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 Trump341
Joe Biden292
Jo Jorgensen195
Howie Hawkins36
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders228
Andrew Yang56
Elizabeth Warren36
John Kasich15
Jeb Bush8
Rand Paul39
Ted Cruz27
TOTAL:1394

The winner is Donald Trump with 24.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump465
Joe Biden524
Jo Jorgensen438
Howie Hawkins239
Tulsi Gabbard377
Dan Crenshaw174
Justin Amash334
Amy Klobuchar225
Bernie Sanders587
Andrew Yang513
Elizabeth Warren420
John Kasich169
Jeb Bush141
Rand Paul393
Ted Cruz302
Ballots Cast:1394

The winner is Bernie Sanders with 42.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump303
Joe Biden134
Jo Jorgensen171
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders274
Andrew Yang98
Elizabeth Warren72
John Kasich20
Jeb Bush10
Rand Paul59
Ted Cruz39

Jeb Bush eliminated in this round.

Round 2:

Donald Trump304
Joe Biden134
Jo Jorgensen171
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Amy Klobuchar20
Bernie Sanders275
Andrew Yang98
Elizabeth Warren72
John Kasich23
Rand Paul59
Ted Cruz43

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump304
Joe Biden142
Jo Jorgensen173
Howie Hawkins52
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Bernie Sanders278
Andrew Yang99
Elizabeth Warren75
John Kasich24
Rand Paul59
Ted Cruz43

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump305
Joe Biden143
Jo Jorgensen177
Howie Hawkins52
Tulsi Gabbard44
Justin Amash85
Bernie Sanders278
Andrew Yang100
Elizabeth Warren75
John Kasich26
Rand Paul61
Ted Cruz48

John Kasich eliminated in this round.

Round 5:

Donald Trump306
Joe Biden147
Jo Jorgensen177
Howie Hawkins52
Tulsi Gabbard48
Justin Amash87
Bernie Sanders280
Andrew Yang102
Elizabeth Warren78
Rand Paul66
Ted Cruz51

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump309
Joe Biden153
Jo Jorgensen187
Howie Hawkins55
Justin Amash96
Bernie Sanders287
Andrew Yang107
Elizabeth Warren80
Rand Paul69
Ted Cruz51

Ted Cruz eliminated in this round.

Round 7:

Donald Trump333
Joe Biden155
Jo Jorgensen190
Howie Hawkins56
Justin Amash97
Bernie Sanders289
Andrew Yang108
Elizabeth Warren80
Rand Paul86

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump336
Joe Biden161
Jo Jorgensen192
Justin Amash97
Bernie Sanders328
Andrew Yang111
Elizabeth Warren83
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump336
Joe Biden179
Jo Jorgensen199
Justin Amash98
Bernie Sanders371
Andrew Yang125
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump369
Joe Biden180
Jo Jorgensen215
Justin Amash123
Bernie Sanders372
Andrew Yang135

Justin Amash eliminated in this round.

Round 11:

Donald Trump378
Joe Biden184
Jo Jorgensen312
Bernie Sanders376
Andrew Yang144

Andrew Yang eliminated in this round.

Round 12:

Donald Trump389
Joe Biden213
Jo Jorgensen344
Bernie Sanders448

Joe Biden eliminated in this round.

Round 13:

Donald Trump406
Jo Jorgensen403
Bernie Sanders585

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump611
Bernie Sanders783

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 Trump0/14/0 636 to
758
459 to
935
610 to
784
513 to
881
569 to
825
484 to
910
613 to
781
611 to
783
542 to
852
646 to
748
600 to
794
598 to
796
465 to
929
558 to
836
Joe Biden6/8/0758 to
636
624 to
770
677 to
717
605 to
789
739 to
655
679 to
715
708 to
686
558 to
836
463 to
931
623 to
771
727 to
667
740 to
654
695 to
699
754 to
640
Jo Jorgensen13/1/0935 to
459
770 to
624
865 to
529
775 to
619
953 to
441
850 to
544
825 to
569
701 to
693
694 to
700
781 to
613
946 to
448
976 to
418
928 to
466
959 to
435
Howie Hawkins10/4/0784 to
610
717 to
677
529 to
865
601 to
793
791 to
603
721 to
673
761 to
633
605 to
789
556 to
838
750 to
644
789 to
605
805 to
589
749 to
645
797 to
597
Tulsi Gabbard13/1/0881 to
513
789 to
605
619 to
775
793 to
601
961 to
433
858 to
536
944 to
450
718 to
676
733 to
661
846 to
548
1002 to
392
1007 to
387
863 to
531
925 to
469
Dan Crenshaw6/8/0825 to
569
655 to
739
441 to
953
603 to
791
433 to
961
615 to
779
716 to
678
605 to
789
575 to
819
716 to
678
772 to
622
805 to
589
683 to
711
826 to
568
Justin Amash9/5/0910 to
484
715 to
679
544 to
850
673 to
721
536 to
858
779 to
615
774 to
620
662 to
732
655 to
739
753 to
641
932 to
462
965 to
429
909 to
485
958 to
436
Amy Klobuchar6/8/0781 to
613
686 to
708
569 to
825
633 to
761
450 to
944
678 to
716
620 to
774
615 to
779
506 to
888
737 to
657
866 to
528
873 to
521
778 to
616
828 to
566
Bernie Sanders11/3/0783 to
611
836 to
558
693 to
701
789 to
605
676 to
718
789 to
605
732 to
662
779 to
615
677 to
717
852 to
542
863 to
531
865 to
529
809 to
585
825 to
569
Andrew Yang13/1/0852 to
542
931 to
463
700 to
694
838 to
556
661 to
733
819 to
575
739 to
655
888 to
506
717 to
677
926 to
468
1014 to
380
1003 to
391
878 to
516
910 to
484
Elizabeth Warren6/8/0748 to
646
771 to
623
613 to
781
644 to
750
548 to
846
678 to
716
641 to
753
657 to
737
542 to
852
468 to
926
785 to
609
816 to
578
756 to
638
788 to
606
John Kasich4/10/0794 to
600
667 to
727
448 to
946
605 to
789
392 to
1002
622 to
772
462 to
932
528 to
866
531 to
863
380 to
1014
609 to
785
886 to
508
732 to
662
848 to
546
Jeb Bush2/12/0796 to
598
654 to
740
418 to
976
589 to
805
387 to
1007
589 to
805
429 to
965
521 to
873
529 to
865
391 to
1003
578 to
816
508 to
886
657 to
737
826 to
568
Rand Paul5/9/0929 to
465
699 to
695
466 to
928
645 to
749
531 to
863
711 to
683
485 to
909
616 to
778
585 to
809
516 to
878
638 to
756
662 to
732
737 to
657
988 to
406
Ted Cruz1/13/0836 to
558
640 to
754
435 to
959
597 to
797
469 to
925
568 to
826
436 to
958
566 to
828
569 to
825
484 to
910
606 to
788
546 to
848
568 to
826
406 to
988

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 Trump4644 3.3
Joe Biden4733 3.4
Jo Jorgensen5392 3.9
Howie Hawkins3722 2.7
Tulsi Gabbard4922 3.5
Dan Crenshaw3409 2.4
Justin Amash4732 3.4
Amy Klobuchar3735 2.7
Bernie Sanders6144 4.4
Andrew Yang5926 4.3
Elizabeth Warren4797 3.4
John Kasich3255 2.3
Jeb Bush3152 2.3
Rand Paul4840 3.5
Ted Cruz3891 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 Trump4644
Joe Biden4733
Jo Jorgensen5392
Howie Hawkins3722
Tulsi Gabbard4922
Dan Crenshaw3409
Justin Amash4732
Amy Klobuchar3735
Bernie Sanders6144
Andrew Yang5926
Elizabeth Warren4797
John Kasich3255
Jeb Bush3152
Rand Paul4840
Ted Cruz3891

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 Sanders911
Andrew Yang880

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 Trump5/9/0 563 to
671
430 to
740
581 to
549
470 to
662
499 to
416
457 to
651
577 to
589
555 to
712
499 to
763
600 to
624
564 to
495
551 to
481
400 to
578
453 to
355
Joe Biden10/4/0671 to
563
591 to
578
599 to
434
538 to
632
688 to
437
614 to
508
562 to
328
334 to
623
354 to
702
422 to
477
647 to
368
678 to
378
652 to
586
695 to
505
Jo Jorgensen11/3/0740 to
430
578 to
591
598 to
302
515 to
470
669 to
271
467 to
363
581 to
419
514 to
664
441 to
631
573 to
538
646 to
328
673 to
326
587 to
377
727 to
332
Howie Hawkins3/11/0549 to
581
434 to
599
302 to
598
296 to
618
453 to
414
351 to
518
391 to
442
266 to
678
257 to
714
377 to
485
439 to
420
467 to
451
420 to
578
513 to
523
Tulsi Gabbard11/3/0662 to
470
632 to
538
470 to
515
618 to
296
629 to
280
493 to
429
612 to
348
504 to
634
439 to
589
569 to
483
641 to
274
665 to
309
519 to
451
656 to
395
Dan Crenshaw0/14/0416 to
499
437 to
688
271 to
669
414 to
453
280 to
629
259 to
535
388 to
507
403 to
730
328 to
734
437 to
582
383 to
402
398 to
423
274 to
539
379 to
402
Justin Amash8/6/0651 to
457
508 to
614
363 to
467
518 to
351
429 to
493
535 to
259
472 to
442
464 to
669
390 to
642
487 to
552
521 to
313
568 to
327
489 to
371
622 to
355
Amy Klobuchar6/8/0589 to
577
328 to
562
419 to
581
442 to
391
348 to
612
507 to
388
442 to
472
285 to
685
223 to
727
311 to
505
471 to
322
515 to
373
478 to
567
559 to
503
Bernie Sanders14/0/0712 to
555
623 to
334
664 to
514
678 to
266
634 to
504
730 to
403
669 to
464
685 to
285
514 to
483
600 to
246
708 to
342
719 to
367
677 to
540
722 to
490
Andrew Yang13/1/0763 to
499
702 to
354
631 to
441
714 to
257
589 to
439
734 to
328
642 to
390
727 to
223
483 to
514
612 to
333
764 to
247
770 to
285
648 to
459
744 to
431
Elizabeth Warren9/5/0624 to
600
477 to
422
538 to
573
485 to
377
483 to
569
582 to
437
552 to
487
505 to
311
246 to
600
333 to
612
559 to
345
582 to
405
572 to
575
616 to
535
John Kasich2/12/0495 to
564
368 to
647
328 to
646
420 to
439
274 to
641
402 to
383
313 to
521
322 to
471
342 to
708
247 to
764
345 to
559
366 to
299
359 to
532
458 to
459
Jeb Bush1/13/0481 to
551
378 to
678
326 to
673
451 to
467
309 to
665
423 to
398
327 to
568
373 to
515
367 to
719
285 to
770
405 to
582
299 to
366
320 to
530
418 to
436
Rand Paul8/6/0578 to
400
586 to
652
377 to
587
578 to
420
451 to
519
539 to
274
371 to
489
567 to
478
540 to
677
459 to
648
575 to
572
532 to
359
530 to
320
547 to
254
Ted Cruz4/10/0355 to
453
505 to
695
332 to
727
523 to
513
395 to
656
402 to
379
355 to
622
503 to
559
490 to
722
431 to
744
535 to
616
459 to
458
436 to
418
254 to
547

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
0746735.71%
116717.99%
214626.99%
316788.02%
414717.03%
518028.62%
611555.52%
711275.39%
810154.85%
97883.77%
1012746.09%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump652556471547255656249195
Joe Biden45910881110121107105118734666
Jo Jorgensen37511810613310513659726467159
Howie Hawkins562138102115901286949513060
Tulsi Gabbard37692100136141174117107644542
Dan Crenshaw596128108129811226163463129
Justin Amash475112991209313659516561123
Amy Klobuchar52511110114910814410074491716
Bernie Sanders43082817471735689100110228
Andrew Yang323909210711314511310911381108
Elizabeth Warren511108947491788776968792
John Kasich5751201151371181507647311114
Jeb Bush5481541331541231225843281516
Rand Paul46012310098801128192967577
Ted Cruz6001328671821035972776349

Number of bullet votes: 38 (2.73%).
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.