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 Trump421
Joe Biden314
Jo Jorgensen196
Howie Hawkins43
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders245
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul43
Ted Cruz31
TOTAL:1543

The winner is Donald Trump with 27.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump549
Joe Biden562
Jo Jorgensen451
Howie Hawkins257
Tulsi Gabbard396
Dan Crenshaw186
Justin Amash346
Amy Klobuchar250
Bernie Sanders627
Andrew Yang535
Elizabeth Warren451
John Kasich182
Jeb Bush166
Rand Paul418
Ted Cruz348
Ballots Cast:1543

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump369
Joe Biden153
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders294
Andrew Yang102
Elizabeth Warren77
John Kasich22
Jeb Bush13
Rand Paul66
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump370
Joe Biden153
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders295
Andrew Yang102
Elizabeth Warren77
John Kasich25
Rand Paul67
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump370
Joe Biden162
Jo Jorgensen176
Howie Hawkins59
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders298
Andrew Yang104
Elizabeth Warren81
John Kasich26
Rand Paul67
Ted Cruz48

John Kasich eliminated in this round.

Round 4:

Donald Trump371
Joe Biden166
Jo Jorgensen177
Howie Hawkins59
Tulsi Gabbard44
Dan Crenshaw28
Justin Amash87
Bernie Sanders300
Andrew Yang106
Elizabeth Warren84
Rand Paul71
Ted Cruz50

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump374
Joe Biden167
Jo Jorgensen181
Howie Hawkins59
Tulsi Gabbard50
Justin Amash88
Bernie Sanders300
Andrew Yang107
Elizabeth Warren85
Rand Paul75
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump377
Joe Biden173
Jo Jorgensen191
Howie Hawkins63
Justin Amash97
Bernie Sanders307
Andrew Yang113
Elizabeth Warren87
Rand Paul78
Ted Cruz57

Ted Cruz eliminated in this round.

Round 7:

Donald Trump404
Joe Biden175
Jo Jorgensen194
Howie Hawkins64
Justin Amash99
Bernie Sanders309
Andrew Yang115
Elizabeth Warren87
Rand Paul96

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump409
Joe Biden182
Jo Jorgensen199
Justin Amash99
Bernie Sanders349
Andrew Yang119
Elizabeth Warren90
Rand Paul96

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump409
Joe Biden200
Jo Jorgensen207
Justin Amash101
Bernie Sanders394
Andrew Yang136
Rand Paul96

Rand Paul eliminated in this round.

Round 10:

Donald Trump447
Joe Biden201
Jo Jorgensen223
Justin Amash129
Bernie Sanders396
Andrew Yang147

Justin Amash eliminated in this round.

Round 11:

Donald Trump458
Joe Biden205
Jo Jorgensen323
Bernie Sanders401
Andrew Yang156

Andrew Yang eliminated in this round.

Round 12:

Donald Trump470
Joe Biden237
Jo Jorgensen356
Bernie Sanders480

Joe Biden eliminated in this round.

Round 13:

Donald Trump490
Jo Jorgensen419
Bernie Sanders634

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump701
Bernie Sanders842

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 Trump0/14/0 729 to
813		552 to
990		703 to
839		605 to
938		660 to
883		577 to
966		710 to
833		701 to
842		632 to
911		743 to
800		693 to
850		692 to
851		552 to
991		654 to
889
Joe Biden5/9/0813 to
729		 682 to
860		732 to
810		664 to
879		801 to
742		739 to
804		766 to
777		611 to
932		516 to
1027		687 to
856		787 to
756		799 to
744		756 to
787		820 to
723
Jo Jorgensen14/0/0990 to
552		860 to
682		 942 to
600		854 to
689		1027 to
516		933 to
610		907 to
636		775 to
768		772 to
771		863 to
680		1039 to
504		1057 to
486		1005 to
538		1030 to
513
Howie Hawkins10/4/0839 to
703		810 to
732		600 to
942		 697 to
846		877 to
666		821 to
722		850 to
693		683 to
860		638 to
905		839 to
704		885 to
658		889 to
654		839 to
704		871 to
672
Tulsi Gabbard13/1/0937 to
605		878 to
664		688 to
854		845 to
697		 1040 to
503		954 to
589		1032 to
511		805 to
738		822 to
721		941 to
602		1104 to
439		1094 to
449		949 to
594		1005 to
538
Dan Crenshaw7/7/0882 to
660		741 to
801		515 to
1027		665 to
877		503 to
1040		 712 to
831		808 to
735		692 to
851		664 to
879		809 to
734		873 to
670		897 to
646		779 to
764		910 to
633
Justin Amash9/5/0965 to
577		803 to
739		609 to
933		721 to
821		589 to
954		831 to
712		 853 to
690		739 to
804		736 to
807		840 to
703		1033 to
510		1058 to
485		995 to
548		1035 to
508
Amy Klobuchar7/7/0832 to
710		776 to
766		635 to
907		692 to
850		511 to
1032		735 to
808		690 to
853		 701 to
842		591 to
952		838 to
705		966 to
577		966 to
577		870 to
673		910 to
633
Bernie Sanders11/3/0841 to
701		931 to
611		767 to
775		859 to
683		738 to
805		851 to
692		804 to
739		842 to
701		 761 to
782		940 to
603		952 to
591		953 to
590		902 to
641		906 to
637
Andrew Yang12/2/0910 to
632		1026 to
516		770 to
772		904 to
638		721 to
822		879 to
664		807 to
736		952 to
591		782 to
761		 1019 to
524		1121 to
422		1102 to
441		973 to
570		991 to
552
Elizabeth Warren6/8/0799 to
743		855 to
687		679 to
863		703 to
839		602 to
941		734 to
809		703 to
840		705 to
838		603 to
940		524 to
1019		 876 to
667		908 to
635		849 to
694		868 to
675
John Kasich4/10/0849 to
693		755 to
787		503 to
1039		657 to
885		439 to
1104		670 to
873		510 to
1033		577 to
966		591 to
952		422 to
1121		667 to
876		 971 to
572		822 to
721		926 to
617
Jeb Bush2/12/0850 to
692		743 to
799		485 to
1057		653 to
889		449 to
1094		646 to
897		485 to
1058		577 to
966		590 to
953		441 to
1102		635 to
908		572 to
971		 756 to
787		908 to
635
Rand Paul4/10/0990 to
552		786 to
756		537 to
1005		703 to
839		594 to
949		764 to
779		548 to
995		673 to
870		641 to
902		570 to
973		694 to
849		721 to
822		787 to
756		 1067 to
476
Ted Cruz1/13/0888 to
654		722 to
820		512 to
1030		671 to
871		538 to
1005		633 to
910		508 to
1035		633 to
910		637 to
906		552 to
991		675 to
868		617 to
926		635 to
908		476 to
1067

And the Condorcet winner is: Jo Jorgensen.

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 Trump5452 3.5
Joe Biden5173 3.4
Jo Jorgensen5755 3.7
Howie Hawkins4131 2.7
Tulsi Gabbard5330 3.5
Dan Crenshaw3814 2.5
Justin Amash5086 3.3
Amy Klobuchar4159 2.7
Bernie Sanders6684 4.3
Andrew Yang6415 4.2
Elizabeth Warren5260 3.4
John Kasich3649 2.4
Jeb Bush3583 2.3
Rand Paul5283 3.4
Ted Cruz4410 2.9

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 Trump5452
Joe Biden5173
Jo Jorgensen5755
Howie Hawkins4131
Tulsi Gabbard5330
Dan Crenshaw3814
Justin Amash5086
Amy Klobuchar4159
Bernie Sanders6684
Andrew Yang6415
Elizabeth Warren5260
John Kasich3649
Jeb Bush3583
Rand Paul5283
Ted Cruz4410

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 Sanders1008
Andrew Yang984

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 Trump7/7/0 652 to
712		522 to
777		669 to
589		558 to
695		585 to
448		549 to
685		666 to
633		639 to
765		582 to
813		689 to
665		652 to
533		635 to
518		480 to
617		531 to
377
Joe Biden10/4/0712 to
652		 644 to
630		650 to
490		593 to
690		742 to
495		669 to
558		611 to
379		370 to
681		393 to
766		467 to
527		699 to
423		728 to
439		708 to
645		751 to
571
Jo Jorgensen11/3/0777 to
522		630 to
644		 632 to
342		550 to
508		715 to
313		507 to
389		618 to
468		548 to
730		466 to
685		609 to
589		681 to
370		707 to
377		626 to
423		764 to
399
Howie Hawkins3/11/0589 to
669		490 to
650		342 to
632		 336 to
653		493 to
451		392 to
551		428 to
481		297 to
738		282 to
773		416 to
530		476 to
456		500 to
499		464 to
620		554 to
586
Tulsi Gabbard11/3/0695 to
558		690 to
593		508 to
550		653 to
336		 669 to
315		534 to
457		654 to
392		542 to
695		470 to
646		613 to
534		677 to
311		703 to
354		560 to
490		695 to
451
Dan Crenshaw0/14/0448 to
585		495 to
742		313 to
715		451 to
493		315 to
669		 299 to
570		431 to
555		446 to
793		356 to
798		482 to
633		416 to
444		435 to
472		309 to
583		417 to
461
Justin Amash8/6/0685 to
549		558 to
669		389 to
507		551 to
392		457 to
534		570 to
299		 505 to
489		497 to
731		414 to
699		522 to
605		553 to
357		599 to
377		521 to
412		657 to
418
Amy Klobuchar5/9/0633 to
666		379 to
611		468 to
618		481 to
428		392 to
654		555 to
431		489 to
505		 323 to
742		253 to
783		351 to
539		510 to
361		553 to
419		523 to
613		605 to
565
Bernie Sanders14/0/0765 to
639		681 to
370		730 to
548		738 to
297		695 to
542		793 to
446		731 to
497		742 to
323		 559 to
535		650 to
280		764 to
379		778 to
411		738 to
578		778 to
546
Andrew Yang13/1/0813 to
582		766 to
393		685 to
466		773 to
282		646 to
470		798 to
356		699 to
414		783 to
253		535 to
559		 668 to
371		817 to
275		828 to
322		709 to
491		798 to
485
Elizabeth Warren9/5/0665 to
689		527 to
467		589 to
609		530 to
416		534 to
613		633 to
482		605 to
522		539 to
351		280 to
650		371 to
668		 606 to
386		626 to
456		623 to
618		666 to
596
John Kasich2/12/0533 to
652		423 to
699		370 to
681		456 to
476		311 to
677		444 to
416		357 to
553		361 to
510		379 to
764		275 to
817		386 to
606		 400 to
338		397 to
570		497 to
520
Jeb Bush1/13/0518 to
635		439 to
728		377 to
707		499 to
500		354 to
703		472 to
435		377 to
599		419 to
553		411 to
778		322 to
828		456 to
626		338 to
400		 363 to
568		458 to
493
Rand Paul7/7/0617 to
480		645 to
708		423 to
626		620 to
464		490 to
560		583 to
309		412 to
521		613 to
523		578 to
738		491 to
709		618 to
623		570 to
397		568 to
363		 586 to
306
Ted Cruz4/10/0377 to
531		571 to
751		399 to
764		586 to
554		451 to
695		461 to
417		418 to
657		565 to
605		546 to
778		485 to
798		596 to
666		520 to
497		493 to
458		306 to
586

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
0817935.34%
118518.00%
217057.37%
318978.20%
416437.10%
520348.79%
612635.46%
712535.41%
811104.80%
98393.62%
1013715.92%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump692587273617864777360235
Joe Biden51712195117129121111129814775
Jo Jorgensen42713312514512315463766869160
Howie Hawkins6111521181341001467556553165
Tulsi Gabbard423105117156152193124113694744
Dan Crenshaw637145130151911386769503332
Justin Amash53012511913410915363546664126
Amy Klobuchar57012411817211615911083541918
Bernie Sanders474899788828960100110116238
Andrew Yang36410310512212616312312212183111
Elizabeth Warren559119114841029393871039396
John Kasich6241331301551341688354351116
Jeb Bush5931681511691321397251341816
Rand Paul5081371131179012889971047684
Ted Cruz65013910180961126685877255

Number of bullet votes: 47 (3.05%).
Number of "approval" votes: 20 (1%).

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