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 Trump340
Joe Biden290
Jo Jorgensen195
Howie Hawkins35
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash52
Amy Klobuchar17
Bernie Sanders228
Andrew Yang55
Elizabeth Warren35
John Kasich15
Jeb Bush8
Rand Paul39
Ted Cruz27
TOTAL:1387

The winner is Donald Trump with 24.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump462
Joe Biden522
Jo Jorgensen437
Howie Hawkins237
Tulsi Gabbard375
Dan Crenshaw173
Justin Amash332
Amy Klobuchar222
Bernie Sanders584
Andrew Yang510
Elizabeth Warren417
John Kasich167
Jeb Bush140
Rand Paul391
Ted Cruz301
Ballots Cast:1387

The winner is Bernie Sanders with 42.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump302
Joe Biden133
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash82
Amy Klobuchar20
Bernie Sanders274
Andrew Yang97
Elizabeth Warren71
John Kasich20
Jeb Bush9
Rand Paul59
Ted Cruz39

Jeb Bush eliminated in this round.

Round 2:

Donald Trump303
Joe Biden133
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders275
Andrew Yang97
Elizabeth Warren71
John Kasich22
Rand Paul59
Ted Cruz43

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump303
Joe Biden141
Jo Jorgensen173
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Bernie Sanders278
Andrew Yang98
Elizabeth Warren74
John Kasich23
Rand Paul59
Ted Cruz43

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump304
Joe Biden142
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard44
Justin Amash84
Bernie Sanders278
Andrew Yang99
Elizabeth Warren74
John Kasich25
Rand Paul61
Ted Cruz48

John Kasich eliminated in this round.

Round 5:

Donald Trump305
Joe Biden146
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard48
Justin Amash86
Bernie Sanders280
Andrew Yang101
Elizabeth Warren76
Rand Paul66
Ted Cruz51

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump308
Joe Biden152
Jo Jorgensen187
Howie Hawkins54
Justin Amash95
Bernie Sanders287
Andrew Yang106
Elizabeth Warren78
Rand Paul69
Ted Cruz51

Ted Cruz eliminated in this round.

Round 7:

Donald Trump332
Joe Biden154
Jo Jorgensen190
Howie Hawkins55
Justin Amash96
Bernie Sanders289
Andrew Yang107
Elizabeth Warren78
Rand Paul86

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump335
Joe Biden160
Jo Jorgensen192
Justin Amash96
Bernie Sanders327
Andrew Yang110
Elizabeth Warren81
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump335
Joe Biden178
Jo Jorgensen199
Justin Amash97
Bernie Sanders369
Andrew Yang123
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump368
Joe Biden179
Jo Jorgensen215
Justin Amash122
Bernie Sanders370
Andrew Yang133

Justin Amash eliminated in this round.

Round 11:

Donald Trump376
Joe Biden183
Jo Jorgensen312
Bernie Sanders374
Andrew Yang142

Andrew Yang eliminated in this round.

Round 12:

Donald Trump387
Joe Biden212
Jo Jorgensen344
Bernie Sanders444

Joe Biden eliminated in this round.

Round 13:

Donald Trump404
Jo Jorgensen402
Bernie Sanders581

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump609
Bernie Sanders778

And the winner is: Bernie Sanders

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 Trump0/14/0 634 to
753		457 to
930		608 to
779		511 to
876		568 to
819		483 to
904		611 to
776		609 to
778		540 to
847		644 to
743		598 to
789		596 to
791		463 to
924		556 to
831
Joe Biden6/8/0753 to
634		 621 to
766		674 to
713		603 to
784		736 to
651		676 to
711		705 to
682		555 to
832		461 to
926		622 to
765		724 to
663		737 to
650		692 to
695		750 to
637
Jo Jorgensen13/1/0930 to
457		766 to
621		 861 to
526		772 to
615		950 to
437		847 to
540		821 to
566		698 to
689		692 to
695		778 to
609		942 to
445		971 to
416		922 to
465		953 to
434
Howie Hawkins10/4/0779 to
608		713 to
674		526 to
861		 598 to
789		789 to
598		719 to
668		758 to
629		601 to
786		554 to
833		747 to
640		786 to
601		802 to
585		744 to
643		792 to
595
Tulsi Gabbard13/1/0876 to
511		784 to
603		615 to
772		789 to
598		 958 to
429		854 to
533		940 to
447		715 to
672		730 to
657		842 to
545		998 to
389		1003 to
384		858 to
529		920 to
467
Dan Crenshaw6/8/0819 to
568		651 to
736		437 to
950		598 to
789		429 to
958		 612 to
775		713 to
674		602 to
785		572 to
815		713 to
674		768 to
619		800 to
587		677 to
710		820 to
567
Justin Amash9/5/0904 to
483		711 to
676		540 to
847		668 to
719		533 to
854		775 to
612		 770 to
617		660 to
727		652 to
735		750 to
637		927 to
460		960 to
427		903 to
484		952 to
435
Amy Klobuchar6/8/0776 to
611		682 to
705		566 to
821		629 to
758		447 to
940		674 to
713		617 to
770		 613 to
774		504 to
883		734 to
653		861 to
526		868 to
519		773 to
614		823 to
564
Bernie Sanders11/3/0778 to
609		832 to
555		689 to
698		786 to
601		672 to
715		785 to
602		727 to
660		774 to
613		 674 to
713		849 to
538		859 to
528		861 to
526		804 to
583		820 to
567
Andrew Yang13/1/0847 to
540		926 to
461		695 to
692		833 to
554		657 to
730		815 to
572		735 to
652		883 to
504		713 to
674		 923 to
464		1009 to
378		997 to
390		872 to
515		905 to
482
Elizabeth Warren6/8/0743 to
644		765 to
622		609 to
778		640 to
747		545 to
842		674 to
713		637 to
750		653 to
734		538 to
849		464 to
923		 781 to
606		812 to
575		751 to
636		783 to
604
John Kasich4/10/0789 to
598		663 to
724		445 to
942		601 to
786		389 to
998		619 to
768		460 to
927		526 to
861		528 to
859		378 to
1009		606 to
781		 881 to
506		727 to
660		843 to
544
Jeb Bush2/12/0791 to
596		650 to
737		416 to
971		585 to
802		384 to
1003		587 to
800		427 to
960		519 to
868		526 to
861		390 to
997		575 to
812		506 to
881		 654 to
733		823 to
564
Rand Paul5/9/0924 to
463		695 to
692		465 to
922		643 to
744		529 to
858		710 to
677		484 to
903		614 to
773		583 to
804		515 to
872		636 to
751		660 to
727		733 to
654		 984 to
403
Ted Cruz1/13/0831 to
556		637 to
750		434 to
953		595 to
792		467 to
920		567 to
820		435 to
952		564 to
823		567 to
820		482 to
905		604 to
783		544 to
843		564 to
823		403 to
984

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 Trump4619 3.3
Joe Biden4706 3.4
Jo Jorgensen5370 3.9
Howie Hawkins3700 2.7
Tulsi Gabbard4901 3.5
Dan Crenshaw3385 2.4
Justin Amash4706 3.4
Amy Klobuchar3702 2.7
Bernie Sanders6109 4.4
Andrew Yang5890 4.2
Elizabeth Warren4762 3.4
John Kasich3223 2.3
Jeb Bush3133 2.3
Rand Paul4816 3.5
Ted Cruz3876 2.8

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 Trump4619
Joe Biden4706
Jo Jorgensen5370
Howie Hawkins3700
Tulsi Gabbard4901
Dan Crenshaw3385
Justin Amash4706
Amy Klobuchar3702
Bernie Sanders6109
Andrew Yang5890
Elizabeth Warren4762
John Kasich3223
Jeb Bush3133
Rand Paul4816
Ted Cruz3876

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 Sanders907
Andrew Yang875

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 Trump5/9/0 560 to
667		427 to
738		578 to
547		468 to
660		497 to
414		455 to
649		575 to
585		553 to
708		497 to
759		598 to
620		561 to
492		548 to
479		398 to
577		450 to
355
Joe Biden10/4/0667 to
560		 587 to
575		596 to
430		535 to
628		685 to
434		611 to
504		559 to
324		332 to
619		351 to
698		421 to
473		644 to
364		675 to
374		649 to
582		690 to
503
Jo Jorgensen11/3/0738 to
427		575 to
587		 595 to
301		513 to
468		668 to
268		466 to
361		580 to
416		512 to
661		439 to
628		572 to
534		645 to
324		671 to
324		585 to
375		723 to
331
Howie Hawkins3/11/0547 to
578		430 to
596		301 to
595		 294 to
617		452 to
411		350 to
515		390 to
438		263 to
676		256 to
710		375 to
482		438 to
416		465 to
450		419 to
575		511 to
520
Tulsi Gabbard11/3/0660 to
468		628 to
535		468 to
513		617 to
294		 627 to
278		491 to
427		611 to
344		502 to
631		438 to
585		568 to
479		640 to
271		664 to
309		517 to
449		653 to
393
Dan Crenshaw0/14/0414 to
497		434 to
685		268 to
668		411 to
452		278 to
627		 258 to
533		387 to
504		401 to
727		327 to
731		436 to
579		382 to
398		396 to
421		273 to
537		376 to
401
Justin Amash8/6/0649 to
455		504 to
611		361 to
466		515 to
350		427 to
491		533 to
258		 471 to
438		462 to
666		389 to
638		486 to
548		520 to
309		566 to
326		488 to
370		619 to
354
Amy Klobuchar6/8/0585 to
575		324 to
559		416 to
580		438 to
390		344 to
611		504 to
387		438 to
471		 283 to
682		222 to
725		310 to
503		469 to
320		511 to
372		475 to
566		555 to
502
Bernie Sanders14/0/0708 to
553		619 to
332		661 to
512		676 to
263		631 to
502		727 to
401		666 to
462		682 to
283		 512 to
480		598 to
245		705 to
340		716 to
365		674 to
538		718 to
488
Andrew Yang13/1/0759 to
497		698 to
351		628 to
439		710 to
256		585 to
438		731 to
327		638 to
389		725 to
222		480 to
512		 610 to
331		761 to
245		766 to
284		644 to
458		739 to
430
Elizabeth Warren9/5/0620 to
598		473 to
421		534 to
572		482 to
375		479 to
568		579 to
436		548 to
486		503 to
310		245 to
598		331 to
610		 556 to
343		578 to
404		569 to
573		612 to
533
John Kasich2/12/0492 to
561		364 to
644		324 to
645		416 to
438		271 to
640		398 to
382		309 to
520		320 to
469		340 to
705		245 to
761		343 to
556		 362 to
299		356 to
531		454 to
458
Jeb Bush1/13/0479 to
548		374 to
675		324 to
671		450 to
465		309 to
664		421 to
396		326 to
566		372 to
511		365 to
716		284 to
766		404 to
578		299 to
362		 319 to
528		415 to
434
Rand Paul8/6/0577 to
398		582 to
649		375 to
585		575 to
419		449 to
517		537 to
273		370 to
488		566 to
475		538 to
674		458 to
644		573 to
569		531 to
356		528 to
319		 544 to
254
Ted Cruz4/10/0355 to
450		503 to
690		331 to
723		520 to
511		393 to
653		401 to
376		354 to
619		502 to
555		488 to
718		430 to
739		533 to
612		458 to
454		434 to
415		254 to
544

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
0744735.79%
116658.00%
214546.99%
316557.95%
414657.04%
517868.58%
611475.51%
711215.39%
810134.87%
97833.76%
1012696.10%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump649556470547253656249194
Joe Biden45810880108120107104118734566
Jo Jorgensen37411810413210513359726467159
Howie Hawkins560137102114891276949512960
Tulsi Gabbard37591100133141173116107644542
Dan Crenshaw594128108127811216062463129
Justin Amash473112991199213459516560123
Amy Klobuchar525111991481081439973481716
Bernie Sanders42981817371725688100109227
Andrew Yang323899210511314411210911281107
Elizabeth Warren510108947390778675968791
John Kasich5751201141351181487645311114
Jeb Bush5471531331511221215843281516
Rand Paul4581239997791118192967576
Ted Cruz5971318570821035972776249

Number of bullet votes: 38 (2.74%).
Number of "approval" votes: 18 (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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