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 Trump249
Joe Biden238
Jo Jorgensen187
Howie Hawkins28
Tulsi Gabbard29
Dan Crenshaw14
Justin Amash51
Amy Klobuchar11
Bernie Sanders183
Andrew Yang50
Elizabeth Warren32
John Kasich14
Jeb Bush7
Rand Paul32
Ted Cruz18
TOTAL:1143

The winner is Donald Trump with 21.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump349
Joe Biden436
Jo Jorgensen406
Howie Hawkins194
Tulsi Gabbard330
Dan Crenshaw152
Justin Amash309
Amy Klobuchar194
Bernie Sanders490
Andrew Yang456
Elizabeth Warren360
John Kasich149
Jeb Bush112
Rand Paul353
Ted Cruz236
Ballots Cast:1143

The winner is Bernie Sanders with 42.9% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump220
Joe Biden96
Jo Jorgensen162
Howie Hawkins41
Tulsi Gabbard27
Dan Crenshaw19
Justin Amash81
Amy Klobuchar14
Bernie Sanders225
Andrew Yang90
Elizabeth Warren66
John Kasich18
Jeb Bush7
Rand Paul46
Ted Cruz31

Jeb Bush eliminated in this round.

Round 2:

Donald Trump220
Joe Biden96
Jo Jorgensen162
Howie Hawkins41
Tulsi Gabbard27
Dan Crenshaw19
Justin Amash82
Amy Klobuchar14
Bernie Sanders226
Andrew Yang90
Elizabeth Warren66
John Kasich20
Rand Paul46
Ted Cruz34

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump220
Joe Biden103
Jo Jorgensen163
Howie Hawkins43
Tulsi Gabbard27
Dan Crenshaw19
Justin Amash82
Bernie Sanders227
Andrew Yang91
Elizabeth Warren67
John Kasich21
Rand Paul46
Ted Cruz34

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump221
Joe Biden104
Jo Jorgensen167
Howie Hawkins43
Tulsi Gabbard30
Justin Amash83
Bernie Sanders227
Andrew Yang92
Elizabeth Warren67
John Kasich22
Rand Paul48
Ted Cruz39

John Kasich eliminated in this round.

Round 5:

Donald Trump222
Joe Biden108
Jo Jorgensen167
Howie Hawkins43
Tulsi Gabbard34
Justin Amash85
Bernie Sanders229
Andrew Yang94
Elizabeth Warren69
Rand Paul51
Ted Cruz41

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump224
Joe Biden112
Jo Jorgensen175
Howie Hawkins44
Justin Amash92
Bernie Sanders233
Andrew Yang98
Elizabeth Warren70
Rand Paul54
Ted Cruz41

Ted Cruz eliminated in this round.

Round 7:

Donald Trump242
Joe Biden114
Jo Jorgensen178
Howie Hawkins45
Justin Amash93
Bernie Sanders235
Andrew Yang98
Elizabeth Warren70
Rand Paul68

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump242
Joe Biden120
Jo Jorgensen180
Justin Amash93
Bernie Sanders267
Andrew Yang101
Elizabeth Warren72
Rand Paul68

Rand Paul eliminated in this round.

Round 9:

Donald Trump265
Joe Biden120
Jo Jorgensen195
Justin Amash116
Bernie Sanders268
Andrew Yang105
Elizabeth Warren74

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump265
Joe Biden137
Jo Jorgensen199
Justin Amash117
Bernie Sanders306
Andrew Yang119

Justin Amash eliminated in this round.

Round 11:

Donald Trump273
Joe Biden141
Jo Jorgensen292
Bernie Sanders310
Andrew Yang127

Andrew Yang eliminated in this round.

Round 12:

Donald Trump280
Joe Biden167
Jo Jorgensen321
Bernie Sanders375

Joe Biden eliminated in this round.

Round 13:

Donald Trump290
Jo Jorgensen364
Bernie Sanders489

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen584
Bernie Sanders559

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 Trump0/14/0 507 to
636
329 to
814
479 to
664
386 to
757
429 to
714
352 to
791
472 to
671
483 to
660
411 to
732
505 to
638
461 to
682
458 to
685
338 to
805
428 to
715
Joe Biden6/8/0636 to
507
497 to
646
559 to
584
488 to
655
605 to
538
546 to
597
587 to
556
453 to
690
349 to
794
501 to
642
594 to
549
607 to
536
567 to
576
622 to
521
Jo Jorgensen13/1/0814 to
329
646 to
497
731 to
412
641 to
502
793 to
350
693 to
450
682 to
461
584 to
559
566 to
577
639 to
504
777 to
366
808 to
335
772 to
371
812 to
331
Howie Hawkins9/5/0664 to
479
584 to
559
412 to
731
472 to
671
637 to
506
557 to
586
601 to
542
486 to
657
420 to
723
595 to
548
619 to
524
644 to
499
587 to
556
650 to
493
Tulsi Gabbard13/1/0757 to
386
655 to
488
502 to
641
671 to
472
790 to
353
682 to
461
773 to
370
587 to
556
579 to
564
678 to
465
819 to
324
827 to
316
692 to
451
768 to
375
Dan Crenshaw5/9/0714 to
429
538 to
605
350 to
793
506 to
637
353 to
790
479 to
664
573 to
570
490 to
653
445 to
698
565 to
578
617 to
526
648 to
495
533 to
610
685 to
458
Justin Amash10/4/0791 to
352
597 to
546
450 to
693
586 to
557
461 to
682
664 to
479
628 to
515
550 to
593
527 to
616
604 to
539
758 to
385
796 to
347
744 to
399
805 to
338
Amy Klobuchar6/8/0671 to
472
556 to
587
461 to
682
542 to
601
370 to
773
570 to
573
515 to
628
501 to
642
386 to
757
583 to
560
699 to
444
707 to
436
619 to
524
685 to
458
Bernie Sanders11/3/0660 to
483
690 to
453
559 to
584
657 to
486
556 to
587
653 to
490
593 to
550
642 to
501
528 to
615
684 to
459
696 to
447
698 to
445
644 to
499
678 to
465
Andrew Yang13/1/0732 to
411
794 to
349
577 to
566
723 to
420
564 to
579
698 to
445
616 to
527
757 to
386
615 to
528
766 to
377
831 to
312
825 to
318
705 to
438
760 to
383
Elizabeth Warren7/7/0638 to
505
642 to
501
504 to
639
548 to
595
465 to
678
578 to
565
539 to
604
560 to
583
459 to
684
377 to
766
643 to
500
669 to
474
608 to
535
655 to
488
John Kasich4/10/0682 to
461
549 to
594
366 to
777
524 to
619
324 to
819
526 to
617
385 to
758
444 to
699
447 to
696
312 to
831
500 to
643
725 to
418
586 to
557
709 to
434
Jeb Bush2/12/0685 to
458
536 to
607
335 to
808
499 to
644
316 to
827
495 to
648
347 to
796
436 to
707
445 to
698
318 to
825
474 to
669
418 to
725
520 to
623
680 to
463
Rand Paul5/9/0805 to
338
576 to
567
371 to
772
556 to
587
451 to
692
610 to
533
399 to
744
524 to
619
499 to
644
438 to
705
535 to
608
557 to
586
623 to
520
834 to
309
Ted Cruz1/13/0715 to
428
521 to
622
331 to
812
493 to
650
375 to
768
458 to
685
338 to
805
458 to
685
465 to
678
383 to
760
488 to
655
434 to
709
463 to
680
309 to
834

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 Trump3495 3.1
Joe Biden3889 3.4
Jo Jorgensen4709 4.1
Howie Hawkins2999 2.6
Tulsi Gabbard4131 3.6
Dan Crenshaw2776 2.4
Justin Amash4081 3.6
Amy Klobuchar3062 2.7
Bernie Sanders5147 4.5
Andrew Yang5113 4.5
Elizabeth Warren4068 3.6
John Kasich2619 2.3
Jeb Bush2459 2.2
Rand Paul4030 3.5
Ted Cruz3038 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 Trump3495
Joe Biden3889
Jo Jorgensen4709
Howie Hawkins2999
Tulsi Gabbard4131
Dan Crenshaw2776
Justin Amash4081
Amy Klobuchar3062
Bernie Sanders5147
Andrew Yang5113
Elizabeth Warren4068
John Kasich2619
Jeb Bush2459
Rand Paul4030
Ted Cruz3038

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 Sanders728
Andrew Yang736

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 Trump4/10/0 435 to
566
303 to
656
448 to
464
350 to
575
368 to
354
326 to
575
438 to
499
433 to
600
371 to
663
458 to
534
428 to
422
420 to
411
285 to
504
336 to
302
Joe Biden9/5/0566 to
435
480 to
504
494 to
355
425 to
537
569 to
362
497 to
429
453 to
258
262 to
513
263 to
603
325 to
396
531 to
292
554 to
299
532 to
493
575 to
403
Jo Jorgensen12/2/0656 to
303
504 to
480
531 to
246
455 to
385
592 to
208
405 to
298
512 to
353
445 to
545
386 to
532
490 to
457
573 to
260
598 to
248
520 to
287
644 to
238
Howie Hawkins5/9/0464 to
448
355 to
494
246 to
531
233 to
535
378 to
348
286 to
450
324 to
378
211 to
563
200 to
613
297 to
415
364 to
347
391 to
363
347 to
487
429 to
412
Tulsi Gabbard11/3/0575 to
350
537 to
425
385 to
455
535 to
233
542 to
224
411 to
369
520 to
281
428 to
522
360 to
501
475 to
406
557 to
217
579 to
229
442 to
370
564 to
300
Dan Crenshaw1/13/0354 to
368
362 to
569
208 to
592
348 to
378
224 to
542
208 to
468
322 to
426
339 to
609
272 to
631
362 to
503
327 to
338
339 to
347
222 to
452
323 to
301
Justin Amash8/6/0575 to
326
429 to
497
298 to
405
450 to
286
369 to
411
468 to
208
405 to
372
394 to
554
340 to
540
411 to
474
453 to
250
496 to
255
428 to
295
541 to
257
Amy Klobuchar6/8/0499 to
438
258 to
453
353 to
512
378 to
324
281 to
520
426 to
322
372 to
405
232 to
566
178 to
629
249 to
431
398 to
257
441 to
294
404 to
482
477 to
394
Bernie Sanders13/1/0600 to
433
513 to
262
545 to
445
563 to
211
522 to
428
609 to
339
554 to
394
566 to
232
407 to
415
481 to
194
592 to
274
608 to
289
563 to
455
614 to
389
Andrew Yang14/0/0663 to
371
603 to
263
532 to
386
613 to
200
501 to
360
631 to
272
540 to
340
629 to
178
415 to
407
518 to
267
657 to
193
670 to
215
556 to
389
641 to
331
Elizabeth Warren10/4/0534 to
458
396 to
325
457 to
490
415 to
297
406 to
475
503 to
362
474 to
411
431 to
249
194 to
481
267 to
518
476 to
269
503 to
312
486 to
481
526 to
422
John Kasich3/11/0422 to
428
292 to
531
260 to
573
347 to
364
217 to
557
338 to
327
250 to
453
257 to
398
274 to
592
193 to
657
269 to
476
314 to
229
303 to
455
389 to
358
Jeb Bush2/12/0411 to
420
299 to
554
248 to
598
363 to
391
229 to
579
347 to
339
255 to
496
294 to
441
289 to
608
215 to
670
312 to
503
229 to
314
253 to
455
351 to
348
Rand Paul7/7/0504 to
285
493 to
532
287 to
520
487 to
347
370 to
442
452 to
222
295 to
428
482 to
404
455 to
563
389 to
556
481 to
486
455 to
303
455 to
253
475 to
173
Ted Cruz0/14/0302 to
336
403 to
575
238 to
644
412 to
429
300 to
564
301 to
323
257 to
541
394 to
477
389 to
614
331 to
641
422 to
526
358 to
389
348 to
351
173 to
475

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
0628236.64%
113527.89%
211356.62%
312617.35%
411746.85%
513858.08%
69335.44%
79345.45%
88785.12%
96803.97%
1011316.60%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump573494861405641494238146
Joe Biden38190678395898396673557
Jo Jorgensen29594841008010348625766154
Howie Hawkins483108838378945143442551
Tulsi Gabbard306738010810813310996573538
Dan Crenshaw503106859268955052412526
Justin Amash3909272877210147446059119
Amy Klobuchar4448576120921137763421714
Bernie Sanders361626454525346688492207
Andrew Yang25867717889111919510278103
Elizabeth Warren43181685070596962858286
John Kasich4909490106101118603625914
Jeb Bush465135103124107934033191014
Rand Paul384103746961857480846366
Ted Cruz518113704661824755694636

Number of bullet votes: 29 (2.54%).
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.