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 Biden300
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:1414

The winner is Donald Trump with 24.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump474
Joe Biden532
Jo Jorgensen438
Howie Hawkins239
Tulsi Gabbard377
Dan Crenshaw175
Justin Amash334
Amy Klobuchar227
Bernie Sanders594
Andrew Yang518
Elizabeth Warren420
John Kasich171
Jeb Bush144
Rand Paul394
Ted Cruz307
Ballots Cast:1414

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 Biden141
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 Biden141
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 Biden149
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 Biden150
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 Biden154
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 Biden160
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 Biden162
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 Biden168
Jo Jorgensen192
Justin Amash97
Bernie Sanders330
Andrew Yang112
Elizabeth Warren84
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump345
Joe Biden186
Jo Jorgensen199
Justin Amash98
Bernie Sanders374
Andrew Yang126
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump378
Joe Biden187
Jo Jorgensen215
Justin Amash123
Bernie Sanders375
Andrew Yang136

Justin Amash eliminated in this round.

Round 11:

Donald Trump387
Joe Biden191
Jo Jorgensen312
Bernie Sanders379
Andrew Yang145

Andrew Yang eliminated in this round.

Round 12:

Donald Trump398
Joe Biden220
Jo Jorgensen344
Bernie Sanders452

Joe Biden eliminated in this round.

Round 13:

Donald Trump416
Jo Jorgensen404
Bernie Sanders594

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump621
Bernie Sanders793

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
768
469 to
945
620 to
794
524 to
890
580 to
834
495 to
919
624 to
790
621 to
793
552 to
862
657 to
757
611 to
803
609 to
805
476 to
938
570 to
844
Joe Biden6/8/0768 to
646
633 to
781
686 to
728
614 to
800
748 to
666
688 to
726
717 to
697
569 to
845
472 to
942
634 to
780
736 to
678
749 to
665
704 to
710
763 to
651
Jo Jorgensen13/1/0945 to
469
781 to
633
874 to
540
787 to
627
962 to
452
860 to
554
835 to
579
709 to
705
704 to
710
791 to
623
957 to
457
985 to
429
937 to
477
968 to
446
Howie Hawkins10/4/0794 to
620
728 to
686
540 to
874
615 to
799
803 to
611
734 to
680
772 to
642
613 to
801
567 to
847
762 to
652
801 to
613
815 to
599
761 to
653
808 to
606
Tulsi Gabbard13/1/0890 to
524
800 to
614
627 to
787
799 to
615
968 to
446
869 to
545
953 to
461
727 to
687
742 to
672
858 to
556
1012 to
402
1015 to
399
873 to
541
934 to
480
Dan Crenshaw6/8/0834 to
580
666 to
748
452 to
962
611 to
803
446 to
968
629 to
785
728 to
686
613 to
801
586 to
828
728 to
686
786 to
628
816 to
598
695 to
719
836 to
578
Justin Amash9/5/0919 to
495
726 to
688
554 to
860
680 to
734
545 to
869
785 to
629
786 to
628
670 to
744
665 to
749
764 to
650
946 to
468
975 to
439
922 to
492
968 to
446
Amy Klobuchar6/8/0790 to
624
697 to
717
579 to
835
642 to
772
461 to
953
686 to
728
628 to
786
624 to
790
516 to
898
752 to
662
879 to
535
884 to
530
791 to
623
839 to
575
Bernie Sanders11/3/0793 to
621
845 to
569
705 to
709
801 to
613
687 to
727
801 to
613
744 to
670
790 to
624
690 to
724
863 to
551
875 to
539
875 to
539
823 to
591
835 to
579
Andrew Yang13/1/0862 to
552
942 to
472
710 to
704
847 to
567
672 to
742
828 to
586
749 to
665
898 to
516
724 to
690
940 to
474
1027 to
387
1014 to
400
891 to
523
919 to
495
Elizabeth Warren6/8/0757 to
657
780 to
634
623 to
791
652 to
762
556 to
858
686 to
728
650 to
764
662 to
752
551 to
863
474 to
940
796 to
618
827 to
587
768 to
646
798 to
616
John Kasich4/10/0803 to
611
678 to
736
457 to
957
613 to
801
402 to
1012
628 to
786
468 to
946
535 to
879
539 to
875
387 to
1027
618 to
796
895 to
519
744 to
670
858 to
556
Jeb Bush2/12/0805 to
609
665 to
749
429 to
985
599 to
815
399 to
1015
598 to
816
439 to
975
530 to
884
539 to
875
400 to
1014
587 to
827
519 to
895
673 to
741
837 to
577
Rand Paul5/9/0938 to
476
710 to
704
477 to
937
653 to
761
541 to
873
719 to
695
492 to
922
623 to
791
591 to
823
523 to
891
646 to
768
670 to
744
741 to
673
997 to
417
Ted Cruz1/13/0844 to
570
651 to
763
446 to
968
606 to
808
480 to
934
578 to
836
446 to
968
575 to
839
579 to
835
495 to
919
616 to
798
556 to
858
577 to
837
417 to
997

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 Biden4799 3.4
Jo Jorgensen5424 3.8
Howie Hawkins3752 2.7
Tulsi Gabbard4965 3.5
Dan Crenshaw3454 2.4
Justin Amash4756 3.4
Amy Klobuchar3784 2.7
Bernie Sanders6212 4.4
Andrew Yang5971 4.2
Elizabeth Warren4851 3.4
John Kasich3294 2.3
Jeb Bush3208 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 Biden4799
Jo Jorgensen5424
Howie Hawkins3752
Tulsi Gabbard4965
Dan Crenshaw3454
Justin Amash4756
Amy Klobuchar3784
Bernie Sanders6212
Andrew Yang5971
Elizabeth Warren4851
John Kasich3294
Jeb Bush3208
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 Sanders927
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
678
440 to
745
591 to
553
480 to
666
508 to
420
467 to
655
587 to
597
565 to
722
509 to
770
610 to
632
574 to
500
561 to
487
409 to
583
461 to
359
Joe Biden10/4/0678 to
573
600 to
583
608 to
440
547 to
638
697 to
443
623 to
511
571 to
334
340 to
629
362 to
709
430 to
483
656 to
374
686 to
386
661 to
593
703 to
514
Jo Jorgensen11/3/0745 to
440
583 to
600
601 to
303
517 to
473
672 to
274
471 to
363
582 to
426
517 to
675
442 to
637
574 to
547
648 to
331
673 to
334
588 to
383
728 to
343
Howie Hawkins3/11/0553 to
591
440 to
608
303 to
601
296 to
623
454 to
418
355 to
519
393 to
448
269 to
689
259 to
721
378 to
493
439 to
424
468 to
460
420 to
584
514 to
534
Tulsi Gabbard11/3/0666 to
480
638 to
547
473 to
517
623 to
296
630 to
283
499 to
430
616 to
354
508 to
645
443 to
596
571 to
491
645 to
276
667 to
317
521 to
456
657 to
406
Dan Crenshaw0/14/0420 to
508
443 to
697
274 to
672
418 to
454
283 to
630
265 to
536
391 to
514
407 to
741
331 to
741
439 to
590
386 to
405
401 to
431
276 to
543
380 to
411
Justin Amash8/6/0655 to
467
511 to
623
363 to
471
519 to
355
430 to
499
536 to
265
472 to
451
466 to
680
391 to
649
488 to
562
521 to
320
568 to
336
489 to
379
623 to
366
Amy Klobuchar6/8/0597 to
587
334 to
571
426 to
582
448 to
393
354 to
616
514 to
391
451 to
472
290 to
694
228 to
732
313 to
509
475 to
325
519 to
378
483 to
572
564 to
513
Bernie Sanders14/0/0722 to
565
629 to
340
675 to
517
689 to
269
645 to
508
741 to
407
680 to
466
694 to
290
524 to
487
607 to
250
718 to
346
728 to
373
688 to
545
730 to
498
Andrew Yang13/1/0770 to
509
709 to
362
637 to
442
721 to
259
596 to
443
741 to
331
649 to
391
732 to
228
487 to
524
617 to
340
769 to
250
776 to
291
654 to
465
748 to
440
Elizabeth Warren10/4/0632 to
610
483 to
430
547 to
574
493 to
378
491 to
571
590 to
439
562 to
488
509 to
313
250 to
607
340 to
617
566 to
348
588 to
410
579 to
578
622 to
544
John Kasich2/12/0500 to
574
374 to
656
331 to
648
424 to
439
276 to
645
405 to
386
320 to
521
325 to
475
346 to
718
250 to
769
348 to
566
368 to
306
362 to
536
460 to
469
Jeb Bush1/13/0487 to
561
386 to
686
334 to
673
460 to
468
317 to
667
431 to
401
336 to
568
378 to
519
373 to
728
291 to
776
410 to
588
306 to
368
327 to
532
422 to
445
Rand Paul7/7/0583 to
409
593 to
661
383 to
588
584 to
420
456 to
521
543 to
276
379 to
489
572 to
483
545 to
688
465 to
654
578 to
579
536 to
362
532 to
327
549 to
262
Ted Cruz4/10/0359 to
461
514 to
703
343 to
728
534 to
514
406 to
657
411 to
380
366 to
623
513 to
564
498 to
730
440 to
748
544 to
622
469 to
460
445 to
422
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
0759235.79%
117038.03%
214887.02%
316847.94%
414957.05%
518368.66%
611655.49%
711465.40%
810234.82%
97923.73%
1012866.06%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump659566471567256666250202
Joe Biden46811081110122108107119754668
Jo Jorgensen38512110813310613960726467159
Howie Hawkins571142104115931306949513060
Tulsi Gabbard38594102136142179117107654542
Dan Crenshaw605130110130821256164463130
Justin Amash4861161001209513859516561123
Amy Klobuchar53211410414910914710077491716
Bernie Sanders43782827475765792101110228
Andrew Yang331929310911614711411011381108
Elizabeth Warren518109987592818778968892
John Kasich5841231161371211537648311114
Jeb Bush5551561371541231245945301516
Rand Paul46812610199801148393977578
Ted Cruz6081328872831036075786550

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.