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 Sanders239
Andrew Yang56
Elizabeth Warren39
John Kasich17
Jeb Bush9
Rand Paul40
Ted Cruz30
TOTAL:1481

The winner is Donald Trump with 26.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump513
Joe Biden545
Jo Jorgensen445
Howie Hawkins248
Tulsi Gabbard386
Dan Crenshaw181
Justin Amash341
Amy Klobuchar236
Bernie Sanders612
Andrew Yang526
Elizabeth Warren437
John Kasich177
Jeb Bush160
Rand Paul406
Ted Cruz327
Ballots Cast:1481

The winner is Bernie Sanders with 41.3% 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 Sanders289
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 Sanders290
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 Sanders293
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 Sanders295
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 Sanders302
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 Sanders304
Andrew Yang112
Elizabeth Warren85
Rand Paul91

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump379
Joe Biden172
Jo Jorgensen194
Justin Amash98
Bernie Sanders344
Andrew Yang115
Elizabeth Warren88
Rand Paul91

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump379
Joe Biden190
Jo Jorgensen202
Justin Amash100
Bernie Sanders389
Andrew Yang130
Rand Paul91

Rand Paul eliminated in this round.

Round 9:

Donald Trump415
Joe Biden191
Jo Jorgensen218
Justin Amash126
Bernie Sanders390
Andrew Yang141

Justin Amash eliminated in this round.

Round 10:

Donald Trump425
Joe Biden195
Jo Jorgensen316
Bernie Sanders395
Andrew Yang150

Andrew Yang eliminated in this round.

Round 11:

Donald Trump437
Joe Biden224
Jo Jorgensen349
Bernie Sanders471

Joe Biden eliminated in this round.

Round 12:

Donald Trump455
Jo Jorgensen409
Bernie Sanders617

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump662
Bernie Sanders819

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
790		514 to
966		664 to
816		566 to
915		622 to
859		540 to
941		668 to
813		662 to
819		593 to
888		702 to
779		656 to
825		654 to
827		517 to
964		615 to
866
Joe Biden6/8/0790 to
690		 658 to
822		710 to
770		641 to
840		778 to
703		715 to
766		745 to
736		587 to
894		497 to
984		660 to
821		765 to
716		776 to
705		732 to
749		795 to
686
Jo Jorgensen12/2/0966 to
514		822 to
658		 909 to
571		821 to
660		996 to
485		901 to
580		874 to
607		740 to
741		738 to
743		828 to
653		1002 to
479		1023 to
458		973 to
508		999 to
482
Howie Hawkins10/4/0816 to
664		770 to
710		571 to
909		 656 to
825		842 to
639		779 to
702		811 to
670		647 to
834		604 to
877		802 to
679		844 to
637		850 to
631		799 to
682		840 to
641
Tulsi Gabbard13/1/0914 to
566		839 to
641		659 to
821		824 to
656		 1007 to
474		914 to
567		994 to
487		764 to
717		786 to
695		902 to
579		1061 to
420		1058 to
423		913 to
568		973 to
508
Dan Crenshaw6/8/0858 to
622		702 to
778		484 to
996		638 to
842		474 to
1007		 671 to
810		766 to
715		649 to
832		626 to
855		770 to
711		832 to
649		854 to
627		737 to
744		875 to
606
Justin Amash9/5/0940 to
540		765 to
715		579 to
901		701 to
779		567 to
914		810 to
671		 819 to
662		701 to
780		703 to
778		804 to
677		992 to
489		1015 to
466		959 to
522		1003 to
478
Amy Klobuchar6/8/0812 to
668		735 to
745		606 to
874		669 to
811		487 to
994		715 to
766		662 to
819		 661 to
820		557 to
924		799 to
682		926 to
555		927 to
554		833 to
648		878 to
603
Bernie Sanders11/2/1818 to
662		893 to
587		740 to
740		833 to
647		717 to
764		832 to
649		780 to
701		820 to
661		 729 to
752		904 to
577		917 to
564		917 to
564		865 to
616		874 to
607
Andrew Yang13/1/0887 to
593		983 to
497		742 to
738		876 to
604		695 to
786		855 to
626		778 to
703		924 to
557		752 to
729		 980 to
501		1079 to
402		1062 to
419		935 to
546		959 to
522
Elizabeth Warren6/8/0778 to
702		820 to
660		652 to
828		678 to
802		579 to
902		711 to
770		677 to
804		682 to
799		577 to
904		501 to
980		 840 to
641		868 to
613		809 to
672		836 to
645
John Kasich4/10/0824 to
656		715 to
765		478 to
1002		636 to
844		420 to
1061		649 to
832		489 to
992		555 to
926		564 to
917		402 to
1079		641 to
840		 932 to
549		784 to
697		894 to
587
Jeb Bush2/12/0826 to
654		704 to
776		457 to
1023		630 to
850		423 to
1058		627 to
854		466 to
1015		554 to
927		564 to
917		419 to
1062		613 to
868		549 to
932		 717 to
764		877 to
604
Rand Paul5/9/0963 to
517		748 to
732		507 to
973		681 to
799		568 to
913		744 to
737		522 to
959		648 to
833		616 to
865		546 to
935		672 to
809		697 to
784		764 to
717		 1032 to
449
Ted Cruz1/13/0865 to
615		685 to
795		481 to
999		640 to
840		508 to
973		606 to
875		478 to
1003		603 to
878		607 to
874		522 to
959		645 to
836		587 to
894		604 to
877		449 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 Biden4986 3.4
Jo Jorgensen5581 3.8
Howie Hawkins3937 2.7
Tulsi Gabbard5152 3.5
Dan Crenshaw3637 2.5
Justin Amash4907 3.3
Amy Klobuchar3962 2.7
Bernie Sanders6462 4.4
Andrew Yang6209 4.2
Elizabeth Warren5042 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 Biden4986
Jo Jorgensen5581
Howie Hawkins3937
Tulsi Gabbard5152
Dan Crenshaw3637
Justin Amash4907
Amy Klobuchar3962
Bernie Sanders6462
Andrew Yang6209
Elizabeth Warren5042
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 Sanders971
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
693		484 to
761		631 to
570		522 to
682		550 to
433		513 to
668		630 to
614		604 to
743		546 to
793		653 to
647		617 to
515		602 to
504		448 to
600		498 to
369
Joe Biden10/4/0693 to
614		 623 to
605		631 to
462		570 to
662		720 to
466		648 to
531		594 to
352		353 to
659		377 to
740		452 to
506		680 to
399		707 to
413		685 to
618		729 to
544
Jo Jorgensen11/3/0761 to
484		605 to
623		 617 to
325		530 to
494		691 to
297		490 to
375		600 to
446		528 to
707		451 to
666		589 to
564		662 to
354		686 to
359		604 to
406		746 to
374
Howie Hawkins3/11/0570 to
631		462 to
631		325 to
617		 311 to
637		471 to
435		375 to
533		412 to
463		278 to
717		268 to
750		398 to
509		455 to
441		481 to
480		439 to
603		533 to
560
Tulsi Gabbard11/3/0682 to
522		662 to
570		494 to
530		637 to
311		 648 to
300		519 to
444		634 to
372		520 to
673		454 to
623		590 to
509		659 to
295		685 to
337		541 to
475		678 to
428
Dan Crenshaw0/14/0433 to
550		466 to
720		297 to
691		435 to
471		300 to
648		 285 to
548		414 to
533		424 to
769		341 to
771		461 to
608		402 to
423		417 to
452		293 to
562		396 to
437
Justin Amash8/6/0668 to
513		531 to
648		375 to
490		533 to
375		444 to
519		548 to
285		 488 to
470		477 to
708		398 to
677		503 to
582		533 to
342		580 to
361		500 to
401		637 to
395
Amy Klobuchar5/9/0614 to
630		352 to
594		446 to
600		463 to
412		372 to
634		533 to
414		470 to
488		 304 to
721		235 to
761		329 to
523		487 to
345		531 to
401		501 to
595		583 to
541
Bernie Sanders14/0/0743 to
604		659 to
353		707 to
528		717 to
278		673 to
520		769 to
424		708 to
477		721 to
304		 544 to
510		634 to
262		743 to
360		755 to
391		714 to
561		754 to
521
Andrew Yang13/1/0793 to
546		740 to
377		666 to
451		750 to
268		623 to
454		771 to
341		677 to
398		761 to
235		510 to
544		 644 to
351		794 to
262		803 to
306		680 to
480		775 to
462
Elizabeth Warren8/6/0647 to
653		506 to
452		564 to
589		509 to
398		509 to
590		608 to
461		582 to
503		523 to
329		262 to
634		351 to
644		 583 to
368		605 to
436		597 to
599		642 to
571
John Kasich2/12/0515 to
617		399 to
680		354 to
662		441 to
455		295 to
659		423 to
402		342 to
533		345 to
487		360 to
743		262 to
794		368 to
583		 384 to
322		379 to
553		477 to
494
Jeb Bush1/13/0504 to
602		413 to
707		359 to
686		480 to
481		337 to
685		452 to
417		361 to
580		401 to
531		391 to
755		306 to
803		436 to
605		322 to
384		 347 to
551		441 to
468
Rand Paul8/6/0600 to
448		618 to
685		406 to
604		603 to
439		475 to
541		562 to
293		401 to
500		595 to
501		561 to
714		480 to
680		599 to
597		553 to
379		551 to
347		 567 to
285
Ted Cruz4/10/0369 to
498		544 to
729		374 to
746		560 to
533		428 to
678		437 to
396		395 to
637		541 to
583		521 to
754		462 to
775		571 to
642		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
0791235.62%
117878.04%
215827.12%
317838.03%
415757.09%
519398.73%
612275.52%
712095.44%
810714.82%
98113.65%
1013195.94%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump675566872607563726954217
Joe Biden49311688113126117110124784670
Jo Jorgensen40812911514011414763736568159
Howie Hawkins593150110122971387255523062
Tulsi Gabbard406100110144147185122111684642
Dan Crenshaw624139121136871306567483331
Justin Amash51212111012610114661536563123
Amy Klobuchar55412111015811415410481511816
Bernie Sanders45785888278845995107112234
Andrew Yang348999811611815512011811783109
Elizabeth Warren5431151028198888983998994
John Kasich6071271231461261608052341115
Jeb Bush5741621431591301336848321616
Rand Paul4901311031108612187971017679
Ted Cruz6281369378931066480856652

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.

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