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 Trump268
Joe Biden255
Jo Jorgensen192
Howie Hawkins32
Tulsi Gabbard35
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders198
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1217

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump378
Joe Biden462
Jo Jorgensen422
Howie Hawkins209
Tulsi Gabbard353
Dan Crenshaw162
Justin Amash319
Amy Klobuchar201
Bernie Sanders520
Andrew Yang474
Elizabeth Warren377
John Kasich155
Jeb Bush122
Rand Paul364
Ted Cruz250
Ballots Cast:1217

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump238
Joe Biden106
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard34
Dan Crenshaw22
Justin Amash81
Amy Klobuchar15
Bernie Sanders241
Andrew Yang91
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul50
Ted Cruz33

Jeb Bush eliminated in this round.

Round 2:

Donald Trump239
Joe Biden106
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard34
Dan Crenshaw22
Justin Amash82
Amy Klobuchar15
Bernie Sanders242
Andrew Yang91
Elizabeth Warren68
John Kasich20
Rand Paul50
Ted Cruz36

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump239
Joe Biden113
Jo Jorgensen169
Howie Hawkins46
Tulsi Gabbard34
Dan Crenshaw22
Justin Amash82
Bernie Sanders244
Andrew Yang92
Elizabeth Warren69
John Kasich21
Rand Paul50
Ted Cruz36

John Kasich eliminated in this round.

Round 4:

Donald Trump240
Joe Biden117
Jo Jorgensen169
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw23
Justin Amash84
Bernie Sanders246
Andrew Yang94
Elizabeth Warren71
Rand Paul53
Ted Cruz37

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump241
Joe Biden118
Jo Jorgensen173
Howie Hawkins46
Tulsi Gabbard43
Justin Amash85
Bernie Sanders246
Andrew Yang95
Elizabeth Warren71
Rand Paul56
Ted Cruz43

Eliminated in this round:

Round 6:

Donald Trump263
Joe Biden126
Jo Jorgensen185
Howie Hawkins50
Justin Amash95
Bernie Sanders253
Andrew Yang99
Elizabeth Warren72
Rand Paul74

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump266
Joe Biden132
Jo Jorgensen187
Justin Amash95
Bernie Sanders287
Andrew Yang102
Elizabeth Warren74
Rand Paul74

Eliminated in this round:

Round 8:

Donald Trump292
Joe Biden150
Jo Jorgensen207
Justin Amash120
Bernie Sanders327
Andrew Yang121

Justin Amash eliminated in this round.

Round 9:

Donald Trump300
Joe Biden154
Jo Jorgensen302
Bernie Sanders331
Andrew Yang130

Andrew Yang eliminated in this round.

Round 10:

Donald Trump308
Joe Biden181
Jo Jorgensen331
Bernie Sanders397

Joe Biden eliminated in this round.

Round 11:

Donald Trump321
Jo Jorgensen377
Bernie Sanders519

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen620
Bernie Sanders597

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 Trump0/14/0 541 to
676
365 to
852
509 to
708
420 to
797
468 to
749
390 to
827
514 to
703
518 to
699
449 to
768
544 to
673
502 to
715
497 to
720
373 to
844
464 to
753
Joe Biden6/8/0676 to
541
532 to
685
593 to
624
518 to
699
643 to
574
586 to
631
623 to
594
482 to
735
382 to
835
535 to
682
632 to
585
645 to
572
603 to
614
660 to
557
Jo Jorgensen13/1/0852 to
365
685 to
532
772 to
445
682 to
535
841 to
376
744 to
473
726 to
491
620 to
597
607 to
610
682 to
535
833 to
384
861 to
356
825 to
392
858 to
359
Howie Hawkins9/5/0708 to
509
624 to
593
445 to
772
508 to
709
683 to
534
607 to
610
651 to
566
521 to
696
460 to
757
642 to
575
674 to
543
696 to
521
640 to
577
696 to
521
Tulsi Gabbard13/1/0797 to
420
699 to
518
535 to
682
709 to
508
841 to
376
735 to
482
828 to
389
627 to
590
627 to
590
729 to
488
877 to
340
884 to
333
749 to
468
820 to
397
Dan Crenshaw6/8/0749 to
468
574 to
643
376 to
841
534 to
683
376 to
841
519 to
698
615 to
602
526 to
691
487 to
730
610 to
607
668 to
549
697 to
520
583 to
634
730 to
487
Justin Amash10/4/0827 to
390
631 to
586
473 to
744
610 to
607
482 to
735
698 to
519
672 to
545
585 to
632
560 to
657
649 to
568
810 to
407
844 to
373
798 to
419
851 to
366
Amy Klobuchar6/8/0703 to
514
594 to
623
491 to
726
566 to
651
389 to
828
602 to
615
545 to
672
535 to
682
422 to
795
627 to
590
747 to
470
756 to
461
669 to
548
728 to
489
Bernie Sanders11/3/0699 to
518
735 to
482
597 to
620
696 to
521
590 to
627
691 to
526
632 to
585
682 to
535
574 to
643
735 to
482
745 to
472
748 to
469
694 to
523
725 to
492
Andrew Yang13/1/0768 to
449
835 to
382
610 to
607
757 to
460
590 to
627
730 to
487
657 to
560
795 to
422
643 to
574
816 to
401
887 to
330
877 to
340
763 to
454
805 to
412
Elizabeth Warren6/8/0673 to
544
682 to
535
535 to
682
575 to
642
488 to
729
607 to
610
568 to
649
590 to
627
482 to
735
401 to
816
686 to
531
713 to
504
656 to
561
699 to
518
John Kasich4/10/0715 to
502
585 to
632
384 to
833
543 to
674
340 to
877
549 to
668
407 to
810
470 to
747
472 to
745
330 to
887
531 to
686
774 to
443
633 to
584
754 to
463
Jeb Bush2/12/0720 to
497
572 to
645
356 to
861
521 to
696
333 to
884
520 to
697
373 to
844
461 to
756
469 to
748
340 to
877
504 to
713
443 to
774
564 to
653
728 to
489
Rand Paul5/9/0844 to
373
614 to
603
392 to
825
577 to
640
468 to
749
634 to
583
419 to
798
548 to
669
523 to
694
454 to
763
561 to
656
584 to
633
653 to
564
882 to
335
Ted Cruz1/13/0753 to
464
557 to
660
359 to
858
521 to
696
397 to
820
487 to
730
366 to
851
489 to
728
492 to
725
412 to
805
518 to
699
463 to
754
489 to
728
335 to
882

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 Trump3805 3.1
Joe Biden4136 3.4
Jo Jorgensen4938 4.1
Howie Hawkins3252 2.7
Tulsi Gabbard4416 3.6
Dan Crenshaw2983 2.5
Justin Amash4290 3.5
Amy Klobuchar3256 2.7
Bernie Sanders5438 4.5
Andrew Yang5355 4.4
Elizabeth Warren4286 3.5
John Kasich2805 2.3
Jeb Bush2676 2.2
Rand Paul4264 3.5
Ted Cruz3291 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 Trump3805
Joe Biden4136
Jo Jorgensen4938
Howie Hawkins3252
Tulsi Gabbard4416
Dan Crenshaw2983
Justin Amash4290
Amy Klobuchar3256
Bernie Sanders5438
Andrew Yang5355
Elizabeth Warren4286
John Kasich2805
Jeb Bush2676
Rand Paul4264
Ted Cruz3291

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 Sanders778
Andrew Yang773

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 Trump4/10/0 468 to
601
336 to
683
482 to
493
380 to
609
403 to
377
363 to
601
476 to
527
466 to
637
404 to
699
499 to
563
466 to
447
454 to
435
317 to
530
371 to
321
Joe Biden9/5/0601 to
468
511 to
536
522 to
384
452 to
575
601 to
387
528 to
457
486 to
284
283 to
549
287 to
636
353 to
422
566 to
319
591 to
324
567 to
521
610 to
436
Jo Jorgensen12/2/0683 to
336
536 to
511
557 to
264
470 to
419
614 to
229
430 to
316
538 to
369
468 to
583
403 to
564
521 to
478
598 to
281
627 to
274
544 to
314
668 to
268
Howie Hawkins5/9/0493 to
482
384 to
522
264 to
557
254 to
570
401 to
369
310 to
475
351 to
393
230 to
599
220 to
647
329 to
432
394 to
371
422 to
390
376 to
515
458 to
445
Tulsi Gabbard11/3/0609 to
380
575 to
452
419 to
470
570 to
254
577 to
242
448 to
386
559 to
297
457 to
554
390 to
529
509 to
424
593 to
228
615 to
251
475 to
389
598 to
326
Dan Crenshaw1/13/0377 to
403
387 to
601
229 to
614
369 to
401
242 to
577
229 to
491
347 to
451
361 to
646
294 to
666
391 to
524
350 to
356
364 to
372
243 to
480
342 to
332
Justin Amash8/6/0601 to
363
457 to
528
316 to
430
475 to
310
386 to
448
491 to
229
429 to
392
420 to
589
357 to
573
440 to
494
480 to
272
522 to
279
452 to
319
567 to
286
Amy Klobuchar6/8/0527 to
476
284 to
486
369 to
538
393 to
351
297 to
559
451 to
347
392 to
429
249 to
603
189 to
663
270 to
453
419 to
279
462 to
323
426 to
510
501 to
429
Bernie Sanders14/0/0637 to
466
549 to
283
583 to
468
599 to
230
554 to
457
646 to
361
589 to
420
603 to
249
444 to
439
518 to
210
627 to
299
640 to
318
594 to
483
643 to
424
Andrew Yang13/1/0699 to
404
636 to
287
564 to
403
647 to
220
529 to
390
666 to
294
573 to
357
663 to
189
439 to
444
555 to
284
694 to
210
702 to
238
589 to
411
673 to
363
Elizabeth Warren10/4/0563 to
499
422 to
353
478 to
521
432 to
329
424 to
509
524 to
391
494 to
440
453 to
270
210 to
518
284 to
555
500 to
292
526 to
346
512 to
510
553 to
460
John Kasich3/11/0447 to
466
319 to
566
281 to
598
371 to
394
228 to
593
356 to
350
272 to
480
279 to
419
299 to
627
210 to
694
292 to
500
329 to
254
320 to
481
411 to
388
Jeb Bush2/12/0435 to
454
324 to
591
274 to
627
390 to
422
251 to
615
372 to
364
279 to
522
323 to
462
318 to
640
238 to
702
346 to
526
254 to
329
276 to
481
375 to
373
Rand Paul7/7/0530 to
317
521 to
567
314 to
544
515 to
376
389 to
475
480 to
243
319 to
452
510 to
426
483 to
594
411 to
589
510 to
512
481 to
320
481 to
276
501 to
196
Ted Cruz0/14/0321 to
371
436 to
610
268 to
668
445 to
458
326 to
598
332 to
342
286 to
567
429 to
501
424 to
643
363 to
673
460 to
553
388 to
411
373 to
375
196 to
501

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
0655535.91%
114688.04%
212736.97%
313967.65%
412777.00%
514878.15%
610025.49%
79915.43%
89225.05%
97193.94%
1011656.38%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump594535667446143524740160
Joe Biden4029772911039589100703959
Jo Jorgensen311104911128911052656067156
Howie Hawkins496120929581986047472655
Tulsi Gabbard3197888115119144112104603939
Dan Crenshaw5261159410371995455442927
Justin Amash40896861007910951476260119
Amy Klobuchar4649485130991228465431714
Bernie Sanders3806773595660517287102210
Andrew Yang2737481831011229610010678103
Elizabeth Warren44893775780637665888288
John Kasich5101051011171061246439271014
Jeb Bush4841401191331121014334241215
Rand Paul402111857869907684866967
Ted Cruz538121735668895162714939

Number of bullet votes: 30 (2.47%).
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.