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 Trump219
Joe Biden228
Jo Jorgensen184
Howie Hawkins28
Tulsi Gabbard27
Dan Crenshaw12
Justin Amash50
Amy Klobuchar11
Bernie Sanders165
Andrew Yang47
Elizabeth Warren31
John Kasich13
Jeb Bush6
Rand Paul30
Ted Cruz17
TOTAL:1068

The winner is Joe Biden with 21.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump315
Joe Biden412
Jo Jorgensen398
Howie Hawkins183
Tulsi Gabbard317
Dan Crenshaw139
Justin Amash302
Amy Klobuchar186
Bernie Sanders459
Andrew Yang445
Elizabeth Warren346
John Kasich138
Jeb Bush103
Rand Paul342
Ted Cruz214
Ballots Cast:1068

The winner is Bernie Sanders with 43.0% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump194
Joe Biden85
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Amy Klobuchar14
Bernie Sanders210
Andrew Yang84
Elizabeth Warren65
John Kasich18
Jeb Bush6
Rand Paul42
Ted Cruz28

Jeb Bush eliminated in this round.

Round 2:

Donald Trump194
Joe Biden85
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash81
Amy Klobuchar14
Bernie Sanders211
Andrew Yang84
Elizabeth Warren65
John Kasich19
Rand Paul42
Ted Cruz31

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump194
Joe Biden92
Jo Jorgensen160
Howie Hawkins43
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash81
Bernie Sanders212
Andrew Yang85
Elizabeth Warren66
John Kasich20
Rand Paul42
Ted Cruz31

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump195
Joe Biden93
Jo Jorgensen164
Howie Hawkins43
Tulsi Gabbard29
Justin Amash81
Bernie Sanders212
Andrew Yang86
Elizabeth Warren66
John Kasich20
Rand Paul44
Ted Cruz35

John Kasich eliminated in this round.

Round 5:

Donald Trump196
Joe Biden97
Jo Jorgensen164
Howie Hawkins43
Tulsi Gabbard33
Justin Amash82
Bernie Sanders214
Andrew Yang88
Elizabeth Warren68
Rand Paul47
Ted Cruz36

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump198
Joe Biden101
Jo Jorgensen172
Howie Hawkins44
Justin Amash89
Bernie Sanders217
Andrew Yang92
Elizabeth Warren69
Rand Paul50
Ted Cruz36

Ted Cruz eliminated in this round.

Round 7:

Donald Trump213
Joe Biden103
Jo Jorgensen175
Howie Hawkins45
Justin Amash89
Bernie Sanders218
Andrew Yang92
Elizabeth Warren69
Rand Paul64

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump213
Joe Biden109
Jo Jorgensen177
Justin Amash89
Bernie Sanders250
Andrew Yang95
Elizabeth Warren71
Rand Paul64

Rand Paul eliminated in this round.

Round 9:

Donald Trump234
Joe Biden109
Jo Jorgensen192
Justin Amash111
Bernie Sanders251
Andrew Yang99
Elizabeth Warren72

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump234
Joe Biden126
Jo Jorgensen196
Justin Amash112
Bernie Sanders288
Andrew Yang112

Eliminated in this round:

Round 11:

Donald Trump247
Joe Biden156
Jo Jorgensen315
Bernie Sanders350

Joe Biden eliminated in this round.

Round 12:

Donald Trump254
Jo Jorgensen354
Bernie Sanders460

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen554
Bernie Sanders514

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 Trump0/14/0 465 to
603
285 to
783
431 to
637
344 to
724
388 to
680
310 to
758
429 to
639
444 to
624
371 to
697
460 to
608
417 to
651
414 to
654
295 to
773
384 to
684
Joe Biden6/8/0603 to
465
464 to
604
523 to
545
454 to
614
567 to
501
511 to
557
552 to
516
427 to
641
323 to
745
465 to
603
558 to
510
571 to
497
529 to
539
582 to
486
Jo Jorgensen13/1/0783 to
285
604 to
464
691 to
377
605 to
463
749 to
319
652 to
416
638 to
430
554 to
514
529 to
539
596 to
472
729 to
339
764 to
304
724 to
344
772 to
296
Howie Hawkins9/5/0637 to
431
545 to
523
377 to
691
429 to
639
597 to
471
514 to
554
556 to
512
458 to
610
384 to
684
553 to
515
574 to
494
602 to
466
543 to
525
616 to
452
Tulsi Gabbard13/1/0724 to
344
614 to
454
463 to
605
639 to
429
743 to
325
633 to
435
721 to
347
551 to
517
535 to
533
630 to
438
766 to
302
775 to
293
639 to
429
726 to
342
Dan Crenshaw4/10/0680 to
388
501 to
567
319 to
749
471 to
597
325 to
743
434 to
634
529 to
539
451 to
617
401 to
667
517 to
551
567 to
501
599 to
469
483 to
585
640 to
428
Justin Amash10/4/0758 to
310
557 to
511
416 to
652
554 to
514
435 to
633
634 to
434
590 to
478
516 to
552
486 to
582
559 to
509
706 to
362
748 to
320
691 to
377
765 to
303
Amy Klobuchar7/7/0639 to
429
516 to
552
430 to
638
512 to
556
347 to
721
539 to
529
478 to
590
469 to
599
347 to
721
539 to
529
652 to
416
659 to
409
569 to
499
644 to
424
Bernie Sanders11/3/0624 to
444
641 to
427
514 to
554
610 to
458
517 to
551
617 to
451
552 to
516
599 to
469
487 to
581
636 to
432
648 to
420
651 to
417
593 to
475
637 to
431
Andrew Yang13/1/0697 to
371
745 to
323
539 to
529
684 to
384
533 to
535
667 to
401
582 to
486
721 to
347
581 to
487
719 to
349
778 to
290
774 to
294
654 to
414
720 to
348
Elizabeth Warren7/7/0608 to
460
603 to
465
472 to
596
515 to
553
438 to
630
551 to
517
509 to
559
529 to
539
432 to
636
349 to
719
605 to
463
626 to
442
562 to
506
618 to
450
John Kasich4/10/0651 to
417
510 to
558
339 to
729
494 to
574
302 to
766
501 to
567
362 to
706
416 to
652
420 to
648
290 to
778
463 to
605
678 to
390
539 to
529
670 to
398
Jeb Bush2/12/0654 to
414
497 to
571
304 to
764
466 to
602
293 to
775
469 to
599
320 to
748
409 to
659
417 to
651
294 to
774
442 to
626
390 to
678
477 to
591
641 to
427
Rand Paul5/9/0773 to
295
539 to
529
344 to
724
525 to
543
429 to
639
585 to
483
377 to
691
499 to
569
475 to
593
414 to
654
506 to
562
529 to
539
591 to
477
795 to
273
Ted Cruz1/13/0684 to
384
486 to
582
296 to
772
452 to
616
342 to
726
428 to
640
303 to
765
424 to
644
431 to
637
348 to
720
450 to
618
398 to
670
427 to
641
273 to
795

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 Trump3168 3.0
Joe Biden3652 3.4
Jo Jorgensen4503 4.2
Howie Hawkins2793 2.6
Tulsi Gabbard3892 3.6
Dan Crenshaw2561 2.4
Justin Amash3862 3.6
Amy Klobuchar2846 2.7
Bernie Sanders4799 4.5
Andrew Yang4857 4.5
Elizabeth Warren3845 3.6
John Kasich2419 2.3
Jeb Bush2226 2.1
Rand Paul3818 3.6
Ted Cruz2792 2.6

And the winner is: Andrew Yang

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 Trump3168
Joe Biden3652
Jo Jorgensen4503
Howie Hawkins2793
Tulsi Gabbard3892
Dan Crenshaw2561
Justin Amash3862
Amy Klobuchar2846
Bernie Sanders4799
Andrew Yang4857
Elizabeth Warren3845
John Kasich2419
Jeb Bush2226
Rand Paul3818
Ted Cruz2792

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
Andrew Yang694
Bernie Sanders671

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 Trump1/13/0 397 to
537
265 to
632
406 to
441
313 to
552
330 to
331
289 to
551
400 to
473
400 to
568
334 to
636
418 to
510
391 to
400
385 to
389
248 to
487
304 to
284
Joe Biden9/5/0537 to
397
450 to
477
467 to
330
398 to
506
539 to
335
471 to
405
432 to
234
246 to
472
239 to
571
298 to
371
500 to
269
525 to
268
500 to
466
542 to
372
Jo Jorgensen12/2/0632 to
265
477 to
450
512 to
228
438 to
363
571 to
188
389 to
278
492 to
332
429 to
504
369 to
505
469 to
432
546 to
240
576 to
222
495 to
268
616 to
211
Howie Hawkins5/9/0441 to
406
330 to
467
228 to
512
220 to
514
358 to
323
269 to
431
309 to
355
205 to
521
185 to
585
282 to
398
340 to
329
371 to
336
326 to
464
403 to
379
Tulsi Gabbard11/3/0552 to
313
506 to
398
363 to
438
514 to
220
518 to
208
391 to
354
496 to
264
410 to
485
342 to
479
451 to
390
530 to
203
557 to
209
417 to
354
540 to
275
Dan Crenshaw2/12/0331 to
330
335 to
539
188 to
571
323 to
358
208 to
518
190 to
448
303 to
405
319 to
571
252 to
603
335 to
482
303 to
323
318 to
327
199 to
435
300 to
275
Justin Amash8/6/0551 to
289
405 to
471
278 to
389
431 to
269
354 to
391
448 to
190
387 to
353
380 to
518
322 to
518
391 to
452
429 to
234
476 to
232
404 to
280
514 to
230
Amy Klobuchar6/8/0473 to
400
234 to
432
332 to
492
355 to
309
264 to
496
405 to
303
353 to
387
219 to
527
161 to
601
229 to
414
372 to
241
418 to
269
380 to
464
447 to
365
Bernie Sanders13/1/0568 to
400
472 to
246
504 to
429
521 to
205
485 to
410
571 to
319
518 to
380
527 to
219
374 to
397
444 to
185
554 to
257
576 to
268
525 to
437
577 to
362
Andrew Yang14/0/0636 to
334
571 to
239
505 to
369
585 to
185
479 to
342
603 to
252
518 to
322
601 to
161
397 to
374
492 to
250
627 to
179
644 to
194
525 to
374
612 to
302
Elizabeth Warren10/4/0510 to
418
371 to
298
432 to
469
398 to
282
390 to
451
482 to
335
452 to
391
414 to
229
185 to
444
250 to
492
455 to
246
483 to
285
462 to
459
499 to
388
John Kasich4/10/0400 to
391
269 to
500
240 to
546
329 to
340
203 to
530
323 to
303
234 to
429
241 to
372
257 to
554
179 to
627
246 to
455
301 to
211
284 to
439
364 to
332
Jeb Bush3/11/0389 to
385
268 to
525
222 to
576
336 to
371
209 to
557
327 to
318
232 to
476
269 to
418
268 to
576
194 to
644
285 to
483
211 to
301
233 to
444
331 to
327
Rand Paul7/7/0487 to
248
466 to
500
268 to
495
464 to
326
354 to
417
435 to
199
280 to
404
464 to
380
437 to
525
374 to
525
459 to
462
439 to
284
444 to
233
457 to
150
Ted Cruz0/14/0284 to
304
372 to
542
211 to
616
379 to
403
275 to
540
275 to
300
230 to
514
365 to
447
362 to
577
302 to
612
388 to
499
332 to
364
327 to
331
150 to
457

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
0591836.94%
112607.87%
210506.55%
311707.30%
410616.62%
512537.82%
68735.45%
78835.51%
88205.12%
96454.03%
1010876.79%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump548484555374840423733135
Joe Biden36084607187847894643155
Jo Jorgensen270877694729344605565152
Howie Hawkins457101738072854739392451
Tulsi Gabbard281687510310212210292533337
Dan Crenshaw48098828060854749392325
Justin Amash366846981619043425559118
Amy Klobuchar4198073109851027159401614
Bernie Sanders340586051494642618087194
Andrew Yang2376464717710287949674102
Elizabeth Warren40574644361526559827984
John Kasich463848510194111553321813
Jeb Bush440129981199685382815911
Rand Paul35797646754747278806263
Ted Cruz495104624554744253644233

Number of bullet votes: 25 (2.34%).
Number of "approval" votes: 15 (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.