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 Trump288
Joe Biden264
Jo Jorgensen192
Howie Hawkins34
Tulsi Gabbard35
Dan Crenshaw15
Justin Amash51
Amy Klobuchar16
Bernie Sanders210
Andrew Yang52
Elizabeth Warren34
John Kasich14
Jeb Bush8
Rand Paul34
Ted Cruz20
TOTAL:1267

The winner is Donald Trump with 22.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump400
Joe Biden480
Jo Jorgensen426
Howie Hawkins217
Tulsi Gabbard360
Dan Crenshaw165
Justin Amash320
Amy Klobuchar210
Bernie Sanders541
Andrew Yang486
Elizabeth Warren389
John Kasich160
Jeb Bush125
Rand Paul371
Ted Cruz262
Ballots Cast:1267

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump255
Joe Biden116
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash81
Amy Klobuchar19
Bernie Sanders252
Andrew Yang92
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul51
Ted Cruz34

Jeb Bush eliminated in this round.

Round 2:

Donald Trump256
Joe Biden116
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Amy Klobuchar19
Bernie Sanders253
Andrew Yang92
Elizabeth Warren68
John Kasich20
Rand Paul51
Ted Cruz37

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump256
Joe Biden124
Jo Jorgensen170
Howie Hawkins48
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Bernie Sanders256
Andrew Yang93
Elizabeth Warren70
John Kasich21
Rand Paul51
Ted Cruz37

John Kasich eliminated in this round.

Round 4:

Donald Trump257
Joe Biden128
Jo Jorgensen170
Howie Hawkins48
Tulsi Gabbard40
Dan Crenshaw23
Justin Amash84
Bernie Sanders258
Andrew Yang95
Elizabeth Warren72
Rand Paul54
Ted Cruz38

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump258
Joe Biden129
Jo Jorgensen174
Howie Hawkins48
Tulsi Gabbard46
Justin Amash85
Bernie Sanders258
Andrew Yang96
Elizabeth Warren72
Rand Paul57
Ted Cruz44

Ted Cruz eliminated in this round.

Round 6:

Donald Trump278
Joe Biden131
Jo Jorgensen177
Howie Hawkins49
Tulsi Gabbard48
Justin Amash86
Bernie Sanders260
Andrew Yang96
Elizabeth Warren72
Rand Paul70

Tulsi Gabbard eliminated in this round.

Round 7:

Donald Trump281
Joe Biden137
Jo Jorgensen186
Howie Hawkins52
Justin Amash95
Bernie Sanders266
Andrew Yang101
Elizabeth Warren74
Rand Paul75

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump284
Joe Biden143
Jo Jorgensen188
Justin Amash95
Bernie Sanders301
Andrew Yang104
Elizabeth Warren77
Rand Paul75

Rand Paul eliminated in this round.

Round 9:

Donald Trump310
Joe Biden144
Jo Jorgensen204
Justin Amash119
Bernie Sanders302
Andrew Yang109
Elizabeth Warren79

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump310
Joe Biden161
Jo Jorgensen210
Justin Amash120
Bernie Sanders342
Andrew Yang124

Justin Amash eliminated in this round.

Round 11:

Donald Trump318
Joe Biden165
Jo Jorgensen305
Bernie Sanders346
Andrew Yang133

Andrew Yang eliminated in this round.

Round 12:

Donald Trump326
Joe Biden194
Jo Jorgensen335
Bernie Sanders412

Joe Biden eliminated in this round.

Round 13:

Donald Trump342
Jo Jorgensen384
Bernie Sanders541

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen638
Bernie Sanders629

And the winner is: Jo Jorgensen

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 Trump0/14/0 564 to
703
390 to
877
535 to
732
445 to
822
497 to
770
416 to
851
540 to
727
540 to
727
475 to
792
569 to
698
529 to
738
524 to
743
400 to
867
491 to
776
Joe Biden6/8/0703 to
564
559 to
708
616 to
651
545 to
722
672 to
595
614 to
653
646 to
621
502 to
765
406 to
861
562 to
705
660 to
607
674 to
593
630 to
637
689 to
578
Jo Jorgensen13/1/0877 to
390
708 to
559
796 to
471
713 to
554
875 to
392
776 to
491
754 to
513
638 to
629
633 to
634
711 to
556
865 to
402
896 to
371
859 to
408
887 to
380
Howie Hawkins10/4/0732 to
535
651 to
616
471 to
796
536 to
731
717 to
550
643 to
624
686 to
581
541 to
726
491 to
776
676 to
591
712 to
555
734 to
533
678 to
589
728 to
539
Tulsi Gabbard13/1/0822 to
445
722 to
545
554 to
713
731 to
536
875 to
392
770 to
497
859 to
408
648 to
619
655 to
612
764 to
503
915 to
352
922 to
345
785 to
482
850 to
417
Dan Crenshaw6/8/0770 to
497
595 to
672
392 to
875
550 to
717
392 to
875
545 to
722
643 to
624
543 to
724
510 to
757
640 to
627
701 to
566
731 to
536
617 to
650
758 to
509
Justin Amash9/5/0851 to
416
653 to
614
491 to
776
624 to
643
497 to
770
722 to
545
698 to
569
602 to
665
586 to
681
676 to
591
846 to
421
882 to
385
834 to
433
881 to
386
Amy Klobuchar6/8/0727 to
540
621 to
646
513 to
754
581 to
686
408 to
859
624 to
643
569 to
698
553 to
714
445 to
822
659 to
608
784 to
483
794 to
473
703 to
564
758 to
509
Bernie Sanders11/3/0727 to
540
765 to
502
629 to
638
726 to
541
619 to
648
724 to
543
665 to
602
714 to
553
609 to
658
769 to
498
781 to
486
785 to
482
730 to
537
754 to
513
Andrew Yang13/1/0792 to
475
861 to
406
634 to
633
776 to
491
612 to
655
757 to
510
681 to
586
822 to
445
658 to
609
842 to
425
926 to
341
917 to
350
797 to
470
834 to
433
Elizabeth Warren6/8/0698 to
569
705 to
562
556 to
711
591 to
676
503 to
764
627 to
640
591 to
676
608 to
659
498 to
769
425 to
842
718 to
549
748 to
519
687 to
580
725 to
542
John Kasich4/10/0738 to
529
607 to
660
402 to
865
555 to
712
352 to
915
566 to
701
421 to
846
483 to
784
486 to
781
341 to
926
549 to
718
805 to
462
660 to
607
780 to
487
Jeb Bush2/12/0743 to
524
593 to
674
371 to
896
533 to
734
345 to
922
536 to
731
385 to
882
473 to
794
482 to
785
350 to
917
519 to
748
462 to
805
591 to
676
753 to
514
Rand Paul5/9/0867 to
400
637 to
630
408 to
859
589 to
678
482 to
785
650 to
617
433 to
834
564 to
703
537 to
730
470 to
797
580 to
687
607 to
660
676 to
591
910 to
357
Ted Cruz1/13/0776 to
491
578 to
689
380 to
887
539 to
728
417 to
850
509 to
758
386 to
881
509 to
758
513 to
754
433 to
834
542 to
725
487 to
780
514 to
753
357 to
910

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 Trump4022 3.2
Joe Biden4331 3.4
Jo Jorgensen5076 4.0
Howie Hawkins3403 2.7
Tulsi Gabbard4551 3.6
Dan Crenshaw3086 2.4
Justin Amash4424 3.5
Amy Klobuchar3419 2.7
Bernie Sanders5666 4.5
Andrew Yang5525 4.4
Elizabeth Warren4444 3.5
John Kasich2925 2.3
Jeb Bush2803 2.2
Rand Paul4434 3.5
Ted Cruz3457 2.7

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 Trump4022
Joe Biden4331
Jo Jorgensen5076
Howie Hawkins3403
Tulsi Gabbard4551
Dan Crenshaw3086
Justin Amash4424
Amy Klobuchar3419
Bernie Sanders5666
Andrew Yang5525
Elizabeth Warren4444
John Kasich2925
Jeb Bush2803
Rand Paul4434
Ted Cruz3457

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 Sanders822
Andrew Yang798

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 Trump4/10/0 492 to
623
361 to
702
508 to
510
406 to
623
431 to
387
389 to
615
502 to
547
487 to
661
431 to
718
526 to
583
492 to
459
480 to
449
340 to
545
391 to
331
Joe Biden9/5/0623 to
492
537 to
544
547 to
397
479 to
588
630 to
396
556 to
472
510 to
299
299 to
570
312 to
651
378 to
438
592 to
330
619 to
334
592 to
538
636 to
451
Jo Jorgensen12/2/0702 to
361
544 to
537
567 to
276
485 to
431
632 to
240
443 to
332
550 to
386
477 to
609
415 to
582
535 to
497
615 to
293
643 to
289
556 to
335
686 to
286
Howie Hawkins5/9/0510 to
508
397 to
547
276 to
567
269 to
581
418 to
380
323 to
489
361 to
408
238 to
625
234 to
665
339 to
450
410 to
383
437 to
407
389 to
534
474 to
466
Tulsi Gabbard11/3/0623 to
406
588 to
479
431 to
485
581 to
269
592 to
253
457 to
400
573 to
313
468 to
580
403 to
548
522 to
443
609 to
238
631 to
271
488 to
408
614 to
347
Dan Crenshaw0/13/1387 to
431
396 to
630
240 to
632
380 to
418
253 to
592
233 to
506
353 to
469
366 to
674
300 to
688
399 to
543
359 to
368
371 to
388
250 to
498
352 to
352
Justin Amash8/6/0615 to
389
472 to
556
332 to
443
489 to
323
400 to
457
506 to
233
442 to
408
430 to
613
370 to
590
455 to
510
494 to
281
536 to
294
463 to
335
585 to
305
Amy Klobuchar6/8/0547 to
502
299 to
510
386 to
550
408 to
361
313 to
573
469 to
353
408 to
442
259 to
627
203 to
679
280 to
467
440 to
288
482 to
334
442 to
525
518 to
447
Bernie Sanders14/0/0661 to
487
570 to
299
609 to
477
625 to
238
580 to
468
674 to
366
613 to
430
627 to
259
469 to
445
545 to
220
656 to
306
668 to
326
619 to
495
669 to
437
Andrew Yang13/1/0718 to
431
651 to
312
582 to
415
665 to
234
548 to
403
688 to
300
590 to
370
679 to
203
445 to
469
568 to
300
717 to
217
721 to
251
606 to
425
693 to
381
Elizabeth Warren10/4/0583 to
526
438 to
378
497 to
535
450 to
339
443 to
522
543 to
399
510 to
455
467 to
280
220 to
545
300 to
568
521 to
303
544 to
359
529 to
527
573 to
480
John Kasich3/11/0459 to
492
330 to
592
293 to
615
383 to
410
238 to
609
368 to
359
281 to
494
288 to
440
306 to
656
217 to
717
303 to
521
339 to
271
325 to
499
423 to
407
Jeb Bush1/13/0449 to
480
334 to
619
289 to
643
407 to
437
271 to
631
388 to
371
294 to
536
334 to
482
326 to
668
251 to
721
359 to
544
271 to
339
286 to
495
387 to
391
Rand Paul7/7/0545 to
340
538 to
592
335 to
556
534 to
389
408 to
488
498 to
250
335 to
463
525 to
442
495 to
619
425 to
606
527 to
529
499 to
325
495 to
286
516 to
212
Ted Cruz1/12/1331 to
391
451 to
636
286 to
686
466 to
474
347 to
614
352 to
352
305 to
585
447 to
518
437 to
669
381 to
693
480 to
573
407 to
423
391 to
387
212 to
516

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
0678535.70%
115197.99%
213337.01%
314787.78%
413457.08%
515908.37%
610485.51%
710385.46%
89474.98%
97333.86%
1011896.26%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump613535767496546565241168
Joe Biden41799749410610096109704161
Jo Jorgensen326109951179611953686067157
Howie Hawkins51112496101861056448492756
Tulsi Gabbard3348191123130152112104613940
Dan Crenshaw54612099109751075457442927
Justin Amash423100911068711654486260120
Amy Klobuchar47898891361021289168441716
Bernie Sanders3916974656064538391103214
Andrew Yang28476879110613110010110878105
Elizabeth Warren46198836481698167918488
John Kasich5301071071221091336543271014
Jeb Bush5011451241381151094835251215
Rand Paul416114918471987786907268
Ted Cruz554126756172945465735340

Number of bullet votes: 31 (2.45%).
Number of "approval" votes: 17 (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.