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 Trump350
Joe Biden299
Jo Jorgensen195
Howie Hawkins36
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders229
Andrew Yang56
Elizabeth Warren37
John Kasich15
Jeb Bush8
Rand Paul39
Ted Cruz28
TOTAL:1413

The winner is Donald Trump with 24.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump474
Joe Biden531
Jo Jorgensen438
Howie Hawkins239
Tulsi Gabbard377
Dan Crenshaw175
Justin Amash334
Amy Klobuchar226
Bernie Sanders593
Andrew Yang518
Elizabeth Warren420
John Kasich171
Jeb Bush144
Rand Paul394
Ted Cruz307
Ballots Cast:1413

The winner is Bernie Sanders with 42.0% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump312
Joe Biden140
Jo Jorgensen171
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders276
Andrew Yang98
Elizabeth Warren73
John Kasich20
Jeb Bush10
Rand Paul59
Ted Cruz40

Jeb Bush eliminated in this round.

Round 2:

Donald Trump313
Joe Biden140
Jo Jorgensen171
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Amy Klobuchar20
Bernie Sanders277
Andrew Yang98
Elizabeth Warren73
John Kasich23
Rand Paul59
Ted Cruz44

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump313
Joe Biden148
Jo Jorgensen173
Howie Hawkins52
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Bernie Sanders280
Andrew Yang99
Elizabeth Warren76
John Kasich24
Rand Paul59
Ted Cruz44

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump314
Joe Biden149
Jo Jorgensen177
Howie Hawkins52
Tulsi Gabbard44
Justin Amash85
Bernie Sanders280
Andrew Yang100
Elizabeth Warren76
John Kasich26
Rand Paul61
Ted Cruz49

John Kasich eliminated in this round.

Round 5:

Donald Trump315
Joe Biden153
Jo Jorgensen177
Howie Hawkins52
Tulsi Gabbard48
Justin Amash87
Bernie Sanders282
Andrew Yang102
Elizabeth Warren79
Rand Paul66
Ted Cruz52

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump318
Joe Biden159
Jo Jorgensen187
Howie Hawkins55
Justin Amash96
Bernie Sanders289
Andrew Yang107
Elizabeth Warren81
Rand Paul69
Ted Cruz52

Ted Cruz eliminated in this round.

Round 7:

Donald Trump342
Joe Biden161
Jo Jorgensen190
Howie Hawkins56
Justin Amash97
Bernie Sanders291
Andrew Yang109
Elizabeth Warren81
Rand Paul86

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump345
Joe Biden167
Jo Jorgensen192
Justin Amash97
Bernie Sanders330
Andrew Yang112
Elizabeth Warren84
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump345
Joe Biden185
Jo Jorgensen199
Justin Amash98
Bernie Sanders374
Andrew Yang126
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump378
Joe Biden186
Jo Jorgensen215
Justin Amash123
Bernie Sanders375
Andrew Yang136

Justin Amash eliminated in this round.

Round 11:

Donald Trump387
Joe Biden190
Jo Jorgensen312
Bernie Sanders379
Andrew Yang145

Andrew Yang eliminated in this round.

Round 12:

Donald Trump398
Joe Biden219
Jo Jorgensen344
Bernie Sanders452

Joe Biden eliminated in this round.

Round 13:

Donald Trump416
Jo Jorgensen404
Bernie Sanders593

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump621
Bernie Sanders792

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 Trump0/14/0 646 to
767
469 to
944
620 to
793
524 to
889
580 to
833
495 to
918
624 to
789
621 to
792
552 to
861
657 to
756
611 to
802
609 to
804
476 to
937
570 to
843
Joe Biden6/8/0767 to
646
632 to
781
685 to
728
613 to
800
747 to
666
687 to
726
716 to
697
568 to
845
471 to
942
633 to
780
735 to
678
748 to
665
703 to
710
762 to
651
Jo Jorgensen13/1/0944 to
469
781 to
632
874 to
539
786 to
627
962 to
451
860 to
553
835 to
578
709 to
704
703 to
710
791 to
622
956 to
457
985 to
428
936 to
477
967 to
446
Howie Hawkins10/4/0793 to
620
728 to
685
539 to
874
614 to
799
803 to
610
733 to
680
772 to
641
613 to
800
566 to
847
762 to
651
800 to
613
815 to
598
760 to
653
807 to
606
Tulsi Gabbard13/1/0889 to
524
800 to
613
627 to
786
799 to
614
968 to
445
869 to
544
953 to
460
727 to
686
742 to
671
858 to
555
1012 to
401
1015 to
398
873 to
540
934 to
479
Dan Crenshaw6/8/0833 to
580
666 to
747
451 to
962
610 to
803
445 to
968
628 to
785
728 to
685
613 to
800
585 to
828
728 to
685
785 to
628
816 to
597
694 to
719
835 to
578
Justin Amash9/5/0918 to
495
726 to
687
553 to
860
680 to
733
544 to
869
785 to
628
786 to
627
670 to
743
664 to
749
764 to
649
945 to
468
975 to
438
921 to
492
967 to
446
Amy Klobuchar6/8/0789 to
624
697 to
716
578 to
835
641 to
772
460 to
953
685 to
728
627 to
786
624 to
789
515 to
898
752 to
661
878 to
535
883 to
530
790 to
623
838 to
575
Bernie Sanders11/3/0792 to
621
845 to
568
704 to
709
800 to
613
686 to
727
800 to
613
743 to
670
789 to
624
689 to
724
862 to
551
874 to
539
874 to
539
822 to
591
834 to
579
Andrew Yang13/1/0861 to
552
942 to
471
710 to
703
847 to
566
671 to
742
828 to
585
749 to
664
898 to
515
724 to
689
940 to
473
1026 to
387
1014 to
399
890 to
523
918 to
495
Elizabeth Warren6/8/0756 to
657
780 to
633
622 to
791
651 to
762
555 to
858
685 to
728
649 to
764
661 to
752
551 to
862
473 to
940
795 to
618
826 to
587
767 to
646
797 to
616
John Kasich4/10/0802 to
611
678 to
735
457 to
956
613 to
800
401 to
1012
628 to
785
468 to
945
535 to
878
539 to
874
387 to
1026
618 to
795
895 to
518
743 to
670
857 to
556
Jeb Bush2/12/0804 to
609
665 to
748
428 to
985
598 to
815
398 to
1015
597 to
816
438 to
975
530 to
883
539 to
874
399 to
1014
587 to
826
518 to
895
672 to
741
836 to
577
Rand Paul5/9/0937 to
476
710 to
703
477 to
936
653 to
760
540 to
873
719 to
694
492 to
921
623 to
790
591 to
822
523 to
890
646 to
767
670 to
743
741 to
672
996 to
417
Ted Cruz1/13/0843 to
570
651 to
762
446 to
967
606 to
807
479 to
934
578 to
835
446 to
967
575 to
838
579 to
834
495 to
918
616 to
797
556 to
857
577 to
836
417 to
996

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 Trump4745 3.4
Joe Biden4791 3.4
Jo Jorgensen5424 3.8
Howie Hawkins3752 2.7
Tulsi Gabbard4965 3.5
Dan Crenshaw3454 2.4
Justin Amash4756 3.4
Amy Klobuchar3777 2.7
Bernie Sanders6207 4.4
Andrew Yang5971 4.2
Elizabeth Warren4848 3.4
John Kasich3294 2.3
Jeb Bush3206 2.3
Rand Paul4895 3.5
Ted Cruz3965 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 Trump4745
Joe Biden4791
Jo Jorgensen5424
Howie Hawkins3752
Tulsi Gabbard4965
Dan Crenshaw3454
Justin Amash4756
Amy Klobuchar3777
Bernie Sanders6207
Andrew Yang5971
Elizabeth Warren4848
John Kasich3294
Jeb Bush3206
Rand Paul4895
Ted Cruz3965

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 Sanders926
Andrew Yang890

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 Trump5/9/0 573 to
677
440 to
745
591 to
553
480 to
666
508 to
420
467 to
655
587 to
596
565 to
721
509 to
770
610 to
631
574 to
500
561 to
486
409 to
583
461 to
359
Joe Biden10/4/0677 to
573
599 to
583
607 to
440
546 to
638
696 to
443
622 to
511
570 to
334
339 to
629
361 to
709
429 to
483
655 to
374
685 to
386
660 to
593
702 to
514
Jo Jorgensen11/3/0745 to
440
583 to
599
601 to
303
517 to
473
672 to
274
471 to
363
582 to
425
517 to
674
442 to
637
574 to
546
648 to
331
673 to
333
588 to
383
728 to
343
Howie Hawkins3/11/0553 to
591
440 to
607
303 to
601
296 to
623
454 to
418
355 to
519
393 to
447
269 to
688
259 to
721
378 to
492
439 to
424
468 to
459
420 to
584
514 to
534
Tulsi Gabbard11/3/0666 to
480
638 to
546
473 to
517
623 to
296
630 to
283
499 to
430
616 to
353
508 to
644
443 to
596
571 to
490
645 to
276
667 to
316
521 to
456
657 to
406
Dan Crenshaw0/14/0420 to
508
443 to
696
274 to
672
418 to
454
283 to
630
265 to
536
391 to
513
407 to
740
331 to
741
439 to
589
386 to
405
401 to
430
276 to
543
380 to
411
Justin Amash8/6/0655 to
467
511 to
622
363 to
471
519 to
355
430 to
499
536 to
265
472 to
450
466 to
679
391 to
649
488 to
561
521 to
320
568 to
335
489 to
379
623 to
366
Amy Klobuchar6/8/0596 to
587
334 to
570
425 to
582
447 to
393
353 to
616
513 to
391
450 to
472
289 to
694
227 to
732
312 to
509
474 to
325
518 to
378
482 to
572
563 to
513
Bernie Sanders14/0/0721 to
565
629 to
339
674 to
517
688 to
269
644 to
508
740 to
407
679 to
466
694 to
289
523 to
487
606 to
250
717 to
346
727 to
373
687 to
545
729 to
498
Andrew Yang13/1/0770 to
509
709 to
361
637 to
442
721 to
259
596 to
443
741 to
331
649 to
391
732 to
227
487 to
523
617 to
339
769 to
250
776 to
290
654 to
465
748 to
440
Elizabeth Warren9/4/1631 to
610
483 to
429
546 to
574
492 to
378
490 to
571
589 to
439
561 to
488
509 to
312
250 to
606
339 to
617
565 to
348
587 to
410
578 to
578
621 to
544
John Kasich2/12/0500 to
574
374 to
655
331 to
648
424 to
439
276 to
645
405 to
386
320 to
521
325 to
474
346 to
717
250 to
769
348 to
565
368 to
305
362 to
536
460 to
469
Jeb Bush1/13/0486 to
561
386 to
685
333 to
673
459 to
468
316 to
667
430 to
401
335 to
568
378 to
518
373 to
727
290 to
776
410 to
587
305 to
368
326 to
532
421 to
445
Rand Paul7/6/1583 to
409
593 to
660
383 to
588
584 to
420
456 to
521
543 to
276
379 to
489
572 to
482
545 to
687
465 to
654
578 to
578
536 to
362
532 to
326
549 to
262
Ted Cruz4/10/0359 to
461
514 to
702
343 to
728
534 to
514
406 to
657
411 to
380
366 to
623
513 to
563
498 to
729
440 to
748
544 to
621
469 to
460
445 to
421
262 to
549

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
0758235.77%
117038.03%
214877.02%
316837.94%
414957.05%
518358.66%
611655.50%
711455.40%
810224.82%
97923.74%
1012866.07%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump658566471567256666250202
Joe Biden46811081110122108107119744668
Jo Jorgensen38412110813310613960726467159
Howie Hawkins570142104115931306949513060
Tulsi Gabbard38494102136142179117107654542
Dan Crenshaw604130110130821256164463130
Justin Amash4851161001209513859516561123
Amy Klobuchar53211410414910914710076491716
Bernie Sanders43782827475755792101110228
Andrew Yang330929310911614711411011381108
Elizabeth Warren518109987492818778968892
John Kasich5831231161371211537648311114
Jeb Bush5551561361541231245945301516
Rand Paul46712610199801148393977578
Ted Cruz6071328872831036075786550

Number of bullet votes: 39 (2.76%).
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.