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 Trump211
Joe Biden227
Jo Jorgensen183
Howie Hawkins26
Tulsi Gabbard27
Dan Crenshaw12
Justin Amash49
Amy Klobuchar11
Bernie Sanders161
Andrew Yang45
Elizabeth Warren31
John Kasich13
Jeb Bush6
Rand Paul30
Ted Cruz16
TOTAL:1048

The winner is Joe Biden with 21.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump305
Joe Biden409
Jo Jorgensen393
Howie Hawkins176
Tulsi Gabbard314
Dan Crenshaw136
Justin Amash298
Amy Klobuchar183
Bernie Sanders452
Andrew Yang440
Elizabeth Warren344
John Kasich135
Jeb Bush101
Rand Paul337
Ted Cruz208
Ballots Cast:1048

The winner is Bernie Sanders with 43.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump186
Joe Biden85
Jo Jorgensen158
Howie Hawkins39
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash79
Amy Klobuchar14
Bernie Sanders206
Andrew Yang81
Elizabeth Warren65
John Kasich18
Jeb Bush6
Rand Paul42
Ted Cruz27

Jeb Bush eliminated in this round.

Round 2:

Donald Trump186
Joe Biden85
Jo Jorgensen158
Howie Hawkins39
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Amy Klobuchar14
Bernie Sanders207
Andrew Yang81
Elizabeth Warren65
John Kasich19
Rand Paul42
Ted Cruz30

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump186
Joe Biden92
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Bernie Sanders208
Andrew Yang82
Elizabeth Warren66
John Kasich20
Rand Paul42
Ted Cruz30

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump187
Joe Biden93
Jo Jorgensen163
Howie Hawkins41
Tulsi Gabbard29
Justin Amash80
Bernie Sanders208
Andrew Yang83
Elizabeth Warren66
John Kasich20
Rand Paul44
Ted Cruz34

John Kasich eliminated in this round.

Round 5:

Donald Trump188
Joe Biden97
Jo Jorgensen163
Howie Hawkins41
Tulsi Gabbard33
Justin Amash81
Bernie Sanders210
Andrew Yang85
Elizabeth Warren68
Rand Paul47
Ted Cruz35

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump190
Joe Biden101
Jo Jorgensen171
Howie Hawkins42
Justin Amash88
Bernie Sanders213
Andrew Yang89
Elizabeth Warren69
Rand Paul50
Ted Cruz35

Ted Cruz eliminated in this round.

Round 7:

Donald Trump204
Joe Biden103
Jo Jorgensen174
Howie Hawkins43
Justin Amash88
Bernie Sanders214
Andrew Yang89
Elizabeth Warren69
Rand Paul64

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump204
Joe Biden109
Jo Jorgensen176
Justin Amash88
Bernie Sanders244
Andrew Yang92
Elizabeth Warren71
Rand Paul64

Rand Paul eliminated in this round.

Round 9:

Donald Trump225
Joe Biden109
Jo Jorgensen191
Justin Amash110
Bernie Sanders245
Andrew Yang96
Elizabeth Warren72

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump225
Joe Biden126
Jo Jorgensen195
Justin Amash111
Bernie Sanders282
Andrew Yang109

Andrew Yang eliminated in this round.

Round 11:

Donald Trump229
Joe Biden147
Jo Jorgensen211
Justin Amash125
Bernie Sanders336

Justin Amash eliminated in this round.

Round 12:

Donald Trump238
Joe Biden155
Jo Jorgensen312
Bernie Sanders343

Joe Biden eliminated in this round.

Round 13:

Donald Trump245
Jo Jorgensen350
Bernie Sanders453

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen543
Bernie Sanders505

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 Trump0/14/0 452 to
596
276 to
772
420 to
628
332 to
716
376 to
672
299 to
749
418 to
630
432 to
616
360 to
688
447 to
601
406 to
642
403 to
645
282 to
766
373 to
675
Joe Biden6/8/0596 to
452
457 to
591
518 to
530
447 to
601
558 to
490
504 to
544
545 to
503
423 to
625
321 to
727
458 to
590
550 to
498
563 to
485
522 to
526
573 to
475
Jo Jorgensen13/1/0772 to
276
591 to
457
679 to
369
592 to
456
736 to
312
638 to
410
625 to
423
543 to
505
520 to
528
583 to
465
715 to
333
751 to
297
712 to
336
760 to
288
Howie Hawkins9/5/0628 to
420
530 to
518
369 to
679
418 to
630
585 to
463
504 to
544
541 to
507
448 to
600
375 to
673
538 to
510
561 to
487
589 to
459
535 to
513
607 to
441
Tulsi Gabbard12/1/1716 to
332
601 to
447
456 to
592
630 to
418
728 to
320
620 to
428
705 to
343
541 to
507
524 to
524
618 to
430
752 to
296
762 to
286
626 to
422
715 to
333
Dan Crenshaw4/10/0672 to
376
490 to
558
312 to
736
463 to
585
320 to
728
425 to
623
515 to
533
443 to
605
393 to
655
506 to
542
556 to
492
587 to
461
475 to
573
629 to
419
Justin Amash10/4/0749 to
299
544 to
504
410 to
638
544 to
504
428 to
620
623 to
425
576 to
472
506 to
542
478 to
570
546 to
502
693 to
355
735 to
313
680 to
368
754 to
294
Amy Klobuchar6/7/1630 to
418
503 to
545
423 to
625
507 to
541
343 to
705
533 to
515
472 to
576
460 to
588
339 to
709
524 to
524
641 to
407
646 to
402
559 to
489
633 to
415
Bernie Sanders11/3/0616 to
432
625 to
423
505 to
543
600 to
448
507 to
541
605 to
443
542 to
506
588 to
460
477 to
571
622 to
426
637 to
411
638 to
410
582 to
466
627 to
421
Andrew Yang13/0/1688 to
360
727 to
321
528 to
520
673 to
375
524 to
524
655 to
393
570 to
478
709 to
339
571 to
477
704 to
344
766 to
282
760 to
288
643 to
405
709 to
339
Elizabeth Warren7/6/1601 to
447
590 to
458
465 to
583
510 to
538
430 to
618
542 to
506
502 to
546
524 to
524
426 to
622
344 to
704
599 to
449
620 to
428
553 to
495
609 to
439
John Kasich4/10/0642 to
406
498 to
550
333 to
715
487 to
561
296 to
752
492 to
556
355 to
693
407 to
641
411 to
637
282 to
766
449 to
599
666 to
382
529 to
519
659 to
389
Jeb Bush2/12/0645 to
403
485 to
563
297 to
751
459 to
589
286 to
762
461 to
587
313 to
735
402 to
646
410 to
638
288 to
760
428 to
620
382 to
666
467 to
581
631 to
417
Rand Paul5/9/0766 to
282
526 to
522
336 to
712
513 to
535
422 to
626
573 to
475
368 to
680
489 to
559
466 to
582
405 to
643
495 to
553
519 to
529
581 to
467
784 to
264
Ted Cruz1/13/0675 to
373
475 to
573
288 to
760
441 to
607
333 to
715
419 to
629
294 to
754
415 to
633
421 to
627
339 to
709
439 to
609
389 to
659
417 to
631
264 to
784

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 Trump3074 2.9
Joe Biden3626 3.5
Jo Jorgensen4441 4.2
Howie Hawkins2725 2.6
Tulsi Gabbard3840 3.7
Dan Crenshaw2513 2.4
Justin Amash3804 3.6
Amy Klobuchar2809 2.7
Bernie Sanders4719 4.5
Andrew Yang4800 4.6
Elizabeth Warren3810 3.6
John Kasich2379 2.3
Jeb Bush2188 2.1
Rand Paul3758 3.6
Ted Cruz2724 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 Trump3074
Joe Biden3626
Jo Jorgensen4441
Howie Hawkins2725
Tulsi Gabbard3840
Dan Crenshaw2513
Justin Amash3804
Amy Klobuchar2809
Bernie Sanders4719
Andrew Yang4800
Elizabeth Warren3810
John Kasich2379
Jeb Bush2188
Rand Paul3758
Ted Cruz2724

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 Yang683
Bernie Sanders657

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 Trump1/13/0 386 to
531
255 to
624
395 to
433
301 to
547
319 to
327
279 to
543
390 to
466
389 to
560
324 to
628
406 to
504
381 to
392
375 to
384
237 to
482
295 to
281
Joe Biden9/5/0531 to
386
443 to
468
463 to
320
392 to
499
531 to
329
465 to
397
428 to
227
244 to
461
237 to
560
293 to
364
495 to
261
519 to
261
492 to
457
534 to
364
Jo Jorgensen12/2/0624 to
255
468 to
443
506 to
223
434 to
359
564 to
182
383 to
275
484 to
328
422 to
495
364 to
498
461 to
427
537 to
236
568 to
217
489 to
263
609 to
203
Howie Hawkins5/9/0433 to
395
320 to
463
223 to
506
215 to
509
351 to
316
262 to
425
303 to
352
199 to
513
179 to
580
273 to
395
333 to
324
365 to
331
320 to
457
396 to
370
Tulsi Gabbard11/3/0547 to
301
499 to
392
359 to
434
509 to
215
510 to
204
386 to
350
490 to
260
404 to
476
338 to
472
445 to
384
523 to
198
550 to
203
412 to
349
535 to
266
Dan Crenshaw2/12/0327 to
319
329 to
531
182 to
564
316 to
351
204 to
510
184 to
442
295 to
401
313 to
561
247 to
595
330 to
478
296 to
317
310 to
323
193 to
428
295 to
268
Justin Amash8/6/0543 to
279
397 to
465
275 to
383
425 to
262
350 to
386
442 to
184
379 to
349
372 to
510
316 to
511
384 to
446
422 to
230
469 to
225
399 to
275
507 to
222
Amy Klobuchar6/8/0466 to
390
227 to
428
328 to
484
352 to
303
260 to
490
401 to
295
349 to
379
214 to
516
160 to
595
224 to
407
367 to
236
415 to
262
375 to
454
441 to
357
Bernie Sanders13/1/0560 to
389
461 to
244
495 to
422
513 to
199
476 to
404
561 to
313
510 to
372
516 to
214
365 to
391
431 to
182
543 to
251
564 to
263
516 to
430
567 to
355
Andrew Yang14/0/0628 to
324
560 to
237
498 to
364
580 to
179
472 to
338
595 to
247
511 to
316
595 to
160
391 to
365
485 to
244
620 to
175
637 to
190
518 to
366
604 to
294
Elizabeth Warren10/4/0504 to
406
364 to
293
427 to
461
395 to
273
384 to
445
478 to
330
446 to
384
407 to
224
182 to
431
244 to
485
449 to
240
477 to
277
456 to
450
494 to
379
John Kasich4/10/0392 to
381
261 to
495
236 to
537
324 to
333
198 to
523
317 to
296
230 to
422
236 to
367
251 to
543
175 to
620
240 to
449
297 to
206
279 to
431
358 to
324
Jeb Bush3/11/0384 to
375
261 to
519
217 to
568
331 to
365
203 to
550
323 to
310
225 to
469
262 to
415
263 to
564
190 to
637
277 to
477
206 to
297
227 to
437
325 to
319
Rand Paul7/7/0482 to
237
457 to
492
263 to
489
457 to
320
349 to
412
428 to
193
275 to
399
454 to
375
430 to
516
366 to
518
450 to
456
431 to
279
437 to
227
451 to
143
Ted Cruz0/14/0281 to
295
364 to
534
203 to
609
370 to
396
266 to
535
268 to
295
222 to
507
357 to
441
355 to
567
294 to
604
379 to
494
324 to
358
319 to
325
143 to
451

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
0579936.89%
112207.76%
210326.56%
311517.32%
410366.59%
512357.86%
68615.48%
78725.55%
88105.15%
96364.05%
1010686.79%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump542464355374839413630131
Joe Biden35178597085847893643155
Jo Jorgensen262857693709142595565150
Howie Hawkins44999737871834738392348
Tulsi Gabbard271667510310012110091523336
Dan Crenshaw47097817959844349392225
Justin Amash358836878598943415359117
Amy Klobuchar4107772105841027159381614
Bernie Sanders335555949484541607986191
Andrew Yang2296262707510187939574100
Elizabeth Warren39573604360506359827984
John Kasich45681829992109553221813
Jeb Bush433124971189284382715911
Rand Paul35094646651717278796162
Ted Cruz488100614553734252634031

Number of bullet votes: 25 (2.39%).
Number of "approval" votes: 14 (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.