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 Trump341
Joe Biden292
Jo Jorgensen195
Howie Hawkins36
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders228
Andrew Yang56
Elizabeth Warren36
John Kasich15
Jeb Bush8
Rand Paul39
Ted Cruz27
TOTAL:1394

The winner is Donald Trump with 24.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump465
Joe Biden524
Jo Jorgensen438
Howie Hawkins239
Tulsi Gabbard377
Dan Crenshaw174
Justin Amash334
Amy Klobuchar225
Bernie Sanders587
Andrew Yang513
Elizabeth Warren420
John Kasich169
Jeb Bush141
Rand Paul393
Ted Cruz302
Ballots Cast:1394

The winner is Bernie Sanders with 42.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump303
Joe Biden134
Jo Jorgensen171
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders274
Andrew Yang98
Elizabeth Warren72
John Kasich20
Jeb Bush10
Rand Paul59
Ted Cruz39

Jeb Bush eliminated in this round.

Round 2:

Donald Trump304
Joe Biden134
Jo Jorgensen171
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Amy Klobuchar20
Bernie Sanders275
Andrew Yang98
Elizabeth Warren72
John Kasich23
Rand Paul59
Ted Cruz43

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump304
Joe Biden142
Jo Jorgensen173
Howie Hawkins52
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Bernie Sanders278
Andrew Yang99
Elizabeth Warren75
John Kasich24
Rand Paul59
Ted Cruz43

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump305
Joe Biden143
Jo Jorgensen177
Howie Hawkins52
Tulsi Gabbard44
Justin Amash85
Bernie Sanders278
Andrew Yang100
Elizabeth Warren75
John Kasich26
Rand Paul61
Ted Cruz48

John Kasich eliminated in this round.

Round 5:

Donald Trump306
Joe Biden147
Jo Jorgensen177
Howie Hawkins52
Tulsi Gabbard48
Justin Amash87
Bernie Sanders280
Andrew Yang102
Elizabeth Warren78
Rand Paul66
Ted Cruz51

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump309
Joe Biden153
Jo Jorgensen187
Howie Hawkins55
Justin Amash96
Bernie Sanders287
Andrew Yang107
Elizabeth Warren80
Rand Paul69
Ted Cruz51

Ted Cruz eliminated in this round.

Round 7:

Donald Trump333
Joe Biden155
Jo Jorgensen190
Howie Hawkins56
Justin Amash97
Bernie Sanders289
Andrew Yang108
Elizabeth Warren80
Rand Paul86

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump336
Joe Biden161
Jo Jorgensen192
Justin Amash97
Bernie Sanders328
Andrew Yang111
Elizabeth Warren83
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump336
Joe Biden179
Jo Jorgensen199
Justin Amash98
Bernie Sanders371
Andrew Yang125
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump369
Joe Biden180
Jo Jorgensen215
Justin Amash123
Bernie Sanders372
Andrew Yang135

Justin Amash eliminated in this round.

Round 11:

Donald Trump378
Joe Biden184
Jo Jorgensen312
Bernie Sanders376
Andrew Yang144

Andrew Yang eliminated in this round.

Round 12:

Donald Trump389
Joe Biden213
Jo Jorgensen344
Bernie Sanders448

Joe Biden eliminated in this round.

Round 13:

Donald Trump406
Jo Jorgensen403
Bernie Sanders585

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump611
Bernie Sanders783

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 Trump0/14/0 636 to
758		459 to
935		610 to
784		513 to
881		569 to
825		484 to
910		613 to
781		611 to
783		542 to
852		646 to
748		600 to
794		598 to
796		465 to
929		558 to
836
Joe Biden6/8/0758 to
636		 624 to
770		677 to
717		605 to
789		739 to
655		679 to
715		708 to
686		558 to
836		463 to
931		623 to
771		727 to
667		740 to
654		695 to
699		754 to
640
Jo Jorgensen13/1/0935 to
459		770 to
624		 865 to
529		775 to
619		953 to
441		850 to
544		825 to
569		701 to
693		694 to
700		781 to
613		946 to
448		976 to
418		928 to
466		959 to
435
Howie Hawkins10/4/0784 to
610		717 to
677		529 to
865		 601 to
793		791 to
603		721 to
673		761 to
633		605 to
789		556 to
838		750 to
644		789 to
605		805 to
589		749 to
645		797 to
597
Tulsi Gabbard13/1/0881 to
513		789 to
605		619 to
775		793 to
601		 961 to
433		858 to
536		944 to
450		718 to
676		733 to
661		846 to
548		1002 to
392		1007 to
387		863 to
531		925 to
469
Dan Crenshaw6/8/0825 to
569		655 to
739		441 to
953		603 to
791		433 to
961		 615 to
779		716 to
678		605 to
789		575 to
819		716 to
678		772 to
622		805 to
589		683 to
711		826 to
568
Justin Amash9/5/0910 to
484		715 to
679		544 to
850		673 to
721		536 to
858		779 to
615		 774 to
620		662 to
732		655 to
739		753 to
641		932 to
462		965 to
429		909 to
485		958 to
436
Amy Klobuchar6/8/0781 to
613		686 to
708		569 to
825		633 to
761		450 to
944		678 to
716		620 to
774		 615 to
779		506 to
888		737 to
657		866 to
528		873 to
521		778 to
616		828 to
566
Bernie Sanders11/3/0783 to
611		836 to
558		693 to
701		789 to
605		676 to
718		789 to
605		732 to
662		779 to
615		 677 to
717		852 to
542		863 to
531		865 to
529		809 to
585		825 to
569
Andrew Yang13/1/0852 to
542		931 to
463		700 to
694		838 to
556		661 to
733		819 to
575		739 to
655		888 to
506		717 to
677		 926 to
468		1014 to
380		1003 to
391		878 to
516		910 to
484
Elizabeth Warren6/8/0748 to
646		771 to
623		613 to
781		644 to
750		548 to
846		678 to
716		641 to
753		657 to
737		542 to
852		468 to
926		 785 to
609		816 to
578		756 to
638		788 to
606
John Kasich4/10/0794 to
600		667 to
727		448 to
946		605 to
789		392 to
1002		622 to
772		462 to
932		528 to
866		531 to
863		380 to
1014		609 to
785		 886 to
508		732 to
662		848 to
546
Jeb Bush2/12/0796 to
598		654 to
740		418 to
976		589 to
805		387 to
1007		589 to
805		429 to
965		521 to
873		529 to
865		391 to
1003		578 to
816		508 to
886		 657 to
737		826 to
568
Rand Paul5/9/0929 to
465		699 to
695		466 to
928		645 to
749		531 to
863		711 to
683		485 to
909		616 to
778		585 to
809		516 to
878		638 to
756		662 to
732		737 to
657		 988 to
406
Ted Cruz1/13/0836 to
558		640 to
754		435 to
959		597 to
797		469 to
925		568 to
826		436 to
958		566 to
828		569 to
825		484 to
910		606 to
788		546 to
848		568 to
826		406 to
988

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 Trump4644 3.3
Joe Biden4733 3.4
Jo Jorgensen5392 3.9
Howie Hawkins3722 2.7
Tulsi Gabbard4922 3.5
Dan Crenshaw3409 2.4
Justin Amash4732 3.4
Amy Klobuchar3735 2.7
Bernie Sanders6144 4.4
Andrew Yang5926 4.3
Elizabeth Warren4797 3.4
John Kasich3255 2.3
Jeb Bush3152 2.3
Rand Paul4840 3.5
Ted Cruz3891 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 Trump4644
Joe Biden4733
Jo Jorgensen5392
Howie Hawkins3722
Tulsi Gabbard4922
Dan Crenshaw3409
Justin Amash4732
Amy Klobuchar3735
Bernie Sanders6144
Andrew Yang5926
Elizabeth Warren4797
John Kasich3255
Jeb Bush3152
Rand Paul4840
Ted Cruz3891

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 Sanders911
Andrew Yang880

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 Trump5/9/0 563 to
671		430 to
740		581 to
549		470 to
662		499 to
416		457 to
651		577 to
589		555 to
712		499 to
763		600 to
624		564 to
495		551 to
481		400 to
578		453 to
355
Joe Biden10/4/0671 to
563		 591 to
578		599 to
434		538 to
632		688 to
437		614 to
508		562 to
328		334 to
623		354 to
702		422 to
477		647 to
368		678 to
378		652 to
586		695 to
505
Jo Jorgensen11/3/0740 to
430		578 to
591		 598 to
302		515 to
470		669 to
271		467 to
363		581 to
419		514 to
664		441 to
631		573 to
538		646 to
328		673 to
326		587 to
377		727 to
332
Howie Hawkins3/11/0549 to
581		434 to
599		302 to
598		 296 to
618		453 to
414		351 to
518		391 to
442		266 to
678		257 to
714		377 to
485		439 to
420		467 to
451		420 to
578		513 to
523
Tulsi Gabbard11/3/0662 to
470		632 to
538		470 to
515		618 to
296		 629 to
280		493 to
429		612 to
348		504 to
634		439 to
589		569 to
483		641 to
274		665 to
309		519 to
451		656 to
395
Dan Crenshaw0/14/0416 to
499		437 to
688		271 to
669		414 to
453		280 to
629		 259 to
535		388 to
507		403 to
730		328 to
734		437 to
582		383 to
402		398 to
423		274 to
539		379 to
402
Justin Amash8/6/0651 to
457		508 to
614		363 to
467		518 to
351		429 to
493		535 to
259		 472 to
442		464 to
669		390 to
642		487 to
552		521 to
313		568 to
327		489 to
371		622 to
355
Amy Klobuchar6/8/0589 to
577		328 to
562		419 to
581		442 to
391		348 to
612		507 to
388		442 to
472		 285 to
685		223 to
727		311 to
505		471 to
322		515 to
373		478 to
567		559 to
503
Bernie Sanders14/0/0712 to
555		623 to
334		664 to
514		678 to
266		634 to
504		730 to
403		669 to
464		685 to
285		 514 to
483		600 to
246		708 to
342		719 to
367		677 to
540		722 to
490
Andrew Yang13/1/0763 to
499		702 to
354		631 to
441		714 to
257		589 to
439		734 to
328		642 to
390		727 to
223		483 to
514		 612 to
333		764 to
247		770 to
285		648 to
459		744 to
431
Elizabeth Warren9/5/0624 to
600		477 to
422		538 to
573		485 to
377		483 to
569		582 to
437		552 to
487		505 to
311		246 to
600		333 to
612		 559 to
345		582 to
405		572 to
575		616 to
535
John Kasich2/12/0495 to
564		368 to
647		328 to
646		420 to
439		274 to
641		402 to
383		313 to
521		322 to
471		342 to
708		247 to
764		345 to
559		 366 to
299		359 to
532		458 to
459
Jeb Bush1/13/0481 to
551		378 to
678		326 to
673		451 to
467		309 to
665		423 to
398		327 to
568		373 to
515		367 to
719		285 to
770		405 to
582		299 to
366		 320 to
530		418 to
436
Rand Paul8/6/0578 to
400		586 to
652		377 to
587		578 to
420		451 to
519		539 to
274		371 to
489		567 to
478		540 to
677		459 to
648		575 to
572		532 to
359		530 to
320		 547 to
254
Ted Cruz4/10/0355 to
453		505 to
695		332 to
727		523 to
513		395 to
656		402 to
379		355 to
622		503 to
559		490 to
722		431 to
744		535 to
616		459 to
458		436 to
418		254 to
547

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
0746735.71%
116717.99%
214626.99%
316788.02%
414717.03%
518028.62%
611555.52%
711275.39%
810154.85%
97883.77%
1012746.09%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump652556471547255656249195
Joe Biden45910881110121107105118734666
Jo Jorgensen37511810613310513659726467159
Howie Hawkins562138102115901286949513060
Tulsi Gabbard37692100136141174117107644542
Dan Crenshaw596128108129811226163463129
Justin Amash475112991209313659516561123
Amy Klobuchar52511110114910814410074491716
Bernie Sanders43082817471735689100110228
Andrew Yang323909210711314511310911381108
Elizabeth Warren511108947491788776968792
John Kasich5751201151371181507647311114
Jeb Bush5481541331541231225843281516
Rand Paul46012310098801128192967577
Ted Cruz6001328671821035972776349

Number of bullet votes: 38 (2.73%).
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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