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 Trump389
Joe Biden304
Jo Jorgensen195
Howie Hawkins39
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar18
Bernie Sanders240
Andrew Yang56
Elizabeth Warren39
John Kasich17
Jeb Bush9
Rand Paul40
Ted Cruz30
TOTAL:1482

The winner is Donald Trump with 26.2% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump513
Joe Biden545
Jo Jorgensen445
Howie Hawkins249
Tulsi Gabbard386
Dan Crenshaw181
Justin Amash341
Amy Klobuchar236
Bernie Sanders613
Andrew Yang526
Elizabeth Warren438
John Kasich177
Jeb Bush160
Rand Paul406
Ted Cruz327
Ballots Cast:1482

The winner is Bernie Sanders with 41.4% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump342
Joe Biden144
Jo Jorgensen172
Howie Hawkins53
Tulsi Gabbard39
Dan Crenshaw26
Justin Amash84
Amy Klobuchar20
Bernie Sanders290
Andrew Yang99
Elizabeth Warren76
John Kasich22
Jeb Bush11
Rand Paul62
Ted Cruz42

Jeb Bush eliminated in this round.

Round 2:

Donald Trump343
Joe Biden144
Jo Jorgensen172
Howie Hawkins53
Tulsi Gabbard39
Dan Crenshaw26
Justin Amash85
Amy Klobuchar21
Bernie Sanders291
Andrew Yang99
Elizabeth Warren76
John Kasich25
Rand Paul62
Ted Cruz46

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump343
Joe Biden152
Jo Jorgensen174
Howie Hawkins55
Tulsi Gabbard39
Dan Crenshaw26
Justin Amash85
Bernie Sanders294
Andrew Yang101
Elizabeth Warren79
John Kasich26
Rand Paul62
Ted Cruz46

Eliminated in this round:

Round 4:

Donald Trump346
Joe Biden157
Jo Jorgensen179
Howie Hawkins55
Tulsi Gabbard49
Justin Amash88
Bernie Sanders296
Andrew Yang104
Elizabeth Warren83
Rand Paul70
Ted Cruz55

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump349
Joe Biden163
Jo Jorgensen189
Howie Hawkins58
Justin Amash97
Bernie Sanders303
Andrew Yang110
Elizabeth Warren85
Rand Paul73
Ted Cruz55

Ted Cruz eliminated in this round.

Round 6:

Donald Trump375
Joe Biden165
Jo Jorgensen192
Howie Hawkins59
Justin Amash98
Bernie Sanders305
Andrew Yang112
Elizabeth Warren85
Rand Paul91

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump379
Joe Biden172
Jo Jorgensen194
Justin Amash98
Bernie Sanders345
Andrew Yang115
Elizabeth Warren88
Rand Paul91

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump379
Joe Biden190
Jo Jorgensen202
Justin Amash100
Bernie Sanders390
Andrew Yang130
Rand Paul91

Rand Paul eliminated in this round.

Round 9:

Donald Trump415
Joe Biden191
Jo Jorgensen218
Justin Amash126
Bernie Sanders391
Andrew Yang141

Justin Amash eliminated in this round.

Round 10:

Donald Trump425
Joe Biden195
Jo Jorgensen316
Bernie Sanders396
Andrew Yang150

Andrew Yang eliminated in this round.

Round 11:

Donald Trump437
Joe Biden224
Jo Jorgensen349
Bernie Sanders472

Joe Biden eliminated in this round.

Round 12:

Donald Trump455
Jo Jorgensen409
Bernie Sanders618

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump662
Bernie Sanders820

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 Trump0/14/0 690 to
791		514 to
967		664 to
817		566 to
916		622 to
860		540 to
942		668 to
814		662 to
820		593 to
889		702 to
780		656 to
826		654 to
828		517 to
965		615 to
867
Joe Biden6/8/0791 to
690		 659 to
822		710 to
771		642 to
840		779 to
703		716 to
766		745 to
737		587 to
895		497 to
985		660 to
822		766 to
716		777 to
705		733 to
749		796 to
686
Jo Jorgensen12/2/0967 to
514		822 to
659		 909 to
572		821 to
661		996 to
486		901 to
581		874 to
608		740 to
742		738 to
744		828 to
654		1003 to
479		1024 to
458		974 to
508		1000 to
482
Howie Hawkins10/4/0817 to
664		771 to
710		572 to
909		 657 to
825		843 to
639		780 to
702		812 to
670		647 to
835		605 to
877		803 to
679		845 to
637		851 to
631		800 to
682		841 to
641
Tulsi Gabbard13/1/0915 to
566		839 to
642		660 to
821		824 to
657		 1007 to
475		914 to
568		994 to
488		764 to
718		786 to
696		902 to
580		1062 to
420		1059 to
423		914 to
568		974 to
508
Dan Crenshaw6/8/0859 to
622		702 to
779		485 to
996		638 to
843		475 to
1007		 671 to
811		766 to
716		649 to
833		626 to
856		770 to
712		833 to
649		855 to
627		738 to
744		876 to
606
Justin Amash9/5/0941 to
540		765 to
716		580 to
901		701 to
780		568 to
914		811 to
671		 819 to
663		701 to
781		703 to
779		804 to
678		993 to
489		1016 to
466		960 to
522		1004 to
478
Amy Klobuchar6/8/0813 to
668		736 to
745		607 to
874		669 to
812		488 to
994		716 to
766		663 to
819		 661 to
821		557 to
925		799 to
683		927 to
555		928 to
554		834 to
648		879 to
603
Bernie Sanders12/2/0819 to
662		894 to
587		741 to
740		834 to
647		718 to
764		833 to
649		781 to
701		821 to
661		 730 to
752		905 to
577		918 to
564		918 to
564		866 to
616		875 to
607
Andrew Yang13/1/0888 to
593		984 to
497		743 to
738		876 to
605		696 to
786		856 to
626		779 to
703		925 to
557		752 to
730		 980 to
502		1080 to
402		1063 to
419		936 to
546		960 to
522
Elizabeth Warren6/8/0779 to
702		821 to
660		653 to
828		678 to
803		580 to
902		712 to
770		678 to
804		683 to
799		577 to
905		502 to
980		 841 to
641		869 to
613		810 to
672		837 to
645
John Kasich4/10/0825 to
656		715 to
766		478 to
1003		636 to
845		420 to
1062		649 to
833		489 to
993		555 to
927		564 to
918		402 to
1080		641 to
841		 933 to
549		785 to
697		895 to
587
Jeb Bush2/12/0827 to
654		704 to
777		457 to
1024		630 to
851		423 to
1059		627 to
855		466 to
1016		554 to
928		564 to
918		419 to
1063		613 to
869		549 to
933		 718 to
764		878 to
604
Rand Paul5/9/0964 to
517		748 to
733		507 to
974		681 to
800		568 to
914		744 to
738		522 to
960		648 to
834		616 to
866		546 to
936		672 to
810		697 to
785		764 to
718		 1032 to
450
Ted Cruz1/13/0866 to
615		685 to
796		481 to
1000		640 to
841		508 to
974		606 to
876		478 to
1004		603 to
879		607 to
875		522 to
960		645 to
837		587 to
895		604 to
878		450 to
1032

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 Trump5113 3.5
Joe Biden4990 3.4
Jo Jorgensen5583 3.8
Howie Hawkins3947 2.7
Tulsi Gabbard5154 3.5
Dan Crenshaw3637 2.5
Justin Amash4908 3.3
Amy Klobuchar3968 2.7
Bernie Sanders6472 4.4
Andrew Yang6216 4.2
Elizabeth Warren5052 3.4
John Kasich3480 2.3
Jeb Bush3414 2.3
Rand Paul5099 3.4
Ted Cruz4196 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 Trump5113
Joe Biden4990
Jo Jorgensen5583
Howie Hawkins3947
Tulsi Gabbard5154
Dan Crenshaw3637
Justin Amash4908
Amy Klobuchar3968
Bernie Sanders6472
Andrew Yang6216
Elizabeth Warren5052
John Kasich3480
Jeb Bush3414
Rand Paul5099
Ted Cruz4196

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 Sanders972
Andrew Yang937

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 Trump7/7/0 614 to
694		484 to
762		631 to
571		522 to
683		550 to
433		513 to
669		630 to
615		604 to
744		546 to
794		653 to
648		617 to
515		602 to
504		448 to
600		498 to
369
Joe Biden10/4/0694 to
614		 624 to
605		631 to
463		571 to
662		721 to
466		649 to
531		594 to
353		353 to
660		377 to
741		452 to
507		681 to
399		708 to
413		686 to
618		730 to
544
Jo Jorgensen11/3/0762 to
484		605 to
624		 617 to
326		530 to
494		692 to
297		491 to
375		600 to
447		528 to
708		451 to
667		589 to
565		663 to
354		687 to
359		605 to
406		747 to
374
Howie Hawkins3/11/0571 to
631		463 to
631		326 to
617		 312 to
637		472 to
435		376 to
533		413 to
463		278 to
717		269 to
750		398 to
509		456 to
441		482 to
480		440 to
603		534 to
560
Tulsi Gabbard11/3/0683 to
522		662 to
571		494 to
530		637 to
312		 649 to
300		520 to
444		634 to
373		520 to
674		454 to
624		590 to
510		660 to
295		686 to
337		542 to
475		679 to
428
Dan Crenshaw0/14/0433 to
550		466 to
721		297 to
692		435 to
472		300 to
649		 285 to
549		414 to
534		424 to
770		341 to
772		461 to
609		402 to
423		417 to
452		293 to
562		396 to
437
Justin Amash8/6/0669 to
513		531 to
649		375 to
491		533 to
376		444 to
520		549 to
285		 488 to
471		477 to
709		398 to
678		503 to
583		534 to
342		581 to
361		501 to
401		638 to
395
Amy Klobuchar5/9/0615 to
630		353 to
594		447 to
600		463 to
413		373 to
634		534 to
414		471 to
488		 304 to
722		235 to
762		329 to
524		488 to
345		532 to
401		502 to
595		584 to
541
Bernie Sanders14/0/0744 to
604		660 to
353		708 to
528		717 to
278		674 to
520		770 to
424		709 to
477		722 to
304		 545 to
510		634 to
262		744 to
360		756 to
391		715 to
561		755 to
521
Andrew Yang13/1/0794 to
546		741 to
377		667 to
451		750 to
269		624 to
454		772 to
341		678 to
398		762 to
235		510 to
545		 644 to
352		795 to
262		804 to
306		681 to
480		776 to
462
Elizabeth Warren8/6/0648 to
653		507 to
452		565 to
589		509 to
398		510 to
590		609 to
461		583 to
503		524 to
329		262 to
634		352 to
644		 584 to
368		606 to
436		598 to
599		643 to
571
John Kasich2/12/0515 to
617		399 to
681		354 to
663		441 to
456		295 to
660		423 to
402		342 to
534		345 to
488		360 to
744		262 to
795		368 to
584		 384 to
322		379 to
553		477 to
494
Jeb Bush1/13/0504 to
602		413 to
708		359 to
687		480 to
482		337 to
686		452 to
417		361 to
581		401 to
532		391 to
756		306 to
804		436 to
606		322 to
384		 347 to
551		441 to
468
Rand Paul8/6/0600 to
448		618 to
686		406 to
605		603 to
440		475 to
542		562 to
293		401 to
501		595 to
502		561 to
715		480 to
681		599 to
598		553 to
379		551 to
347		 567 to
285
Ted Cruz4/10/0369 to
498		544 to
730		374 to
747		560 to
534		428 to
679		437 to
396		395 to
638		541 to
584		521 to
755		462 to
776		571 to
643		494 to
477		468 to
441		285 to
567

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
0791835.62%
117888.04%
215847.13%
317838.02%
415767.09%
519398.72%
612285.52%
712105.44%
810714.82%
98113.65%
1013225.95%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump676566872607563726954217
Joe Biden49311688113127117110124784670
Jo Jorgensen40812911614011414763736568159
Howie Hawkins593150110122971387255523063
Tulsi Gabbard406100111144147185122111684642
Dan Crenshaw625139121136871306567483331
Justin Amash51212211012610114661536563123
Amy Klobuchar55412111015811415410581511816
Bernie Sanders45785888278845995107112235
Andrew Yang348999811611815512011911783109
Elizabeth Warren5431151028198888983998995
John Kasich6081271231461261608052341115
Jeb Bush5751621431591301336848321616
Rand Paul4911311031108612187971017679
Ted Cruz6291369378931066480856652

Number of bullet votes: 44 (2.97%).
Number of "approval" votes: 19 (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.

Quiz2D Home | Presidential Poll | Blog | Third Party Strategy | Silly Radio Ads | Privacy | About/Contact