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 Trump263
Joe Biden248
Jo Jorgensen191
Howie Hawkins31
Tulsi Gabbard33
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders191
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1194

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump370
Joe Biden452
Jo Jorgensen418
Howie Hawkins203
Tulsi Gabbard344
Dan Crenshaw160
Justin Amash315
Amy Klobuchar197
Bernie Sanders509
Andrew Yang467
Elizabeth Warren371
John Kasich153
Jeb Bush120
Rand Paul364
Ted Cruz247
Ballots Cast:1194

The winner is Bernie Sanders with 42.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump232
Joe Biden103
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard31
Dan Crenshaw21
Justin Amash81
Amy Klobuchar15
Bernie Sanders233
Andrew Yang90
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul50
Ted Cruz32

Jeb Bush eliminated in this round.

Round 2:

Donald Trump233
Joe Biden103
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard31
Dan Crenshaw21
Justin Amash82
Amy Klobuchar15
Bernie Sanders234
Andrew Yang90
Elizabeth Warren68
John Kasich20
Rand Paul50
Ted Cruz35

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump233
Joe Biden110
Jo Jorgensen169
Howie Hawkins46
Tulsi Gabbard31
Dan Crenshaw21
Justin Amash82
Bernie Sanders236
Andrew Yang91
Elizabeth Warren69
John Kasich21
Rand Paul50
Ted Cruz35

Eliminated in this round:

Round 4:

Donald Trump235
Joe Biden115
Jo Jorgensen173
Howie Hawkins46
Tulsi Gabbard39
Justin Amash85
Bernie Sanders238
Andrew Yang94
Elizabeth Warren71
Rand Paul56
Ted Cruz42

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump238
Joe Biden120
Jo Jorgensen182
Howie Hawkins48
Justin Amash93
Bernie Sanders242
Andrew Yang98
Elizabeth Warren72
Rand Paul59
Ted Cruz42

Ted Cruz eliminated in this round.

Round 6:

Donald Trump257
Joe Biden122
Jo Jorgensen185
Howie Hawkins49
Justin Amash94
Bernie Sanders244
Andrew Yang98
Elizabeth Warren72
Rand Paul73

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump260
Joe Biden128
Jo Jorgensen187
Justin Amash94
Bernie Sanders277
Andrew Yang101
Elizabeth Warren74
Rand Paul73

Rand Paul eliminated in this round.

Round 8:

Donald Trump286
Joe Biden129
Jo Jorgensen202
Justin Amash118
Bernie Sanders278
Andrew Yang105
Elizabeth Warren76

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump286
Joe Biden146
Jo Jorgensen207
Justin Amash119
Bernie Sanders317
Andrew Yang119

Eliminated in this round:

Round 10:

Donald Trump301
Joe Biden176
Jo Jorgensen331
Bernie Sanders386

Joe Biden eliminated in this round.

Round 11:

Donald Trump313
Jo Jorgensen376
Bernie Sanders505

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen613
Bernie Sanders581

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 Trump0/14/0 532 to
662
355 to
839
501 to
693
409 to
785
456 to
738
379 to
815
503 to
691
510 to
684
439 to
755
533 to
661
491 to
703
485 to
709
362 to
832
454 to
740
Joe Biden6/8/0662 to
532
518 to
676
583 to
611
506 to
688
628 to
566
572 to
622
611 to
583
473 to
721
371 to
823
523 to
671
618 to
576
630 to
564
589 to
605
645 to
549
Jo Jorgensen14/0/0839 to
355
676 to
518
761 to
433
669 to
525
824 to
370
729 to
465
715 to
479
613 to
581
598 to
596
673 to
521
817 to
377
844 to
350
809 to
385
844 to
350
Howie Hawkins9/5/0693 to
501
611 to
583
433 to
761
494 to
700
666 to
528
590 to
604
634 to
560
511 to
683
449 to
745
628 to
566
655 to
539
675 to
519
621 to
573
679 to
515
Tulsi Gabbard13/1/0785 to
409
688 to
506
525 to
669
700 to
494
823 to
371
719 to
475
810 to
384
616 to
578
614 to
580
714 to
480
859 to
335
863 to
331
731 to
463
802 to
392
Dan Crenshaw5/8/1738 to
456
566 to
628
370 to
824
528 to
666
371 to
823
509 to
685
603 to
591
517 to
677
478 to
716
597 to
597
655 to
539
682 to
512
569 to
625
715 to
479
Justin Amash10/4/0815 to
379
622 to
572
465 to
729
604 to
590
475 to
719
685 to
509
658 to
536
576 to
618
551 to
643
636 to
558
792 to
402
826 to
368
779 to
415
835 to
359
Amy Klobuchar6/8/0691 to
503
583 to
611
479 to
715
560 to
634
384 to
810
591 to
603
536 to
658
527 to
667
412 to
782
615 to
579
731 to
463
736 to
458
651 to
543
711 to
483
Bernie Sanders11/3/0684 to
510
721 to
473
581 to
613
683 to
511
578 to
616
677 to
517
618 to
576
667 to
527
557 to
637
717 to
477
727 to
467
727 to
467
674 to
520
706 to
488
Andrew Yang12/2/0755 to
439
823 to
371
596 to
598
745 to
449
580 to
614
716 to
478
643 to
551
782 to
412
637 to
557
801 to
393
868 to
326
857 to
337
743 to
451
788 to
406
Elizabeth Warren6/7/1661 to
533
671 to
523
521 to
673
566 to
628
480 to
714
597 to
597
558 to
636
579 to
615
477 to
717
393 to
801
671 to
523
695 to
499
639 to
555
682 to
512
John Kasich4/10/0703 to
491
576 to
618
377 to
817
539 to
655
335 to
859
539 to
655
402 to
792
463 to
731
467 to
727
326 to
868
523 to
671
754 to
440
615 to
579
736 to
458
Jeb Bush2/12/0709 to
485
564 to
630
350 to
844
519 to
675
331 to
863
512 to
682
368 to
826
458 to
736
467 to
727
337 to
857
499 to
695
440 to
754
548 to
646
710 to
484
Rand Paul5/9/0832 to
362
605 to
589
385 to
809
573 to
621
463 to
731
625 to
569
415 to
779
543 to
651
520 to
674
451 to
743
555 to
639
579 to
615
646 to
548
866 to
328
Ted Cruz1/13/0740 to
454
549 to
645
350 to
844
515 to
679
392 to
802
479 to
715
359 to
835
483 to
711
488 to
706
406 to
788
512 to
682
458 to
736
484 to
710
328 to
866

And the Condorcet winner is: Jo Jorgensen.

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 Trump3720 3.1
Joe Biden4046 3.4
Jo Jorgensen4871 4.1
Howie Hawkins3158 2.6
Tulsi Gabbard4326 3.6
Dan Crenshaw2926 2.5
Justin Amash4216 3.5
Amy Klobuchar3189 2.7
Bernie Sanders5324 4.5
Andrew Yang5274 4.4
Elizabeth Warren4205 3.5
John Kasich2744 2.3
Jeb Bush2607 2.2
Rand Paul4210 3.5
Ted Cruz3219 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 Trump3720
Joe Biden4046
Jo Jorgensen4871
Howie Hawkins3158
Tulsi Gabbard4326
Dan Crenshaw2926
Justin Amash4216
Amy Klobuchar3189
Bernie Sanders5324
Andrew Yang5274
Elizabeth Warren4205
John Kasich2744
Jeb Bush2607
Rand Paul4210
Ted Cruz3219

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 Sanders760
Andrew Yang764

And the winner is: Andrew Yang

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 Trump4/10/0 461 to
589
326 to
674
474 to
482
373 to
596
392 to
369
352 to
591
466 to
516
459 to
622
396 to
685
489 to
551
458 to
438
445 to
426
307 to
524
362 to
315
Joe Biden9/5/0589 to
461
499 to
527
512 to
375
441 to
566
589 to
381
517 to
449
476 to
274
275 to
537
278 to
625
344 to
415
553 to
311
577 to
317
554 to
516
596 to
429
Jo Jorgensen12/2/0674 to
326
527 to
499
551 to
257
467 to
408
607 to
224
423 to
309
530 to
364
465 to
569
400 to
555
512 to
471
594 to
275
619 to
267
536 to
307
662 to
259
Howie Hawkins5/9/0482 to
474
375 to
512
257 to
551
245 to
561
393 to
365
303 to
469
342 to
390
225 to
587
214 to
636
320 to
429
384 to
365
410 to
384
364 to
510
446 to
437
Tulsi Gabbard11/3/0596 to
373
566 to
441
408 to
467
561 to
245
566 to
239
438 to
379
547 to
293
452 to
542
380 to
519
501 to
418
584 to
226
603 to
246
461 to
387
585 to
320
Dan Crenshaw1/13/0369 to
392
381 to
589
224 to
607
365 to
393
239 to
566
226 to
482
340 to
442
357 to
634
288 to
651
385 to
517
345 to
350
356 to
365
237 to
473
336 to
323
Justin Amash8/6/0591 to
352
449 to
517
309 to
423
469 to
303
379 to
438
482 to
226
420 to
389
415 to
576
352 to
563
431 to
488
469 to
265
512 to
273
441 to
315
559 to
279
Amy Klobuchar6/8/0516 to
466
274 to
476
364 to
530
390 to
342
293 to
547
442 to
340
389 to
420
246 to
589
187 to
652
265 to
445
413 to
270
455 to
314
417 to
502
492 to
420
Bernie Sanders13/1/0622 to
459
537 to
275
569 to
465
587 to
225
542 to
452
634 to
357
576 to
415
589 to
246
430 to
434
504 to
207
615 to
294
628 to
311
581 to
478
631 to
416
Andrew Yang14/0/0685 to
396
625 to
278
555 to
400
636 to
214
519 to
380
651 to
288
563 to
352
652 to
187
434 to
430
542 to
277
682 to
204
691 to
231
577 to
405
661 to
355
Elizabeth Warren9/5/0551 to
489
415 to
344
471 to
512
429 to
320
418 to
501
517 to
385
488 to
431
445 to
265
207 to
504
277 to
542
491 to
285
515 to
338
501 to
505
542 to
450
John Kasich3/11/0438 to
458
311 to
553
275 to
594
365 to
384
226 to
584
350 to
345
265 to
469
270 to
413
294 to
615
204 to
682
285 to
491
324 to
247
312 to
476
403 to
382
Jeb Bush1/12/1426 to
445
317 to
577
267 to
619
384 to
410
246 to
603
365 to
356
273 to
512
314 to
455
311 to
628
231 to
691
338 to
515
247 to
324
267 to
476
368 to
368
Rand Paul8/6/0524 to
307
516 to
554
307 to
536
510 to
364
387 to
461
473 to
237
315 to
441
502 to
417
478 to
581
405 to
577
505 to
501
476 to
312
476 to
267
496 to
189
Ted Cruz0/13/1315 to
362
429 to
596
259 to
662
437 to
446
320 to
585
323 to
336
279 to
559
420 to
492
416 to
631
355 to
661
450 to
542
382 to
403
368 to
368
189 to
496

And the Condorcet winner is: Andrew Yang.

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
0649436.26%
114307.98%
212266.85%
313377.47%
412376.91%
514628.16%
69785.46%
79695.41%
89135.10%
97113.97%
1011536.44%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump589505166436042504740156
Joe Biden399957086101938797693958
Jo Jorgensen307101881078510952635967156
Howie Hawkins494119888980975547462653
Tulsi Gabbard3167685111118140111101603838
Dan Crenshaw521112909571995354442827
Justin Amash4039584957610748456260119
Amy Klobuchar4619181127931218165431714
Bernie Sanders377666957556049698598209
Andrew Yang27071788296119949810578103
Elizabeth Warren44689745279627264868288
John Kasich50410299113102122643827914
Jeb Bush478138115130110984334231114
Rand Paul397107817565887683866967
Ted Cruz532118735263875161714937

Number of bullet votes: 30 (2.51%).
Number of "approval" votes: 16 (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.