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 Trump260
Joe Biden246
Jo Jorgensen191
Howie Hawkins30
Tulsi Gabbard32
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders188
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush7
Rand Paul33
Ted Cruz20
TOTAL:1183

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump365
Joe Biden448
Jo Jorgensen416
Howie Hawkins200
Tulsi Gabbard338
Dan Crenshaw158
Justin Amash314
Amy Klobuchar197
Bernie Sanders505
Andrew Yang464
Elizabeth Warren368
John Kasich151
Jeb Bush118
Rand Paul360
Ted Cruz246
Ballots Cast:1183

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump230
Joe Biden102
Jo Jorgensen168
Howie Hawkins43
Tulsi Gabbard29
Dan Crenshaw20
Justin Amash81
Amy Klobuchar15
Bernie Sanders230
Andrew Yang90
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul49
Ted Cruz32

Jeb Bush eliminated in this round.

Round 2:

Donald Trump231
Joe Biden102
Jo Jorgensen168
Howie Hawkins43
Tulsi Gabbard29
Dan Crenshaw20
Justin Amash82
Amy Klobuchar15
Bernie Sanders231
Andrew Yang90
Elizabeth Warren68
John Kasich20
Rand Paul49
Ted Cruz35

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump231
Joe Biden109
Jo Jorgensen169
Howie Hawkins45
Tulsi Gabbard29
Dan Crenshaw20
Justin Amash82
Bernie Sanders233
Andrew Yang91
Elizabeth Warren69
John Kasich21
Rand Paul49
Ted Cruz35

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump232
Joe Biden110
Jo Jorgensen173
Howie Hawkins45
Tulsi Gabbard32
Justin Amash83
Bernie Sanders233
Andrew Yang92
Elizabeth Warren69
John Kasich23
Rand Paul51
Ted Cruz40

John Kasich eliminated in this round.

Round 5:

Donald Trump233
Joe Biden114
Jo Jorgensen173
Howie Hawkins45
Tulsi Gabbard36
Justin Amash85
Bernie Sanders235
Andrew Yang94
Elizabeth Warren71
Rand Paul55
Ted Cruz42

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump236
Joe Biden118
Jo Jorgensen181
Howie Hawkins46
Justin Amash93
Bernie Sanders239
Andrew Yang98
Elizabeth Warren72
Rand Paul58
Ted Cruz42

Ted Cruz eliminated in this round.

Round 7:

Donald Trump255
Joe Biden120
Jo Jorgensen184
Howie Hawkins47
Justin Amash94
Bernie Sanders241
Andrew Yang98
Elizabeth Warren72
Rand Paul72

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump256
Joe Biden126
Jo Jorgensen186
Justin Amash94
Bernie Sanders274
Andrew Yang101
Elizabeth Warren74
Rand Paul72

Rand Paul eliminated in this round.

Round 9:

Donald Trump281
Joe Biden127
Jo Jorgensen201
Justin Amash118
Bernie Sanders275
Andrew Yang105
Elizabeth Warren76

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump281
Joe Biden144
Jo Jorgensen206
Justin Amash119
Bernie Sanders314
Andrew Yang119

Eliminated in this round:

Round 11:

Donald Trump296
Joe Biden174
Jo Jorgensen330
Bernie Sanders383

Joe Biden eliminated in this round.

Round 12:

Donald Trump307
Jo Jorgensen375
Bernie Sanders501

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen607
Bernie Sanders576

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 Trump0/14/0 527 to
656
349 to
834
498 to
685
405 to
778
451 to
732
373 to
810
496 to
687
504 to
679
434 to
749
528 to
655
484 to
699
479 to
704
357 to
826
448 to
735
Joe Biden6/8/0656 to
527
515 to
668
578 to
605
504 to
679
623 to
560
566 to
617
606 to
577
468 to
715
366 to
817
518 to
665
613 to
570
625 to
558
584 to
599
639 to
544
Jo Jorgensen14/0/0834 to
349
668 to
515
757 to
426
666 to
517
820 to
363
723 to
460
711 to
472
607 to
576
594 to
589
668 to
515
810 to
373
836 to
347
801 to
382
837 to
346
Howie Hawkins9/5/0685 to
498
605 to
578
426 to
757
492 to
691
662 to
521
584 to
599
628 to
555
507 to
676
445 to
738
622 to
561
648 to
535
668 to
515
613 to
570
672 to
511
Tulsi Gabbard13/1/0778 to
405
679 to
504
517 to
666
691 to
492
814 to
369
709 to
474
801 to
382
608 to
575
605 to
578
704 to
479
849 to
334
854 to
329
721 to
462
792 to
391
Dan Crenshaw5/9/0732 to
451
560 to
623
363 to
820
521 to
662
369 to
814
503 to
680
598 to
585
510 to
673
472 to
711
590 to
593
650 to
533
676 to
507
563 to
620
708 to
475
Justin Amash10/4/0810 to
373
617 to
566
460 to
723
599 to
584
474 to
709
680 to
503
653 to
530
571 to
612
548 to
635
631 to
552
785 to
398
819 to
364
772 to
411
829 to
354
Amy Klobuchar6/8/0687 to
496
577 to
606
472 to
711
555 to
628
382 to
801
585 to
598
530 to
653
521 to
662
407 to
776
609 to
574
725 to
458
729 to
454
644 to
539
705 to
478
Bernie Sanders11/3/0679 to
504
715 to
468
576 to
607
676 to
507
575 to
608
673 to
510
612 to
571
662 to
521
551 to
632
709 to
474
721 to
462
721 to
462
667 to
516
699 to
484
Andrew Yang12/2/0749 to
434
817 to
366
589 to
594
738 to
445
578 to
605
711 to
472
635 to
548
776 to
407
632 to
551
793 to
390
861 to
322
850 to
333
734 to
449
780 to
403
Elizabeth Warren7/7/0655 to
528
665 to
518
515 to
668
561 to
622
479 to
704
593 to
590
552 to
631
574 to
609
474 to
709
390 to
793
665 to
518
688 to
495
632 to
551
675 to
508
John Kasich4/10/0699 to
484
570 to
613
373 to
810
535 to
648
334 to
849
533 to
650
398 to
785
458 to
725
462 to
721
322 to
861
518 to
665
745 to
438
608 to
575
730 to
453
Jeb Bush2/12/0704 to
479
558 to
625
347 to
836
515 to
668
329 to
854
507 to
676
364 to
819
454 to
729
462 to
721
333 to
850
495 to
688
438 to
745
543 to
640
703 to
480
Rand Paul5/9/0826 to
357
599 to
584
382 to
801
570 to
613
462 to
721
620 to
563
411 to
772
539 to
644
516 to
667
449 to
734
551 to
632
575 to
608
640 to
543
858 to
325
Ted Cruz1/13/0735 to
448
544 to
639
346 to
837
511 to
672
391 to
792
475 to
708
354 to
829
478 to
705
484 to
699
403 to
780
508 to
675
453 to
730
480 to
703
325 to
858

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 Trump3672 3.1
Joe Biden4004 3.4
Jo Jorgensen4836 4.1
Howie Hawkins3114 2.6
Tulsi Gabbard4260 3.6
Dan Crenshaw2884 2.4
Justin Amash4186 3.5
Amy Klobuchar3158 2.7
Bernie Sanders5281 4.5
Andrew Yang5224 4.4
Elizabeth Warren4167 3.5
John Kasich2703 2.3
Jeb Bush2563 2.2
Rand Paul4171 3.5
Ted Cruz3186 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 Trump3672
Joe Biden4004
Jo Jorgensen4836
Howie Hawkins3114
Tulsi Gabbard4260
Dan Crenshaw2884
Justin Amash4186
Amy Klobuchar3158
Bernie Sanders5281
Andrew Yang5224
Elizabeth Warren4167
John Kasich2703
Jeb Bush2563
Rand Paul4171
Ted Cruz3186

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 Sanders753
Andrew Yang758

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 Trump4/10/0 456 to
583
321 to
670
470 to
476
369 to
591
388 to
365
346 to
589
460 to
512
453 to
618
392 to
679
483 to
547
452 to
434
440 to
422
302 to
521
355 to
314
Joe Biden9/5/0583 to
456
496 to
520
509 to
370
439 to
557
585 to
377
513 to
445
469 to
271
271 to
530
275 to
620
339 to
410
549 to
305
572 to
313
548 to
511
590 to
424
Jo Jorgensen12/2/0670 to
321
520 to
496
546 to
254
467 to
400
604 to
219
419 to
307
526 to
361
461 to
563
397 to
548
507 to
467
591 to
269
614 to
263
532 to
303
658 to
255
Howie Hawkins5/9/0476 to
470
370 to
509
254 to
546
243 to
553
388 to
361
299 to
464
337 to
387
222 to
581
211 to
631
314 to
425
380 to
360
405 to
379
359 to
507
440 to
433
Tulsi Gabbard11/3/0591 to
369
557 to
439
400 to
467
553 to
243
560 to
236
431 to
379
538 to
292
446 to
539
373 to
516
493 to
416
577 to
224
597 to
243
455 to
385
579 to
319
Dan Crenshaw1/13/0365 to
388
377 to
585
219 to
604
361 to
388
236 to
560
221 to
481
335 to
439
352 to
630
285 to
646
378 to
513
342 to
345
352 to
360
232 to
470
332 to
319
Justin Amash8/6/0589 to
346
445 to
513
307 to
419
464 to
299
379 to
431
481 to
221
416 to
386
411 to
571
350 to
556
427 to
484
468 to
259
511 to
267
437 to
311
556 to
274
Amy Klobuchar6/8/0512 to
460
271 to
469
361 to
526
387 to
337
292 to
538
439 to
335
386 to
416
241 to
584
184 to
645
261 to
439
412 to
263
453 to
307
414 to
498
488 to
415
Bernie Sanders13/1/0618 to
453
530 to
271
563 to
461
581 to
222
539 to
446
630 to
352
571 to
411
584 to
241
425 to
430
498 to
204
611 to
287
624 to
304
576 to
473
627 to
410
Andrew Yang14/0/0679 to
392
620 to
275
548 to
397
631 to
211
516 to
373
646 to
285
556 to
350
645 to
184
430 to
425
536 to
276
675 to
201
686 to
226
569 to
402
654 to
351
Elizabeth Warren9/5/0547 to
483
410 to
339
467 to
507
425 to
314
416 to
493
513 to
378
484 to
427
439 to
261
204 to
498
276 to
536
487 to
279
511 to
331
494 to
501
537 to
446
John Kasich3/11/0434 to
452
305 to
549
269 to
591
360 to
380
224 to
577
345 to
342
259 to
468
263 to
412
287 to
611
201 to
675
279 to
487
321 to
243
307 to
474
399 to
379
Jeb Bush1/13/0422 to
440
313 to
572
263 to
614
379 to
405
243 to
597
360 to
352
267 to
511
307 to
453
304 to
624
226 to
686
331 to
511
243 to
321
262 to
472
362 to
366
Rand Paul8/6/0521 to
302
511 to
548
303 to
532
507 to
359
385 to
455
470 to
232
311 to
437
498 to
414
473 to
576
402 to
569
501 to
494
474 to
307
472 to
262
491 to
186
Ted Cruz1/13/0314 to
355
424 to
590
255 to
658
433 to
440
319 to
579
319 to
332
274 to
556
415 to
488
410 to
627
351 to
654
446 to
537
379 to
399
366 to
362
186 to
491

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
0646036.40%
114127.96%
212096.81%
313227.45%
412226.89%
514508.17%
69635.43%
79565.39%
89035.09%
96993.94%
1011496.48%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump585505065436042494638155
Joe Biden39892708599928696693957
Jo Jorgensen30599871068310950635867156
Howie Hawkins493117868879975446452652
Tulsi Gabbard314768411111814011198583538
Dan Crenshaw517111909570975354432726
Justin Amash4009482947410747456160119
Amy Klobuchar4598979126931197965431714
Bernie Sanders374656856555849698595209
Andrew Yang26970778293118949610378103
Elizabeth Warren44488735176627162868288
John Kasich50210198112102120613727914
Jeb Bush477137113128110964234221014
Rand Paul394107807264887583866767
Ted Cruz529116725163874959714937

Number of bullet votes: 30 (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.