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 Trump207
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:1044

The winner is Joe Biden with 21.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump301
Joe Biden409
Jo Jorgensen393
Howie Hawkins176
Tulsi Gabbard314
Dan Crenshaw136
Justin Amash298
Amy Klobuchar183
Bernie Sanders451
Andrew Yang439
Elizabeth Warren344
John Kasich135
Jeb Bush100
Rand Paul336
Ted Cruz205
Ballots Cast:1044

The winner is Bernie Sanders with 43.2% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump182
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 Trump182
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 Trump182
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 Trump183
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 Trump184
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 Trump186
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 Trump200
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 Trump200
Joe Biden109
Jo Jorgensen176
Justin Amash88
Bernie Sanders244
Andrew Yang92
Elizabeth Warren71
Rand Paul64

Rand Paul eliminated in this round.

Round 9:

Donald Trump221
Joe Biden109
Jo Jorgensen191
Justin Amash110
Bernie Sanders245
Andrew Yang96
Elizabeth Warren72

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump221
Joe Biden126
Jo Jorgensen195
Justin Amash111
Bernie Sanders282
Andrew Yang109

Andrew Yang eliminated in this round.

Round 11:

Donald Trump225
Joe Biden147
Jo Jorgensen211
Justin Amash125
Bernie Sanders336

Justin Amash eliminated in this round.

Round 12:

Donald Trump234
Joe Biden155
Jo Jorgensen312
Bernie Sanders343

Joe Biden eliminated in this round.

Round 13:

Donald Trump241
Jo Jorgensen350
Bernie Sanders453

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen540
Bernie Sanders504

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 Trump0/14/0 448 to
596
272 to
772
416 to
628
328 to
716
372 to
672
295 to
749
414 to
630
428 to
616
356 to
688
443 to
601
402 to
642
399 to
645
278 to
766
369 to
675
Joe Biden6/8/0596 to
448
457 to
587
518 to
526
447 to
597
558 to
486
504 to
540
545 to
499
423 to
621
321 to
723
458 to
586
550 to
494
562 to
482
521 to
523
573 to
471
Jo Jorgensen13/1/0772 to
272
587 to
457
677 to
367
590 to
454
734 to
310
636 to
408
623 to
421
540 to
504
519 to
525
580 to
464
713 to
331
749 to
295
710 to
334
759 to
285
Howie Hawkins9/5/0628 to
416
526 to
518
367 to
677
416 to
628
583 to
461
501 to
543
538 to
506
446 to
598
373 to
671
535 to
509
558 to
486
587 to
457
532 to
512
606 to
438
Tulsi Gabbard12/1/1716 to
328
597 to
447
454 to
590
628 to
416
727 to
317
617 to
427
702 to
342
539 to
505
522 to
522
615 to
429
749 to
295
760 to
284
623 to
421
714 to
330
Dan Crenshaw4/10/0672 to
372
486 to
558
310 to
734
461 to
583
317 to
727
422 to
622
511 to
533
441 to
603
391 to
653
503 to
541
553 to
491
585 to
459
472 to
572
628 to
416
Justin Amash10/4/0749 to
295
540 to
504
408 to
636
543 to
501
427 to
617
622 to
422
573 to
471
505 to
539
478 to
566
544 to
500
691 to
353
734 to
310
678 to
366
753 to
291
Amy Klobuchar6/8/0630 to
414
499 to
545
421 to
623
506 to
538
342 to
702
533 to
511
471 to
573
458 to
586
338 to
706
521 to
523
639 to
405
644 to
400
557 to
487
632 to
412
Bernie Sanders11/3/0616 to
428
621 to
423
504 to
540
598 to
446
505 to
539
603 to
441
539 to
505
586 to
458
477 to
567
620 to
424
636 to
408
637 to
407
581 to
463
626 to
418
Andrew Yang13/0/1688 to
356
723 to
321
525 to
519
671 to
373
522 to
522
653 to
391
566 to
478
706 to
338
567 to
477
702 to
342
764 to
280
759 to
285
641 to
403
708 to
336
Elizabeth Warren8/6/0601 to
443
586 to
458
464 to
580
509 to
535
429 to
615
541 to
503
500 to
544
523 to
521
424 to
620
342 to
702
598 to
446
619 to
425
552 to
492
608 to
436
John Kasich4/10/0642 to
402
494 to
550
331 to
713
486 to
558
295 to
749
491 to
553
353 to
691
405 to
639
408 to
636
280 to
764
446 to
598
665 to
379
528 to
516
658 to
386
Jeb Bush2/12/0645 to
399
482 to
562
295 to
749
457 to
587
284 to
760
459 to
585
310 to
734
400 to
644
407 to
637
285 to
759
425 to
619
379 to
665
465 to
579
631 to
413
Rand Paul5/9/0766 to
278
523 to
521
334 to
710
512 to
532
421 to
623
572 to
472
366 to
678
487 to
557
463 to
581
403 to
641
492 to
552
516 to
528
579 to
465
784 to
260
Ted Cruz1/13/0675 to
369
471 to
573
285 to
759
438 to
606
330 to
714
416 to
628
291 to
753
412 to
632
418 to
626
336 to
708
436 to
608
386 to
658
413 to
631
260 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 Trump3037 2.9
Joe Biden3622 3.5
Jo Jorgensen4432 4.2
Howie Hawkins2718 2.6
Tulsi Gabbard3833 3.7
Dan Crenshaw2493 2.4
Justin Amash3799 3.6
Amy Klobuchar2800 2.7
Bernie Sanders4713 4.5
Andrew Yang4793 4.6
Elizabeth Warren3807 3.6
John Kasich2368 2.3
Jeb Bush2170 2.1
Rand Paul3743 3.6
Ted Cruz2697 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 Trump3037
Joe Biden3622
Jo Jorgensen4432
Howie Hawkins2718
Tulsi Gabbard3833
Dan Crenshaw2493
Justin Amash3799
Amy Klobuchar2800
Bernie Sanders4713
Andrew Yang4793
Elizabeth Warren3807
John Kasich2368
Jeb Bush2170
Rand Paul3743
Ted Cruz2697

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 Yang680
Bernie Sanders655

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 Trump1/13/0 382 to
531
251 to
624
391 to
433
297 to
547
315 to
327
275 to
543
386 to
466
385 to
560
320 to
628
402 to
504
377 to
392
371 to
384
233 to
482
292 to
281
Joe Biden9/5/0531 to
382
443 to
466
462 to
318
391 to
497
530 to
326
464 to
395
427 to
226
244 to
460
237 to
557
292 to
364
494 to
260
518 to
259
491 to
455
533 to
361
Jo Jorgensen12/2/0624 to
251
466 to
443
503 to
222
432 to
359
563 to
179
381 to
275
482 to
327
420 to
495
363 to
497
458 to
427
534 to
235
566 to
215
487 to
261
608 to
200
Howie Hawkins5/9/0433 to
391
318 to
462
222 to
503
214 to
508
351 to
313
260 to
424
302 to
351
197 to
512
177 to
578
271 to
395
332 to
323
364 to
329
319 to
455
396 to
367
Tulsi Gabbard11/3/0547 to
297
497 to
391
359 to
432
508 to
214
510 to
201
385 to
350
489 to
259
402 to
475
337 to
471
443 to
384
521 to
197
549 to
201
411 to
347
535 to
263
Dan Crenshaw2/12/0327 to
315
326 to
530
179 to
563
313 to
351
201 to
510
181 to
442
293 to
400
310 to
560
244 to
594
327 to
478
294 to
316
309 to
321
191 to
427
295 to
265
Justin Amash8/6/0543 to
275
395 to
464
275 to
381
424 to
260
350 to
385
442 to
181
378 to
348
371 to
508
316 to
510
382 to
446
420 to
229
468 to
223
398 to
273
507 to
219
Amy Klobuchar6/8/0466 to
386
226 to
427
327 to
482
351 to
302
259 to
489
400 to
293
348 to
378
213 to
515
159 to
593
223 to
407
366 to
235
414 to
260
374 to
452
441 to
354
Bernie Sanders13/1/0560 to
385
460 to
244
495 to
420
512 to
197
475 to
402
560 to
310
508 to
371
515 to
213
364 to
389
429 to
182
541 to
250
562 to
261
514 to
428
566 to
352
Andrew Yang14/0/0628 to
320
557 to
237
497 to
363
578 to
177
471 to
337
594 to
244
510 to
316
593 to
159
389 to
364
482 to
244
617 to
174
635 to
188
516 to
364
603 to
291
Elizabeth Warren10/4/0504 to
402
364 to
292
427 to
458
395 to
271
384 to
443
478 to
327
446 to
382
407 to
223
182 to
429
244 to
482
449 to
239
477 to
275
456 to
448
494 to
376
John Kasich4/10/0392 to
377
260 to
494
235 to
534
323 to
332
197 to
521
316 to
294
229 to
420
235 to
366
250 to
541
174 to
617
239 to
449
297 to
204
279 to
429
358 to
321
Jeb Bush3/11/0384 to
371
259 to
518
215 to
566
329 to
364
201 to
549
321 to
309
223 to
468
260 to
414
261 to
562
188 to
635
275 to
477
204 to
297
226 to
437
325 to
316
Rand Paul7/7/0482 to
233
455 to
491
261 to
487
455 to
319
347 to
411
427 to
191
273 to
398
452 to
374
428 to
514
364 to
516
448 to
456
429 to
279
437 to
226
451 to
140
Ted Cruz0/14/0281 to
292
361 to
533
200 to
608
367 to
396
263 to
535
265 to
295
219 to
507
354 to
441
352 to
566
291 to
603
376 to
494
321 to
358
316 to
325
140 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
0578036.91%
112137.75%
210316.58%
311387.27%
410326.59%
512327.87%
68595.49%
78685.54%
88095.17%
96344.05%
1010646.79%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump542464355374839403630128
Joe Biden34878597084847893643155
Jo Jorgensen261847693689142595565150
Howie Hawkins44898737671834738392348
Tulsi Gabbard270657510110012110091523336
Dan Crenshaw47097817859824348392225
Justin Amash357816877598943415359117
Amy Klobuchar4087772104841027059381614
Bernie Sanders333555849474541607986191
Andrew Yang2286062707510087939574100
Elizabeth Warren39273604260506359827984
John Kasich45481829892109553220813
Jeb Bush432124971179284372715811
Rand Paul34994646451717278796062
Ted Cruz488100614453734250634030

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.