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 Hawkins32
Tulsi Gabbard34
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders192
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1197

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump371
Joe Biden452
Jo Jorgensen418
Howie Hawkins204
Tulsi Gabbard347
Dan Crenshaw161
Justin Amash316
Amy Klobuchar197
Bernie Sanders511
Andrew Yang469
Elizabeth Warren371
John Kasich154
Jeb Bush121
Rand Paul364
Ted Cruz247
Ballots Cast:1197

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump232
Joe Biden103
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard32
Dan Crenshaw22
Justin Amash81
Amy Klobuchar15
Bernie Sanders234
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 Gabbard32
Dan Crenshaw22
Justin Amash82
Amy Klobuchar15
Bernie Sanders235
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 Gabbard32
Dan Crenshaw22
Justin Amash82
Bernie Sanders237
Andrew Yang91
Elizabeth Warren69
John Kasich21
Rand Paul50
Ted Cruz35

John Kasich eliminated in this round.

Round 4:

Donald Trump234
Joe Biden114
Jo Jorgensen169
Howie Hawkins46
Tulsi Gabbard35
Dan Crenshaw23
Justin Amash84
Bernie Sanders239
Andrew Yang93
Elizabeth Warren71
Rand Paul53
Ted Cruz36

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump235
Joe Biden115
Jo Jorgensen173
Howie Hawkins46
Tulsi Gabbard41
Justin Amash85
Bernie Sanders239
Andrew Yang94
Elizabeth Warren71
Rand Paul56
Ted Cruz42

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump238
Joe Biden120
Jo Jorgensen182
Howie Hawkins49
Justin Amash93
Bernie Sanders244
Andrew Yang98
Elizabeth Warren72
Rand Paul59
Ted Cruz42

Ted Cruz eliminated in this round.

Round 7:

Donald Trump257
Joe Biden122
Jo Jorgensen185
Howie Hawkins50
Justin Amash94
Bernie Sanders246
Andrew Yang98
Elizabeth Warren72
Rand Paul73

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump260
Joe Biden128
Jo Jorgensen187
Justin Amash94
Bernie Sanders280
Andrew Yang101
Elizabeth Warren74
Rand Paul73

Rand Paul eliminated in this round.

Round 9:

Donald Trump286
Joe Biden129
Jo Jorgensen202
Justin Amash118
Bernie Sanders281
Andrew Yang105
Elizabeth Warren76

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump286
Joe Biden146
Jo Jorgensen207
Justin Amash119
Bernie Sanders320
Andrew Yang119

Eliminated in this round:

Round 11:

Donald Trump301
Joe Biden176
Jo Jorgensen331
Bernie Sanders389

Joe Biden eliminated in this round.

Round 12:

Donald Trump313
Jo Jorgensen376
Bernie Sanders508

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen613
Bernie Sanders584

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 Trump0/14/0 534 to
663
357 to
840
502 to
695
409 to
788
457 to
740
381 to
816
504 to
693
510 to
687
440 to
757
534 to
663
492 to
705
487 to
710
364 to
833
456 to
741
Joe Biden6/8/0663 to
534
520 to
677
583 to
614
506 to
691
628 to
569
573 to
624
611 to
586
473 to
724
372 to
825
523 to
674
618 to
579
631 to
566
590 to
607
647 to
550
Jo Jorgensen14/0/0840 to
357
677 to
520
762 to
435
669 to
528
825 to
372
730 to
467
716 to
481
613 to
584
599 to
598
673 to
524
818 to
379
845 to
352
810 to
387
845 to
352
Howie Hawkins9/5/0695 to
502
614 to
583
435 to
762
494 to
703
667 to
530
592 to
605
636 to
561
512 to
685
450 to
747
630 to
567
657 to
540
678 to
519
623 to
574
681 to
516
Tulsi Gabbard13/1/0788 to
409
691 to
506
528 to
669
703 to
494
825 to
372
722 to
475
813 to
384
618 to
579
617 to
580
717 to
480
862 to
335
866 to
331
734 to
463
805 to
392
Dan Crenshaw6/8/0740 to
457
569 to
628
372 to
825
530 to
667
372 to
825
511 to
686
606 to
591
518 to
679
479 to
718
599 to
598
657 to
540
684 to
513
571 to
626
717 to
480
Justin Amash10/4/0816 to
381
624 to
573
467 to
730
605 to
592
475 to
722
686 to
511
660 to
537
576 to
621
552 to
645
638 to
559
793 to
404
827 to
370
782 to
415
836 to
361
Amy Klobuchar6/8/0693 to
504
586 to
611
481 to
716
561 to
636
384 to
813
591 to
606
537 to
660
528 to
669
413 to
784
617 to
580
732 to
465
738 to
459
652 to
545
713 to
484
Bernie Sanders11/3/0687 to
510
724 to
473
584 to
613
685 to
512
579 to
618
679 to
518
621 to
576
669 to
528
560 to
637
720 to
477
729 to
468
730 to
467
677 to
520
709 to
488
Andrew Yang12/2/0757 to
440
825 to
372
598 to
599
747 to
450
580 to
617
718 to
479
645 to
552
784 to
413
637 to
560
802 to
395
870 to
327
859 to
338
746 to
451
790 to
407
Elizabeth Warren6/8/0663 to
534
674 to
523
524 to
673
567 to
630
480 to
717
598 to
599
559 to
638
580 to
617
477 to
720
395 to
802
672 to
525
697 to
500
641 to
556
684 to
513
John Kasich4/10/0705 to
492
579 to
618
379 to
818
540 to
657
335 to
862
540 to
657
404 to
793
465 to
732
468 to
729
327 to
870
525 to
672
756 to
441
617 to
580
738 to
459
Jeb Bush2/12/0710 to
487
566 to
631
352 to
845
519 to
678
331 to
866
513 to
684
370 to
827
459 to
738
467 to
730
338 to
859
500 to
697
441 to
756
550 to
647
712 to
485
Rand Paul5/9/0833 to
364
607 to
590
387 to
810
574 to
623
463 to
734
626 to
571
415 to
782
545 to
652
520 to
677
451 to
746
556 to
641
580 to
617
647 to
550
867 to
330
Ted Cruz1/13/0741 to
456
550 to
647
352 to
845
516 to
681
392 to
805
480 to
717
361 to
836
484 to
713
488 to
709
407 to
790
513 to
684
459 to
738
485 to
712
330 to
867

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 Trump3733 3.1
Joe Biden4055 3.4
Jo Jorgensen4877 4.1
Howie Hawkins3172 2.6
Tulsi Gabbard4349 3.6
Dan Crenshaw2941 2.5
Justin Amash4226 3.5
Amy Klobuchar3202 2.7
Bernie Sanders5347 4.5
Andrew Yang5286 4.4
Elizabeth Warren4221 3.5
John Kasich2758 2.3
Jeb Bush2617 2.2
Rand Paul4221 3.5
Ted Cruz3226 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 Trump3733
Joe Biden4055
Jo Jorgensen4877
Howie Hawkins3172
Tulsi Gabbard4349
Dan Crenshaw2941
Justin Amash4226
Amy Klobuchar3202
Bernie Sanders5347
Andrew Yang5286
Elizabeth Warren4221
John Kasich2758
Jeb Bush2617
Rand Paul4221
Ted Cruz3226

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 Sanders763
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 Trump4/10/0 462 to
589
328 to
675
475 to
484
373 to
599
393 to
371
354 to
592
467 to
518
459 to
625
397 to
687
490 to
553
459 to
440
447 to
427
309 to
525
365 to
315
Joe Biden9/5/0589 to
462
500 to
529
512 to
378
441 to
569
589 to
384
518 to
451
476 to
277
275 to
540
279 to
627
344 to
417
553 to
314
578 to
318
555 to
517
598 to
430
Jo Jorgensen12/2/0675 to
328
529 to
500
551 to
258
467 to
411
607 to
225
423 to
310
530 to
366
465 to
572
400 to
557
513 to
473
594 to
277
621 to
268
537 to
309
663 to
260
Howie Hawkins5/9/0484 to
475
378 to
512
258 to
551
246 to
563
393 to
366
304 to
470
343 to
391
226 to
589
215 to
638
322 to
430
385 to
366
412 to
384
366 to
511
448 to
437
Tulsi Gabbard11/3/0599 to
373
569 to
441
411 to
467
563 to
246
568 to
240
441 to
379
549 to
293
453 to
543
382 to
519
503 to
418
586 to
227
605 to
247
464 to
387
588 to
320
Dan Crenshaw1/13/0371 to
393
384 to
589
225 to
607
366 to
393
240 to
568
227 to
483
341 to
443
358 to
636
289 to
653
387 to
518
346 to
351
359 to
365
239 to
474
338 to
323
Justin Amash8/6/0592 to
354
451 to
518
310 to
423
470 to
304
379 to
441
483 to
227
421 to
390
415 to
579
353 to
564
432 to
490
470 to
267
514 to
274
443 to
316
560 to
280
Amy Klobuchar6/8/0518 to
467
277 to
476
366 to
530
391 to
343
293 to
549
443 to
341
390 to
421
246 to
591
188 to
654
266 to
446
414 to
272
457 to
315
419 to
503
494 to
420
Bernie Sanders13/1/0625 to
459
540 to
275
572 to
465
589 to
226
543 to
453
636 to
358
579 to
415
591 to
246
433 to
434
506 to
207
617 to
295
630 to
312
584 to
478
634 to
416
Andrew Yang14/0/0687 to
397
627 to
279
557 to
400
638 to
215
519 to
382
653 to
289
564 to
353
654 to
188
434 to
433
543 to
279
684 to
205
693 to
232
578 to
406
663 to
356
Elizabeth Warren9/5/0553 to
490
417 to
344
473 to
513
430 to
322
418 to
503
518 to
387
490 to
432
446 to
266
207 to
506
279 to
543
492 to
287
516 to
339
503 to
505
544 to
451
John Kasich3/11/0440 to
459
314 to
553
277 to
594
366 to
385
227 to
586
351 to
346
267 to
470
272 to
414
295 to
617
205 to
684
287 to
492
326 to
248
314 to
477
406 to
382
Jeb Bush1/12/1427 to
447
318 to
578
268 to
621
384 to
412
247 to
605
365 to
359
274 to
514
315 to
457
312 to
630
232 to
693
339 to
516
248 to
326
268 to
477
369 to
369
Rand Paul8/6/0525 to
309
517 to
555
309 to
537
511 to
366
387 to
464
474 to
239
316 to
443
503 to
419
478 to
584
406 to
578
505 to
503
477 to
314
477 to
268
497 to
190
Ted Cruz0/13/1315 to
365
430 to
598
260 to
663
437 to
448
320 to
588
323 to
338
280 to
560
420 to
494
416 to
634
356 to
663
451 to
544
382 to
406
369 to
369
190 to
497

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
0649936.20%
114307.96%
212326.86%
313477.50%
412416.91%
514668.16%
69835.47%
79735.42%
89175.11%
97133.97%
1011546.43%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump589505266436143504740156
Joe Biden399957286101948797693958
Jo Jorgensen308101881098510952635967156
Howie Hawkins494119889180975547472653
Tulsi Gabbard3167685111118140112102603839
Dan Crenshaw521112909771995354442927
Justin Amash4049584967610748466260119
Amy Klobuchar4619181128941218265431714
Bernie Sanders377666957556050698699209
Andrew Yang27171788296120949910578103
Elizabeth Warren44689755279627364878288
John Kasich50410299114103122643927914
Jeb Bush479138116130110984334241114
Rand Paul397107827566897683866967
Ted Cruz533118735364875161714937

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.