
910 to
657
728 to
840
890 to
678
817 to
751
962 to
606
793 to
775
1035 to
533
1134 to
434
1118 to
450
983 to
585
1002 to
566
Elizabeth Warren6/8/0806 to
761
865 to
702
688 to
879
709 to
858
609 to
959
744 to
824
712 to
856
717 to
851
611 to
957
533 to
1035
887 to
681
919 to
649
860 to
708
877 to
691
John Kasich4/10/0857 to
710
765 to
802
512 to
1055
665 to
902
447 to
1121
682 to
886
520 to
1048
589 to
979
602 to
966
434 to
1134
681 to
887
982 to
586
836 to
732
937 to
631
Jeb Bush2/12/0857 to
710
755 to
812
495 to
1072
664 to
903
460 to
1108
662 to
906
496 to
1072
589 to
979
604 to
964
450 to
1118
649 to
919
586 to
982
770 to
798
919 to
649
Rand Paul4/10/01000 to
567
798 to
769
548 to
1019
714 to
853
606 to
962
778 to
790
561 to
1007
686 to
882
653 to
915
585 to
983
708 to
860
732 to
836
798 to
770
1078 to
490
Ted Cruz1/13/0897 to
670
734 to
833
524 to
1043
685 to
882
550 to
1018
648 to
920
522 to
1046
646 to
922
651 to
917
566 to
1002
691 to
877
631 to
937
649 to
919
490 to
1078

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 Trump5576 3.6
Joe Biden5260 3.4
Jo Jorgensen5826 3.7
Howie Hawkins4202 2.7
Tulsi Gabbard5403 3.4
Dan Crenshaw3875 2.5
Justin Amash5154 3.3
Amy Klobuchar4229 2.7
Bernie Sanders6767 4.3
Andrew Yang6482 4.1
Elizabeth Warren5322 3.4
John Kasich3707 2.4
Jeb Bush3649 2.3
Rand Paul5360 3.4
Ted Cruz4501 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 Trump5576
Joe Biden5260
Jo Jorgensen5826
Howie Hawkins4202
Tulsi Gabbard5403
Dan Crenshaw3875
Justin Amash5154
Amy Klobuchar4229
Bernie Sanders6767
Andrew Yang6482
Elizabeth Warren5322
John Kasich3707
Jeb Bush3649
Rand Paul5360
Ted Cruz4501

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 Sanders1028
Andrew Yang1000

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 Trump7/7/0 665 to
721
536 to
784
684 to
595
571 to
703
598 to
452
563 to
691
679 to
640
653 to
773
597 to
819
704 to
672
666 to
538
650 to
523
494 to
624
544 to
384
Joe Biden10/4/0721 to
665
653 to
642
659 to
501
603 to
700
753 to
503
678 to
567
620 to
387
377 to
688
401 to
775
475 to
534
708 to
434
739 to
449
720 to
654
763 to
583
Jo Jorgensen11/3/0784 to
536
642 to
653
635 to
350
555 to
517
721 to
320
511 to
396
623 to
476
556 to
738
471 to
691
618 to
595
687 to
376
715 to
386
635 to
429
771 to
410
Howie Hawkins2/11/1595 to
684
501 to
659
350 to
635
342 to
662
499 to
457
396 to
555
433 to
486
304 to
746
288 to
777
426 to
535
481 to
461
508 to
508
474 to
625
561 to
598
Tulsi Gabbard11/3/0703 to
571
700 to
603
517 to
555
662 to
342
676 to
319
541 to
463
661 to
398
549 to
704
478 to
653
624 to
541
684 to
316
711 to
362
569 to
497
701 to
461
Dan Crenshaw0/14/0452 to
598
503 to
753
320 to
721
457 to
499
319 to
676
305 to
575
435 to
561
453 to
801
361 to
805
491 to
639
422 to
448
440 to
481
316 to
589
420 to
475
Justin Amash8/6/0691 to
563
567 to
678
396 to
511
555 to
396
463 to
541
575 to
305
509 to
496
504 to
739
418 to
705
532 to
609
558 to
362
605 to
387
529 to
419
664 to
430
Amy Klobuchar5/9/0640 to
679
387 to
620
476 to
623
486 to
433
398 to
661
561 to
435
496 to
509
329 to
751
259 to
786
361 to
543
518 to
364
560 to
428
533 to
617
610 to
577
Bernie Sanders14/0/0773 to
653
688 to
377
738 to
556
746 to
304
704 to
549
801 to
453
739 to
504
751 to
329
568 to
540
661 to
282
772 to
386
786 to
421
746 to
585
787 to
558
Andrew Yang13/1/0819 to
597
775 to
401
691 to
471
777 to
288
653 to
478
805 to
361
705 to
418
786 to
259
540 to
568
675 to
374
823 to
279
836 to
329
716 to
497
804 to
498
Elizabeth Warren9/5/0672 to
704
534 to
475
595 to
618
535 to
426
541 to
624
639 to
491
609 to
532
543 to
361
282 to
661
374 to
675
613 to
395
632 to
468
630 to
628
673 to
611
John Kasich2/12/0538 to
666
434 to
708
376 to
687
461 to
481
316 to
684
448 to
422
362 to
558
364 to
518
386 to
772
279 to
823
395 to
613
406 to
346
405 to
576
501 to
535
Jeb Bush1/12/1523 to
650
449 to
739
386 to
715
508 to
508
362 to
711
481 to
440
387 to
605
428 to
560
421 to
786
329 to
836
468 to
632
346 to
406
371 to
574
462 to
504
Rand Paul7/7/0624 to
494
654 to
720
429 to
635
625 to
474
497 to
569
589 to
316
419 to
529
617 to
533
585 to
746
497 to
716
628 to
630
576 to
405
574 to
371
593 to
318
Ted Cruz4/10/0384 to
544
583 to
763
410 to
771
598 to
561
461 to
701
475 to
420
430 to
664
577 to
610
558 to
787
498 to
804
611 to
673
535 to
501
504 to
462
318 to
593

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
0827035.16%
118978.07%
217757.55%
319218.17%
416757.12%
520778.83%
612835.45%
712705.40%
811224.77%
98463.60%
1013845.88%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump698597373657868777663238
Joe Biden52412498119130123113130814878
Jo Jorgensen43113713114712615863776869161
Howie Hawkins6161551251351021497658563165
Tulsi Gabbard429108119162152198125114694745
Dan Crenshaw645148134153921426871503332
Justin Amash53512812613611115663566764126
Amy Klobuchar57612812217311816311284551918
Bernie Sanders4819410188829062101111118240
Andrew Yang37010711012212916712412312283111
Elizabeth Warren568122119841049495881049496
John Kasich6291381351571381718454351116
Jeb Bush5991691581721351417353341816
Rand Paul5141401181199412989981047687
Ted Cruz65514010681971186886907255

Number of bullet votes: 48 (3.06%).
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.