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 Hawkins36
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders233
Andrew Yang56
Elizabeth Warren38
John Kasich16
Jeb Bush8
Rand Paul39
Ted Cruz29
TOTAL:1435

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 Hawkins242
Tulsi Gabbard382
Dan Crenshaw178
Justin Amash337
Amy Klobuchar230
Bernie Sanders600
Andrew Yang521
Elizabeth Warren428
John Kasich175
Jeb Bush153
Rand Paul402
Ted Cruz313
Ballots Cast:1435

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 Hawkins50
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash83
Amy Klobuchar20
Bernie Sanders281
Andrew Yang98
Elizabeth Warren74
John Kasich21
Jeb Bush10
Rand Paul62
Ted Cruz41

Jeb Bush eliminated in this round.

Round 2:

Donald Trump320
Joe Biden141
Jo Jorgensen172
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Amy Klobuchar20
Bernie Sanders282
Andrew Yang98
Elizabeth Warren74
John Kasich24
Rand Paul62
Ted Cruz45

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump320
Joe Biden149
Jo Jorgensen174
Howie Hawkins52
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Bernie Sanders285
Andrew Yang99
Elizabeth Warren77
John Kasich25
Rand Paul62
Ted Cruz45

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump322
Joe Biden150
Jo Jorgensen178
Howie Hawkins52
Tulsi Gabbard44
Justin Amash85
Bernie Sanders285
Andrew Yang100
Elizabeth Warren77
John Kasich27
Rand Paul65
Ted Cruz50

John Kasich eliminated in this round.

Round 5:

Donald Trump323
Joe Biden154
Jo Jorgensen179
Howie Hawkins52
Tulsi Gabbard48
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 Hawkins55
Justin Amash96
Bernie Sanders294
Andrew Yang107
Elizabeth Warren82
Rand Paul73
Ted Cruz53

Ted Cruz eliminated in this round.

Round 7:

Donald Trump351
Joe Biden162
Jo Jorgensen192
Howie Hawkins56
Justin Amash97
Bernie Sanders296
Andrew Yang109
Elizabeth Warren82
Rand Paul90

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump354
Joe Biden168
Jo Jorgensen194
Justin Amash97
Bernie Sanders335
Andrew Yang112
Elizabeth Warren85
Rand Paul90

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump354
Joe Biden186
Jo Jorgensen201
Justin Amash98
Bernie Sanders380
Andrew Yang126
Rand Paul90

Rand Paul eliminated in this round.

Round 10:

Donald Trump390
Joe Biden187
Jo Jorgensen217
Justin Amash124
Bernie Sanders381
Andrew Yang136

Justin Amash eliminated in this round.

Round 11:

Donald Trump400
Joe Biden191
Jo Jorgensen314
Bernie Sanders385
Andrew Yang145

Andrew Yang eliminated in this round.

Round 12:

Donald Trump411
Joe Biden220
Jo Jorgensen346
Bernie Sanders458

Joe Biden eliminated in this round.

Round 13:

Donald Trump429
Jo Jorgensen406
Bernie Sanders600

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump634
Bernie Sanders801

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
775
484 to
951
634 to
801
538 to
897
593 to
842
509 to
926
638 to
797
634 to
801
566 to
869
671 to
764
625 to
810
623 to
812
486 to
949
585 to
850
Joe Biden6/8/0775 to
660
640 to
795
693 to
742
622 to
813
755 to
680
693 to
742
725 to
710
574 to
861
479 to
956
640 to
795
743 to
692
756 to
679
710 to
725
772 to
663
Jo Jorgensen13/1/0951 to
484
795 to
640
885 to
550
796 to
639
971 to
464
874 to
561
847 to
588
719 to
716
714 to
721
803 to
632
969 to
466
995 to
440
946 to
489
979 to
456
Howie Hawkins10/4/0801 to
634
742 to
693
550 to
885
626 to
809
812 to
623
746 to
689
783 to
652
623 to
812
578 to
857
774 to
661
812 to
623
822 to
613
770 to
665
818 to
617
Tulsi Gabbard13/1/0897 to
538
813 to
622
639 to
796
809 to
626
977 to
458
881 to
554
963 to
472
738 to
697
754 to
681
870 to
565
1024 to
411
1025 to
410
880 to
555
947 to
488
Dan Crenshaw6/8/0842 to
593
680 to
755
464 to
971
623 to
812
458 to
977
643 to
792
741 to
694
625 to
810
599 to
836
742 to
693
801 to
634
826 to
609
707 to
728
850 to
585
Justin Amash9/5/0926 to
509
742 to
693
561 to
874
689 to
746
554 to
881
792 to
643
795 to
640
680 to
755
677 to
758
779 to
656
958 to
477
986 to
449
930 to
505
980 to
455
Amy Klobuchar6/8/0797 to
638
710 to
725
588 to
847
652 to
783
472 to
963
694 to
741
640 to
795
634 to
801
527 to
908
767 to
668
889 to
546
894 to
541
800 to
635
851 to
584
Bernie Sanders11/3/0801 to
634
861 to
574
716 to
719
812 to
623
697 to
738
810 to
625
755 to
680
801 to
634
700 to
735
876 to
559
885 to
550
886 to
549
831 to
604
846 to
589
Andrew Yang13/1/0869 to
566
956 to
479
721 to
714
857 to
578
681 to
754
836 to
599
758 to
677
908 to
527
735 to
700
953 to
482
1042 to
393
1025 to
410
900 to
535
930 to
505
Elizabeth Warren6/8/0764 to
671
795 to
640
632 to
803
661 to
774
565 to
870
693 to
742
656 to
779
668 to
767
559 to
876
482 to
953
805 to
630
836 to
599
776 to
659
810 to
625
John Kasich4/10/0810 to
625
692 to
743
466 to
969
623 to
812
411 to
1024
634 to
801
477 to
958
546 to
889
550 to
885
393 to
1042
630 to
805
905 to
530
755 to
680
869 to
566
Jeb Bush2/12/0812 to
623
679 to
756
440 to
995
613 to
822
410 to
1025
609 to
826
449 to
986
541 to
894
549 to
886
410 to
1025
599 to
836
530 to
905
685 to
750
850 to
585
Rand Paul5/9/0949 to
486
725 to
710
489 to
946
665 to
770
555 to
880
728 to
707
505 to
930
635 to
800
604 to
831
535 to
900
659 to
776
680 to
755
750 to
685
1008 to
427
Ted Cruz1/13/0850 to
585
663 to
772
456 to
979
617 to
818
488 to
947
585 to
850
455 to
980
584 to
851
589 to
846
505 to
930
625 to
810
566 to
869
585 to
850
427 to
1008

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 Biden4855 3.4
Jo Jorgensen5495 3.8
Howie Hawkins3819 2.7
Tulsi Gabbard5044 3.5
Dan Crenshaw3532 2.5
Justin Amash4817 3.4
Amy Klobuchar3846 2.7
Bernie Sanders6298 4.4
Andrew Yang6059 4.2
Elizabeth Warren4921 3.4
John Kasich3375 2.4
Jeb Bush3307 2.3
Rand Paul4994 3.5
Ted Cruz4052 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 Biden4855
Jo Jorgensen5495
Howie Hawkins3819
Tulsi Gabbard5044
Dan Crenshaw3532
Justin Amash4817
Amy Klobuchar3846
Bernie Sanders6298
Andrew Yang6059
Elizabeth Warren4921
John Kasich3375
Jeb Bush3307
Rand Paul4994
Ted Cruz4052

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 Sanders941
Andrew Yang905

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
685
454 to
751
603 to
559
492 to
672
520 to
424
481 to
661
600 to
604
578 to
728
519 to
778
624 to
637
587 to
507
574 to
494
419 to
592
473 to
361
Joe Biden10/4/0685 to
586
605 to
592
613 to
447
552 to
648
703 to
452
628 to
518
576 to
338
342 to
639
363 to
720
436 to
490
661 to
384
689 to
397
667 to
604
711 to
525
Jo Jorgensen11/3/0751 to
454
592 to
605
607 to
310
522 to
481
681 to
282
479 to
365
590 to
431
521 to
684
446 to
646
582 to
552
653 to
340
679 to
344
593 to
391
735 to
354
Howie Hawkins3/11/0559 to
603
447 to
613
310 to
607
302 to
629
459 to
424
363 to
523
401 to
451
271 to
698
262 to
732
385 to
497
442 to
432
471 to
470
428 to
592
521 to
543
Tulsi Gabbard11/3/0672 to
492
648 to
552
481 to
522
629 to
302
638 to
290
507 to
434
622 to
358
512 to
653
448 to
606
578 to
497
649 to
285
674 to
326
528 to
464
665 to
413
Dan Crenshaw0/14/0424 to
520
452 to
703
282 to
681
424 to
459
290 to
638
273 to
541
401 to
520
413 to
749
335 to
753
449 to
595
392 to
414
405 to
442
282 to
553
388 to
419
Justin Amash8/6/0661 to
481
518 to
628
365 to
479
523 to
363
434 to
507
541 to
273
479 to
455
470 to
688
394 to
658
495 to
567
526 to
329
572 to
348
492 to
389
629 to
376
Amy Klobuchar6/8/0604 to
600
338 to
576
431 to
590
451 to
401
358 to
622
520 to
401
455 to
479
293 to
704
230 to
742
318 to
514
478 to
334
522 to
389
488 to
582
572 to
523
Bernie Sanders14/0/0728 to
578
639 to
342
684 to
521
698 to
271
653 to
512
749 to
413
688 to
470
704 to
293
530 to
494
616 to
253
725 to
351
735 to
381
696 to
553
737 to
506
Andrew Yang13/1/0778 to
519
720 to
363
646 to
446
732 to
262
606 to
448
753 to
335
658 to
394
742 to
230
494 to
530
627 to
344
777 to
255
786 to
297
662 to
473
758 to
448
Elizabeth Warren9/5/0637 to
624
490 to
436
552 to
582
497 to
385
497 to
578
595 to
449
567 to
495
514 to
318
253 to
616
344 to
627
570 to
357
592 to
423
584 to
587
629 to
553
John Kasich2/12/0507 to
587
384 to
661
340 to
653
432 to
442
285 to
649
414 to
392
329 to
526
334 to
478
351 to
725
255 to
777
357 to
570
375 to
313
369 to
542
469 to
478
Jeb Bush1/13/0494 to
574
397 to
689
344 to
679
470 to
471
326 to
674
442 to
405
348 to
572
389 to
522
381 to
735
297 to
786
423 to
592
313 to
375
335 to
539
431 to
452
Rand Paul8/6/0592 to
419
604 to
667
391 to
593
592 to
428
464 to
528
553 to
282
389 to
492
582 to
488
553 to
696
473 to
662
587 to
584
542 to
369
539 to
335
558 to
269
Ted Cruz4/10/0361 to
473
525 to
711
354 to
735
543 to
521
413 to
665
419 to
388
376 to
629
523 to
572
506 to
737
448 to
758
553 to
629
478 to
469
452 to
431
269 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
0767435.65%
117127.95%
215046.99%
317248.01%
415287.10%
518748.71%
611945.55%
711735.45%
810434.85%
98013.72%
1012986.03%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump664566472577258696453206
Joe Biden47711282110123112108121764668
Jo Jorgensen39112210813610914362726568159
Howie Hawkins578143105117951337052523060
Tulsi Gabbard39094104139145180120109664642
Dan Crenshaw608131115132851266465463231
Justin Amash4941161011229914160526562123
Amy Klobuchar53911510515211015110279491716
Bernie Sanders44382847776785893103110231
Andrew Yang336929311311715011611311681108
Elizabeth Warren525111987895828780978894
John Kasich5891231161421221577850331114
Jeb Bush5571561381581231296546311616
Rand Paul471126101103841168595997679
Ted Cruz6121339073881046177816551

Number of bullet votes: 40 (2.79%).
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.