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 Trump333
Joe Biden285
Jo Jorgensen194
Howie Hawkins35
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash52
Amy Klobuchar17
Bernie Sanders225
Andrew Yang55
Elizabeth Warren35
John Kasich15
Jeb Bush8
Rand Paul38
Ted Cruz25
TOTAL:1368

The winner is Donald Trump with 24.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump453
Joe Biden516
Jo Jorgensen435
Howie Hawkins232
Tulsi Gabbard373
Dan Crenshaw171
Justin Amash330
Amy Klobuchar220
Bernie Sanders576
Andrew Yang506
Elizabeth Warren412
John Kasich166
Jeb Bush138
Rand Paul385
Ted Cruz295
Ballots Cast:1368

The winner is Bernie Sanders with 42.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump296
Joe Biden131
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash82
Amy Klobuchar20
Bernie Sanders269
Andrew Yang96
Elizabeth Warren70
John Kasich20
Jeb Bush9
Rand Paul56
Ted Cruz38

Jeb Bush eliminated in this round.

Round 2:

Donald Trump297
Joe Biden131
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders270
Andrew Yang96
Elizabeth Warren70
John Kasich22
Rand Paul56
Ted Cruz42

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump297
Joe Biden139
Jo Jorgensen173
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Bernie Sanders273
Andrew Yang97
Elizabeth Warren73
John Kasich23
Rand Paul56
Ted Cruz42

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump298
Joe Biden140
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard44
Justin Amash84
Bernie Sanders273
Andrew Yang98
Elizabeth Warren73
John Kasich25
Rand Paul58
Ted Cruz47

John Kasich eliminated in this round.

Round 5:

Donald Trump299
Joe Biden144
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard48
Justin Amash86
Bernie Sanders275
Andrew Yang100
Elizabeth Warren75
Rand Paul63
Ted Cruz50

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump302
Joe Biden150
Jo Jorgensen187
Howie Hawkins54
Justin Amash95
Bernie Sanders282
Andrew Yang105
Elizabeth Warren77
Rand Paul66
Ted Cruz50

Ted Cruz eliminated in this round.

Round 7:

Donald Trump325
Joe Biden152
Jo Jorgensen190
Howie Hawkins55
Justin Amash96
Bernie Sanders284
Andrew Yang106
Elizabeth Warren77
Rand Paul83

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump328
Joe Biden158
Jo Jorgensen192
Justin Amash96
Bernie Sanders322
Andrew Yang109
Elizabeth Warren80
Rand Paul83

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump328
Joe Biden175
Jo Jorgensen199
Justin Amash97
Bernie Sanders364
Andrew Yang122
Rand Paul83

Rand Paul eliminated in this round.

Round 10:

Donald Trump359
Joe Biden176
Jo Jorgensen215
Justin Amash122
Bernie Sanders365
Andrew Yang131

Justin Amash eliminated in this round.

Round 11:

Donald Trump367
Joe Biden180
Jo Jorgensen312
Bernie Sanders369
Andrew Yang140

Andrew Yang eliminated in this round.

Round 12:

Donald Trump377
Joe Biden209
Jo Jorgensen343
Bernie Sanders439

Joe Biden eliminated in this round.

Round 13:

Donald Trump394
Jo Jorgensen399
Bernie Sanders575

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen685
Bernie Sanders683

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 Trump0/14/0 624 to
744
447 to
921
598 to
770
502 to
866
558 to
810
473 to
895
601 to
767
599 to
769
531 to
837
632 to
736
588 to
780
585 to
783
456 to
912
547 to
821
Joe Biden6/7/1744 to
624
612 to
756
666 to
702
595 to
773
726 to
642
667 to
701
699 to
669
545 to
823
453 to
915
613 to
755
714 to
654
727 to
641
684 to
684
741 to
627
Jo Jorgensen13/1/0921 to
447
756 to
612
850 to
518
760 to
608
935 to
433
835 to
533
810 to
558
685 to
683
678 to
690
765 to
603
929 to
439
958 to
410
912 to
456
942 to
426
Howie Hawkins10/4/0770 to
598
702 to
666
518 to
850
587 to
781
776 to
592
706 to
662
747 to
621
591 to
777
542 to
826
735 to
633
775 to
593
791 to
577
734 to
634
781 to
587
Tulsi Gabbard13/1/0866 to
502
773 to
595
608 to
760
781 to
587
946 to
422
840 to
528
929 to
439
704 to
664
717 to
651
829 to
539
985 to
383
990 to
378
850 to
518
909 to
459
Dan Crenshaw6/8/0810 to
558
642 to
726
433 to
935
592 to
776
422 to
946
600 to
768
702 to
666
590 to
778
560 to
808
700 to
668
758 to
610
789 to
579
669 to
699
808 to
560
Justin Amash9/5/0895 to
473
701 to
667
533 to
835
662 to
706
528 to
840
768 to
600
761 to
607
649 to
719
642 to
726
738 to
630
915 to
453
948 to
420
895 to
473
941 to
427
Amy Klobuchar6/8/0767 to
601
669 to
699
558 to
810
621 to
747
439 to
929
666 to
702
607 to
761
602 to
766
494 to
874
722 to
646
850 to
518
856 to
512
765 to
603
812 to
556
Bernie Sanders11/3/0769 to
599
823 to
545
683 to
685
777 to
591
664 to
704
778 to
590
719 to
649
766 to
602
663 to
705
836 to
532
848 to
520
850 to
518
795 to
573
810 to
558
Andrew Yang13/1/0837 to
531
915 to
453
690 to
678
826 to
542
651 to
717
808 to
560
726 to
642
874 to
494
705 to
663
911 to
457
996 to
372
984 to
384
863 to
505
894 to
474
Elizabeth Warren6/8/0736 to
632
755 to
613
603 to
765
633 to
735
539 to
829
668 to
700
630 to
738
646 to
722
532 to
836
457 to
911
770 to
598
802 to
566
742 to
626
774 to
594
John Kasich4/10/0780 to
588
654 to
714
439 to
929
593 to
775
383 to
985
610 to
758
453 to
915
518 to
850
520 to
848
372 to
996
598 to
770
867 to
501
718 to
650
832 to
536
Jeb Bush2/12/0783 to
585
641 to
727
410 to
958
577 to
791
378 to
990
579 to
789
420 to
948
512 to
856
518 to
850
384 to
984
566 to
802
501 to
867
646 to
722
811 to
557
Rand Paul4/9/1912 to
456
684 to
684
456 to
912
634 to
734
518 to
850
699 to
669
473 to
895
603 to
765
573 to
795
505 to
863
626 to
742
650 to
718
722 to
646
970 to
398
Ted Cruz1/13/0821 to
547
627 to
741
426 to
942
587 to
781
459 to
909
560 to
808
427 to
941
556 to
812
558 to
810
474 to
894
594 to
774
536 to
832
557 to
811
398 to
970

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 Trump4531 3.3
Joe Biden4649 3.4
Jo Jorgensen5317 3.9
Howie Hawkins3634 2.7
Tulsi Gabbard4828 3.5
Dan Crenshaw3341 2.4
Justin Amash4650 3.4
Amy Klobuchar3652 2.7
Bernie Sanders6030 4.4
Andrew Yang5823 4.3
Elizabeth Warren4709 3.4
John Kasich3179 2.3
Jeb Bush3086 2.3
Rand Paul4738 3.5
Ted Cruz3819 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 Trump4531
Joe Biden4649
Jo Jorgensen5317
Howie Hawkins3634
Tulsi Gabbard4828
Dan Crenshaw3341
Justin Amash4650
Amy Klobuchar3652
Bernie Sanders6030
Andrew Yang5823
Elizabeth Warren4709
John Kasich3179
Jeb Bush3086
Rand Paul4738
Ted Cruz3819

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 Sanders893
Andrew Yang863

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 Trump5/9/0 550 to
659
417 to
730
568 to
538
459 to
651
487 to
409
445 to
643
563 to
578
544 to
698
487 to
750
587 to
613
550 to
486
537 to
473
391 to
568
441 to
350
Joe Biden10/4/0659 to
550
581 to
568
592 to
422
530 to
619
678 to
428
604 to
497
554 to
321
329 to
612
347 to
689
416 to
467
637 to
358
668 to
367
643 to
572
683 to
496
Jo Jorgensen11/3/0730 to
417
568 to
581
592 to
295
510 to
461
661 to
266
463 to
356
576 to
411
507 to
654
435 to
620
565 to
530
639 to
322
664 to
321
582 to
366
717 to
326
Howie Hawkins3/11/0538 to
568
422 to
592
295 to
592
290 to
610
443 to
408
344 to
511
382 to
435
261 to
669
251 to
704
368 to
478
430 to
412
457 to
445
413 to
567
503 to
514
Tulsi Gabbard11/3/0651 to
459
619 to
530
461 to
510
610 to
290
618 to
275
484 to
423
603 to
342
496 to
624
431 to
581
559 to
476
632 to
269
656 to
306
513 to
441
645 to
388
Dan Crenshaw0/14/0409 to
487
428 to
678
266 to
661
408 to
443
275 to
618
257 to
528
382 to
498
397 to
718
322 to
723
430 to
573
378 to
394
391 to
418
271 to
527
372 to
395
Justin Amash8/6/0643 to
445
497 to
604
356 to
463
511 to
344
423 to
484
528 to
257
465 to
433
457 to
658
384 to
630
479 to
543
515 to
307
559 to
324
485 to
361
613 to
350
Amy Klobuchar6/8/0578 to
563
321 to
554
411 to
576
435 to
382
342 to
603
498 to
382
433 to
465
280 to
673
218 to
718
305 to
498
464 to
316
505 to
368
472 to
558
549 to
496
Bernie Sanders14/0/0698 to
544
612 to
329
654 to
507
669 to
261
624 to
496
718 to
397
658 to
457
673 to
280
505 to
475
589 to
243
696 to
336
708 to
360
667 to
530
709 to
483
Andrew Yang13/1/0750 to
487
689 to
347
620 to
435
704 to
251
581 to
431
723 to
322
630 to
384
718 to
218
475 to
505
603 to
327
752 to
241
758 to
280
639 to
451
730 to
425
Elizabeth Warren10/4/0613 to
587
467 to
416
530 to
565
478 to
368
476 to
559
573 to
430
543 to
479
498 to
305
243 to
589
327 to
603
550 to
337
573 to
397
565 to
563
606 to
527
John Kasich2/12/0486 to
550
358 to
637
322 to
639
412 to
430
269 to
632
394 to
378
307 to
515
316 to
464
336 to
696
241 to
752
337 to
550
357 to
295
353 to
522
449 to
452
Jeb Bush1/13/0473 to
537
367 to
668
321 to
664
445 to
457
306 to
656
418 to
391
324 to
559
368 to
505
360 to
708
280 to
758
397 to
573
295 to
357
316 to
518
411 to
429
Rand Paul7/7/0568 to
391
572 to
643
366 to
582
567 to
413
441 to
513
527 to
271
361 to
485
558 to
472
530 to
667
451 to
639
563 to
565
522 to
353
518 to
316
538 to
249
Ted Cruz4/10/0350 to
441
496 to
683
326 to
717
514 to
503
388 to
645
395 to
372
350 to
613
496 to
549
483 to
709
425 to
730
527 to
606
452 to
449
429 to
411
249 to
538

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
0735235.83%
116548.06%
214356.99%
316067.83%
414497.06%
517558.55%
611275.49%
711125.42%
810014.88%
97713.76%
1012586.13%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump643546369547153636046192
Joe Biden45210778106117105103118724565
Jo Jorgensen36711810212910413157706467159
Howie Hawkins554137101111881236749512859
Tulsi Gabbard3709199131140167115106644342
Dan Crenshaw587127107120811215862453129
Justin Amash466112981159113257516360123
Amy Klobuchar519111961441061419873471716
Bernie Sanders4228181716971558799108224
Andrew Yang318879210211114211010811280106
Elizabeth Warren503106927189768674948691
John Kasich5691191121291181457545311114
Jeb Bush5401521311471211205643281416
Rand Paul4531229993791088091957474
Ted Cruz5891308468811025772766148

Number of bullet votes: 36 (2.63%).
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.