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 Trump288
Joe Biden264
Jo Jorgensen192
Howie Hawkins34
Tulsi Gabbard35
Dan Crenshaw15
Justin Amash51
Amy Klobuchar16
Bernie Sanders210
Andrew Yang52
Elizabeth Warren34
John Kasich14
Jeb Bush8
Rand Paul34
Ted Cruz20
TOTAL:1267

The winner is Donald Trump with 22.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump400
Joe Biden480
Jo Jorgensen426
Howie Hawkins217
Tulsi Gabbard360
Dan Crenshaw165
Justin Amash320
Amy Klobuchar210
Bernie Sanders541
Andrew Yang486
Elizabeth Warren389
John Kasich160
Jeb Bush125
Rand Paul371
Ted Cruz262
Ballots Cast:1267

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump255
Joe Biden116
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash81
Amy Klobuchar19
Bernie Sanders252
Andrew Yang92
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul51
Ted Cruz34

Jeb Bush eliminated in this round.

Round 2:

Donald Trump256
Joe Biden116
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Amy Klobuchar19
Bernie Sanders253
Andrew Yang92
Elizabeth Warren68
John Kasich20
Rand Paul51
Ted Cruz37

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump256
Joe Biden124
Jo Jorgensen170
Howie Hawkins48
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Bernie Sanders256
Andrew Yang93
Elizabeth Warren70
John Kasich21
Rand Paul51
Ted Cruz37

John Kasich eliminated in this round.

Round 4:

Donald Trump257
Joe Biden128
Jo Jorgensen170
Howie Hawkins48
Tulsi Gabbard40
Dan Crenshaw23
Justin Amash84
Bernie Sanders258
Andrew Yang95
Elizabeth Warren72
Rand Paul54
Ted Cruz38

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump258
Joe Biden129
Jo Jorgensen174
Howie Hawkins48
Tulsi Gabbard46
Justin Amash85
Bernie Sanders258
Andrew Yang96
Elizabeth Warren72
Rand Paul57
Ted Cruz44

Ted Cruz eliminated in this round.

Round 6:

Donald Trump278
Joe Biden131
Jo Jorgensen177
Howie Hawkins49
Tulsi Gabbard48
Justin Amash86
Bernie Sanders260
Andrew Yang96
Elizabeth Warren72
Rand Paul70

Tulsi Gabbard eliminated in this round.

Round 7:

Donald Trump281
Joe Biden137
Jo Jorgensen186
Howie Hawkins52
Justin Amash95
Bernie Sanders266
Andrew Yang101
Elizabeth Warren74
Rand Paul75

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump284
Joe Biden143
Jo Jorgensen188
Justin Amash95
Bernie Sanders301
Andrew Yang104
Elizabeth Warren77
Rand Paul75

Rand Paul eliminated in this round.

Round 9:

Donald Trump310
Joe Biden144
Jo Jorgensen204
Justin Amash119
Bernie Sanders302
Andrew Yang109
Elizabeth Warren79

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump310
Joe Biden161
Jo Jorgensen210
Justin Amash120
Bernie Sanders342
Andrew Yang124

Justin Amash eliminated in this round.

Round 11:

Donald Trump318
Joe Biden165
Jo Jorgensen305
Bernie Sanders346
Andrew Yang133

Andrew Yang eliminated in this round.

Round 12:

Donald Trump326
Joe Biden194
Jo Jorgensen335
Bernie Sanders412

Joe Biden eliminated in this round.

Round 13:

Donald Trump342
Jo Jorgensen384
Bernie Sanders541

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen638
Bernie Sanders629

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 Trump0/14/0 564 to
703		390 to
877		535 to
732		445 to
822		497 to
770		416 to
851		540 to
727		540 to
727		475 to
792		569 to
698		529 to
738		524 to
743		400 to
867		491 to
776
Joe Biden6/8/0703 to
564		 559 to
708		616 to
651		545 to
722		672 to
595		614 to
653		646 to
621		502 to
765		406 to
861		562 to
705		660 to
607		674 to
593		630 to
637		689 to
578
Jo Jorgensen13/1/0877 to
390		708 to
559		 796 to
471		713 to
554		875 to
392		776 to
491		754 to
513		638 to
629		633 to
634		711 to
556		865 to
402		896 to
371		859 to
408		887 to
380
Howie Hawkins10/4/0732 to
535		651 to
616		471 to
796		 536 to
731		717 to
550		643 to
624		686 to
581		541 to
726		491 to
776		676 to
591		712 to
555		734 to
533		678 to
589		728 to
539
Tulsi Gabbard13/1/0822 to
445		722 to
545		554 to
713		731 to
536		 875 to
392		770 to
497		859 to
408		648 to
619		655 to
612		764 to
503		915 to
352		922 to
345		785 to
482		850 to
417
Dan Crenshaw6/8/0770 to
497		595 to
672		392 to
875		550 to
717		392 to
875		 545 to
722		643 to
624		543 to
724		510 to
757		640 to
627		701 to
566		731 to
536		617 to
650		758 to
509
Justin Amash9/5/0851 to
416		653 to
614		491 to
776		624 to
643		497 to
770		722 to
545		 698 to
569		602 to
665		586 to
681		676 to
591		846 to
421		882 to
385		834 to
433		881 to
386
Amy Klobuchar6/8/0727 to
540		621 to
646		513 to
754		581 to
686		408 to
859		624 to
643		569 to
698		 553 to
714		445 to
822		659 to
608		784 to
483		794 to
473		703 to
564		758 to
509
Bernie Sanders11/3/0727 to
540		765 to
502		629 to
638		726 to
541		619 to
648		724 to
543		665 to
602		714 to
553		 609 to
658		769 to
498		781 to
486		785 to
482		730 to
537		754 to
513
Andrew Yang13/1/0792 to
475		861 to
406		634 to
633		776 to
491		612 to
655		757 to
510		681 to
586		822 to
445		658 to
609		 842 to
425		926 to
341		917 to
350		797 to
470		834 to
433
Elizabeth Warren6/8/0698 to
569		705 to
562		556 to
711		591 to
676		503 to
764		627 to
640		591 to
676		608 to
659		498 to
769		425 to
842		 718 to
549		748 to
519		687 to
580		725 to
542
John Kasich4/10/0738 to
529		607 to
660		402 to
865		555 to
712		352 to
915		566 to
701		421 to
846		483 to
784		486 to
781		341 to
926		549 to
718		 805 to
462		660 to
607		780 to
487
Jeb Bush2/12/0743 to
524		593 to
674		371 to
896		533 to
734		345 to
922		536 to
731		385 to
882		473 to
794		482 to
785		350 to
917		519 to
748		462 to
805		 591 to
676		753 to
514
Rand Paul5/9/0867 to
400		637 to
630		408 to
859		589 to
678		482 to
785		650 to
617		433 to
834		564 to
703		537 to
730		470 to
797		580 to
687		607 to
660		676 to
591		 910 to
357
Ted Cruz1/13/0776 to
491		578 to
689		380 to
887		539 to
728		417 to
850		509 to
758		386 to
881		509 to
758		513 to
754		433 to
834		542 to
725		487 to
780		514 to
753		357 to
910

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 Trump4022 3.2
Joe Biden4331 3.4
Jo Jorgensen5076 4.0
Howie Hawkins3403 2.7
Tulsi Gabbard4551 3.6
Dan Crenshaw3086 2.4
Justin Amash4424 3.5
Amy Klobuchar3419 2.7
Bernie Sanders5666 4.5
Andrew Yang5525 4.4
Elizabeth Warren4444 3.5
John Kasich2925 2.3
Jeb Bush2803 2.2
Rand Paul4434 3.5
Ted Cruz3457 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 Trump4022
Joe Biden4331
Jo Jorgensen5076
Howie Hawkins3403
Tulsi Gabbard4551
Dan Crenshaw3086
Justin Amash4424
Amy Klobuchar3419
Bernie Sanders5666
Andrew Yang5525
Elizabeth Warren4444
John Kasich2925
Jeb Bush2803
Rand Paul4434
Ted Cruz3457

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 Sanders822
Andrew Yang798

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 Trump4/10/0 492 to
623		361 to
702		508 to
510		406 to
623		431 to
387		389 to
615		502 to
547		487 to
661		431 to
718		526 to
583		492 to
459		480 to
449		340 to
545		391 to
331
Joe Biden9/5/0623 to
492		 537 to
544		547 to
397		479 to
588		630 to
396		556 to
472		510 to
299		299 to
570		312 to
651		378 to
438		592 to
330		619 to
334		592 to
538		636 to
451
Jo Jorgensen12/2/0702 to
361		544 to
537		 567 to
276		485 to
431		632 to
240		443 to
332		550 to
386		477 to
609		415 to
582		535 to
497		615 to
293		643 to
289		556 to
335		686 to
286
Howie Hawkins5/9/0510 to
508		397 to
547		276 to
567		 269 to
581		418 to
380		323 to
489		361 to
408		238 to
625		234 to
665		339 to
450		410 to
383		437 to
407		389 to
534		474 to
466
Tulsi Gabbard11/3/0623 to
406		588 to
479		431 to
485		581 to
269		 592 to
253		457 to
400		573 to
313		468 to
580		403 to
548		522 to
443		609 to
238		631 to
271		488 to
408		614 to
347
Dan Crenshaw0/13/1387 to
431		396 to
630		240 to
632		380 to
418		253 to
592		 233 to
506		353 to
469		366 to
674		300 to
688		399 to
543		359 to
368		371 to
388		250 to
498		352 to
352
Justin Amash8/6/0615 to
389		472 to
556		332 to
443		489 to
323		400 to
457		506 to
233		 442 to
408		430 to
613		370 to
590		455 to
510		494 to
281		536 to
294		463 to
335		585 to
305
Amy Klobuchar6/8/0547 to
502		299 to
510		386 to
550		408 to
361		313 to
573		469 to
353		408 to
442		 259 to
627		203 to
679		280 to
467		440 to
288		482 to
334		442 to
525		518 to
447
Bernie Sanders14/0/0661 to
487		570 to
299		609 to
477		625 to
238		580 to
468		674 to
366		613 to
430		627 to
259		 469 to
445		545 to
220		656 to
306		668 to
326		619 to
495		669 to
437
Andrew Yang13/1/0718 to
431		651 to
312		582 to
415		665 to
234		548 to
403		688 to
300		590 to
370		679 to
203		445 to
469		 568 to
300		717 to
217		721 to
251		606 to
425		693 to
381
Elizabeth Warren10/4/0583 to
526		438 to
378		497 to
535		450 to
339		443 to
522		543 to
399		510 to
455		467 to
280		220 to
545		300 to
568		 521 to
303		544 to
359		529 to
527		573 to
480
John Kasich3/11/0459 to
492		330 to
592		293 to
615		383 to
410		238 to
609		368 to
359		281 to
494		288 to
440		306 to
656		217 to
717		303 to
521		 339 to
271		325 to
499		423 to
407
Jeb Bush1/13/0449 to
480		334 to
619		289 to
643		407 to
437		271 to
631		388 to
371		294 to
536		334 to
482		326 to
668		251 to
721		359 to
544		271 to
339		 286 to
495		387 to
391
Rand Paul7/7/0545 to
340		538 to
592		335 to
556		534 to
389		408 to
488		498 to
250		335 to
463		525 to
442		495 to
619		425 to
606		527 to
529		499 to
325		495 to
286		 516 to
212
Ted Cruz1/12/1331 to
391		451 to
636		286 to
686		466 to
474		347 to
614		352 to
352		305 to
585		447 to
518		437 to
669		381 to
693		480 to
573		407 to
423		391 to
387		212 to
516

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
0678535.70%
115197.99%
213337.01%
314787.78%
413457.08%
515908.37%
610485.51%
710385.46%
89474.98%
97333.86%
1011896.26%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump613535767496546565241168
Joe Biden41799749410610096109704161
Jo Jorgensen326109951179611953686067157
Howie Hawkins51112496101861056448492756
Tulsi Gabbard3348191123130152112104613940
Dan Crenshaw54612099109751075457442927
Justin Amash423100911068711654486260120
Amy Klobuchar47898891361021289168441716
Bernie Sanders3916974656064538391103214
Andrew Yang28476879110613110010110878105
Elizabeth Warren46198836481698167918488
John Kasich5301071071221091336543271014
Jeb Bush5011451241381151094835251215
Rand Paul416114918471987786907268
Ted Cruz554126756172945465735340

Number of bullet votes: 31 (2.45%).
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.

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