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 Biden261
Jo Jorgensen192
Howie Hawkins34
Tulsi Gabbard35
Dan Crenshaw15
Justin Amash51
Amy Klobuchar16
Bernie Sanders210
Andrew Yang52
Elizabeth Warren34
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1263

The winner is Donald Trump with 22.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump398
Joe Biden477
Jo Jorgensen425
Howie Hawkins217
Tulsi Gabbard360
Dan Crenshaw165
Justin Amash320
Amy Klobuchar210
Bernie Sanders539
Andrew Yang485
Elizabeth Warren388
John Kasich160
Jeb Bush125
Rand Paul370
Ted Cruz261
Ballots Cast:1263

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 Biden114
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash81
Amy Klobuchar18
Bernie Sanders252
Andrew Yang92
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul50
Ted Cruz34

Jeb Bush eliminated in this round.

Round 2:

Donald Trump256
Joe Biden114
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Amy Klobuchar18
Bernie Sanders253
Andrew Yang92
Elizabeth Warren68
John Kasich20
Rand Paul50
Ted Cruz37

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump256
Joe Biden122
Jo Jorgensen169
Howie Hawkins48
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Bernie Sanders256
Andrew Yang93
Elizabeth Warren70
John Kasich21
Rand Paul50
Ted Cruz37

John Kasich eliminated in this round.

Round 4:

Donald Trump257
Joe Biden126
Jo Jorgensen169
Howie Hawkins48
Tulsi Gabbard40
Dan Crenshaw23
Justin Amash84
Bernie Sanders258
Andrew Yang95
Elizabeth Warren72
Rand Paul53
Ted Cruz38

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump258
Joe Biden127
Jo Jorgensen173
Howie Hawkins48
Tulsi Gabbard46
Justin Amash85
Bernie Sanders258
Andrew Yang96
Elizabeth Warren72
Rand Paul56
Ted Cruz44

Ted Cruz eliminated in this round.

Round 6:

Donald Trump278
Joe Biden129
Jo Jorgensen176
Howie Hawkins49
Tulsi Gabbard48
Justin Amash86
Bernie Sanders260
Andrew Yang96
Elizabeth Warren72
Rand Paul69

Tulsi Gabbard eliminated in this round.

Round 7:

Donald Trump281
Joe Biden135
Jo Jorgensen185
Howie Hawkins52
Justin Amash95
Bernie Sanders266
Andrew Yang101
Elizabeth Warren74
Rand Paul74

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump284
Joe Biden141
Jo Jorgensen187
Justin Amash95
Bernie Sanders301
Andrew Yang104
Elizabeth Warren77
Rand Paul74

Rand Paul eliminated in this round.

Round 9:

Donald Trump310
Joe Biden142
Jo Jorgensen202
Justin Amash119
Bernie Sanders302
Andrew Yang109
Elizabeth Warren79

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump310
Joe Biden159
Jo Jorgensen208
Justin Amash120
Bernie Sanders342
Andrew Yang124

Justin Amash eliminated in this round.

Round 11:

Donald Trump318
Joe Biden163
Jo Jorgensen303
Bernie Sanders346
Andrew Yang133

Andrew Yang eliminated in this round.

Round 12:

Donald Trump326
Joe Biden192
Jo Jorgensen333
Bernie Sanders412

Joe Biden eliminated in this round.

Round 13:

Donald Trump342
Jo Jorgensen382
Bernie Sanders539

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen636
Bernie Sanders627

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 Trump0/14/0 563 to
700
389 to
874
532 to
731
443 to
820
494 to
769
414 to
849
538 to
725
539 to
724
473 to
790
567 to
696
527 to
736
521 to
742
399 to
864
489 to
774
Joe Biden6/8/0700 to
563
557 to
706
612 to
651
542 to
721
668 to
595
610 to
653
643 to
620
498 to
765
403 to
860
558 to
705
656 to
607
671 to
592
627 to
636
686 to
577
Jo Jorgensen13/1/0874 to
389
706 to
557
793 to
470
710 to
553
872 to
391
773 to
490
752 to
511
636 to
627
631 to
632
709 to
554
862 to
401
893 to
370
857 to
406
884 to
379
Howie Hawkins10/4/0731 to
532
651 to
612
470 to
793
536 to
727
715 to
548
641 to
622
683 to
580
541 to
722
491 to
772
674 to
589
710 to
553
731 to
532
676 to
587
726 to
537
Tulsi Gabbard13/1/0820 to
443
721 to
542
553 to
710
727 to
536
872 to
391
767 to
496
856 to
407
646 to
617
654 to
609
762 to
501
912 to
351
919 to
344
783 to
480
848 to
415
Dan Crenshaw6/8/0769 to
494
595 to
668
391 to
872
548 to
715
391 to
872
543 to
720
640 to
623
543 to
720
509 to
754
638 to
625
699 to
564
728 to
535
615 to
648
756 to
507
Justin Amash9/5/0849 to
414
653 to
610
490 to
773
622 to
641
496 to
767
720 to
543
695 to
568
601 to
662
585 to
678
675 to
588
843 to
420
879 to
384
831 to
432
878 to
385
Amy Klobuchar6/8/0725 to
538
620 to
643
511 to
752
580 to
683
407 to
856
623 to
640
568 to
695
552 to
711
444 to
819
657 to
606
781 to
482
791 to
472
701 to
562
755 to
508
Bernie Sanders11/3/0724 to
539
765 to
498
627 to
636
722 to
541
617 to
646
720 to
543
662 to
601
711 to
552
606 to
657
767 to
496
778 to
485
782 to
481
728 to
535
752 to
511
Andrew Yang13/1/0790 to
473
860 to
403
632 to
631
772 to
491
609 to
654
754 to
509
678 to
585
819 to
444
657 to
606
840 to
423
923 to
340
914 to
349
795 to
468
832 to
431
Elizabeth Warren6/8/0696 to
567
705 to
558
554 to
709
589 to
674
501 to
762
625 to
638
588 to
675
606 to
657
496 to
767
423 to
840
715 to
548
745 to
518
684 to
579
722 to
541
John Kasich4/10/0736 to
527
607 to
656
401 to
862
553 to
710
351 to
912
564 to
699
420 to
843
482 to
781
485 to
778
340 to
923
548 to
715
802 to
461
659 to
604
778 to
485
Jeb Bush2/12/0742 to
521
592 to
671
370 to
893
532 to
731
344 to
919
535 to
728
384 to
879
472 to
791
481 to
782
349 to
914
518 to
745
461 to
802
590 to
673
751 to
512
Rand Paul5/9/0864 to
399
636 to
627
406 to
857
587 to
676
480 to
783
648 to
615
432 to
831
562 to
701
535 to
728
468 to
795
579 to
684
604 to
659
673 to
590
907 to
356
Ted Cruz1/13/0774 to
489
577 to
686
379 to
884
537 to
726
415 to
848
507 to
756
385 to
878
508 to
755
511 to
752
431 to
832
541 to
722
485 to
778
512 to
751
356 to
907

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 Trump4007 3.2
Joe Biden4308 3.4
Jo Jorgensen5056 4.0
Howie Hawkins3389 2.7
Tulsi Gabbard4539 3.6
Dan Crenshaw3072 2.4
Justin Amash4411 3.5
Amy Klobuchar3404 2.7
Bernie Sanders5648 4.5
Andrew Yang5511 4.4
Elizabeth Warren4427 3.5
John Kasich2915 2.3
Jeb Bush2788 2.2
Rand Paul4416 3.5
Ted Cruz3436 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 Trump4007
Joe Biden4308
Jo Jorgensen5056
Howie Hawkins3389
Tulsi Gabbard4539
Dan Crenshaw3072
Justin Amash4411
Amy Klobuchar3404
Bernie Sanders5648
Andrew Yang5511
Elizabeth Warren4427
John Kasich2915
Jeb Bush2788
Rand Paul4416
Ted Cruz3436

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 Sanders819
Andrew Yang796

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 Trump4/10/0 491 to
620
360 to
699
506 to
509
404 to
622
429 to
386
387 to
614
500 to
545
486 to
659
429 to
717
524 to
581
490 to
458
478 to
447
339 to
543
391 to
329
Joe Biden9/5/0620 to
491
535 to
543
544 to
397
476 to
588
627 to
396
553 to
472
507 to
299
296 to
570
309 to
650
375 to
438
589 to
330
616 to
333
589 to
537
633 to
450
Jo Jorgensen12/2/0699 to
360
543 to
535
565 to
275
482 to
430
629 to
239
440 to
331
547 to
385
475 to
607
412 to
581
532 to
496
612 to
292
640 to
288
554 to
333
684 to
284
Howie Hawkins5/9/0509 to
506
397 to
544
275 to
565
268 to
581
417 to
379
322 to
489
360 to
407
238 to
622
233 to
663
338 to
448
409 to
383
435 to
405
387 to
533
474 to
463
Tulsi Gabbard11/3/0622 to
404
588 to
476
430 to
482
581 to
268
592 to
251
457 to
399
573 to
311
468 to
577
402 to
546
522 to
440
608 to
238
630 to
268
486 to
407
614 to
344
Dan Crenshaw1/13/0386 to
429
396 to
627
239 to
629
379 to
417
251 to
592
232 to
506
352 to
468
366 to
671
299 to
686
399 to
541
357 to
368
370 to
386
248 to
497
351 to
349
Justin Amash8/6/0614 to
387
472 to
553
331 to
440
489 to
322
399 to
457
506 to
232
442 to
407
430 to
610
369 to
588
455 to
508
493 to
281
535 to
292
461 to
334
585 to
302
Amy Klobuchar6/8/0545 to
500
299 to
507
385 to
547
407 to
360
311 to
573
468 to
352
407 to
442
258 to
625
201 to
677
280 to
466
438 to
288
480 to
333
439 to
524
518 to
445
Bernie Sanders14/0/0659 to
486
570 to
296
607 to
475
622 to
238
577 to
468
671 to
366
610 to
430
625 to
258
467 to
444
544 to
219
653 to
306
666 to
325
616 to
494
668 to
435
Andrew Yang13/1/0717 to
429
650 to
309
581 to
412
663 to
233
546 to
402
686 to
299
588 to
369
677 to
201
444 to
467
567 to
298
714 to
217
720 to
248
605 to
424
692 to
378
Elizabeth Warren9/4/1581 to
524
438 to
375
496 to
532
448 to
338
440 to
522
541 to
399
508 to
455
466 to
280
219 to
544
298 to
567
518 to
303
542 to
358
526 to
526
572 to
478
John Kasich3/11/0458 to
490
330 to
589
292 to
612
383 to
409
238 to
608
368 to
357
281 to
493
288 to
438
306 to
653
217 to
714
303 to
518
338 to
268
324 to
497
423 to
404
Jeb Bush1/12/1447 to
478
333 to
616
288 to
640
405 to
435
268 to
630
386 to
370
292 to
535
333 to
480
325 to
666
248 to
720
358 to
542
268 to
338
284 to
494
387 to
387
Rand Paul7/6/1543 to
339
537 to
589
333 to
554
533 to
387
407 to
486
497 to
248
334 to
461
524 to
439
494 to
616
424 to
605
526 to
526
497 to
324
494 to
284
515 to
209
Ted Cruz0/13/1329 to
391
450 to
633
284 to
684
463 to
474
344 to
614
349 to
351
302 to
585
445 to
518
435 to
668
378 to
692
478 to
572
404 to
423
387 to
387
209 to
515

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
0677535.76%
115188.01%
213307.02%
314747.78%
413287.01%
515818.35%
610405.49%
710325.45%
89464.99%
97323.86%
1011896.28%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump612535767476546555241168
Joe Biden41699749410610096107704061
Jo Jorgensen326109941179611852676067157
Howie Hawkins51012496101841056348492756
Tulsi Gabbard3338191123127152112104613940
Dan Crenshaw54512099109741055457442927
Justin Amash422100911068511554486260120
Amy Klobuchar47798891361011279068441716
Bernie Sanders3906974656063528291103214
Andrew Yang2847587901051319910110878105
Elizabeth Warren46098836481687967918488
John Kasich5291071061221071336543271014
Jeb Bush5011451231371151074835251215
Rand Paul416114918270987786897268
Ted Cruz554126756170945364735340

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.