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 Trump395
Joe Biden305
Jo Jorgensen195
Howie Hawkins39
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar19
Bernie Sanders240
Andrew Yang56
Elizabeth Warren39
John Kasich17
Jeb Bush9
Rand Paul40
Ted Cruz30
TOTAL:1490

The winner is Donald Trump with 26.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump519
Joe Biden547
Jo Jorgensen446
Howie Hawkins249
Tulsi Gabbard388
Dan Crenshaw184
Justin Amash342
Amy Klobuchar238
Bernie Sanders613
Andrew Yang526
Elizabeth Warren439
John Kasich179
Jeb Bush161
Rand Paul407
Ted Cruz331
Ballots Cast:1490

The winner is Bernie Sanders with 41.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump347
Joe Biden145
Jo Jorgensen172
Howie Hawkins53
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar21
Bernie Sanders290
Andrew Yang99
Elizabeth Warren76
John Kasich22
Jeb Bush11
Rand Paul62
Ted Cruz42

Jeb Bush eliminated in this round.

Round 2:

Donald Trump348
Joe Biden145
Jo Jorgensen172
Howie Hawkins53
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash85
Amy Klobuchar22
Bernie Sanders291
Andrew Yang99
Elizabeth Warren76
John Kasich25
Rand Paul62
Ted Cruz46

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump348
Joe Biden154
Jo Jorgensen174
Howie Hawkins55
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash85
Bernie Sanders294
Andrew Yang101
Elizabeth Warren79
John Kasich26
Rand Paul62
Ted Cruz46

John Kasich eliminated in this round.

Round 4:

Donald Trump349
Joe Biden158
Jo Jorgensen175
Howie Hawkins55
Tulsi Gabbard43
Dan Crenshaw28
Justin Amash87
Bernie Sanders296
Andrew Yang103
Elizabeth Warren82
Rand Paul66
Ted Cruz48

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump352
Joe Biden159
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 6:

Donald Trump355
Joe Biden165
Jo Jorgensen189
Howie Hawkins58
Justin Amash97
Bernie Sanders303
Andrew Yang110
Elizabeth Warren85
Rand Paul73
Ted Cruz55

Ted Cruz eliminated in this round.

Round 7:

Donald Trump381
Joe Biden167
Jo Jorgensen192
Howie Hawkins59
Justin Amash98
Bernie Sanders305
Andrew Yang112
Elizabeth Warren85
Rand Paul91

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump385
Joe Biden174
Jo Jorgensen194
Justin Amash98
Bernie Sanders345
Andrew Yang115
Elizabeth Warren88
Rand Paul91

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump385
Joe Biden192
Jo Jorgensen202
Justin Amash100
Bernie Sanders390
Andrew Yang130
Rand Paul91

Rand Paul eliminated in this round.

Round 10:

Donald Trump421
Joe Biden193
Jo Jorgensen218
Justin Amash126
Bernie Sanders391
Andrew Yang141

Justin Amash eliminated in this round.

Round 11:

Donald Trump431
Joe Biden197
Jo Jorgensen316
Bernie Sanders396
Andrew Yang150

Andrew Yang eliminated in this round.

Round 12:

Donald Trump443
Joe Biden226
Jo Jorgensen349
Bernie Sanders472

Joe Biden eliminated in this round.

Round 13:

Donald Trump461
Jo Jorgensen410
Bernie Sanders619

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump669
Bernie Sanders821

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 Trump0/14/0 696 to
793		520 to
969		670 to
819		572 to
918		627 to
863		546 to
944		675 to
815		669 to
821		600 to
890		709 to
781		663 to
827		661 to
829		524 to
966		622 to
868
Joe Biden6/8/0793 to
696		 661 to
828		712 to
777		644 to
846		781 to
709		718 to
772		746 to
744		589 to
901		499 to
991		663 to
827		768 to
722		779 to
711		735 to
755		798 to
692
Jo Jorgensen13/1/0969 to
520		828 to
661		 914 to
575		826 to
664		1000 to
490		905 to
585		878 to
612		746 to
744		742 to
748		833 to
657		1008 to
482		1028 to
462		979 to
511		1003 to
487
Howie Hawkins10/4/0819 to
670		777 to
712		575 to
914		 662 to
828		847 to
643		785 to
705		817 to
673		652 to
838		609 to
881		808 to
682		850 to
640		856 to
634		805 to
685		844 to
646
Tulsi Gabbard13/1/0917 to
572		845 to
644		663 to
826		827 to
662		 1013 to
477		921 to
569		999 to
491		771 to
719		793 to
697		909 to
581		1068 to
422		1066 to
424		922 to
568		979 to
511
Dan Crenshaw7/7/0862 to
627		708 to
781		489 to
1000		642 to
847		477 to
1013		 678 to
812		772 to
718		656 to
834		633 to
857		777 to
713		840 to
650		862 to
628		746 to
744		881 to
609
Justin Amash9/5/0943 to
546		771 to
718		584 to
905		704 to
785		569 to
921		812 to
678		 824 to
666		708 to
782		709 to
781		811 to
679		999 to
491		1022 to
468		967 to
523		1008 to
482
Amy Klobuchar6/8/0814 to
675		743 to
746		611 to
878		672 to
817		491 to
999		718 to
772		666 to
824		 668 to
822		564 to
926		807 to
683		934 to
556		935 to
555		841 to
649		883 to
607
Bernie Sanders11/3/0820 to
669		900 to
589		743 to
746		837 to
652		719 to
771		834 to
656		782 to
708		822 to
668		 736 to
754		910 to
580		922 to
568		923 to
567		871 to
619		879 to
611
Andrew Yang13/1/0889 to
600		990 to
499		747 to
742		880 to
609		697 to
793		857 to
633		781 to
709		926 to
564		754 to
736		 986 to
504		1086 to
404		1069 to
421		942 to
548		964 to
526
Elizabeth Warren6/8/0780 to
709		826 to
663		656 to
833		681 to
808		581 to
909		713 to
777		679 to
811		683 to
807		580 to
910		504 to
986		 847 to
643		876 to
614		817 to
673		841 to
649
John Kasich4/10/0826 to
663		721 to
768		481 to
1008		639 to
850		422 to
1068		650 to
840		491 to
999		556 to
934		568 to
922		404 to
1086		643 to
847		 939 to
551		792 to
698		899 to
591
Jeb Bush2/12/0828 to
661		710 to
779		461 to
1028		633 to
856		424 to
1066		628 to
862		468 to
1022		555 to
935		567 to
923		421 to
1069		614 to
876		551 to
939		 724 to
766		882 to
608
Rand Paul4/10/0965 to
524		754 to
735		510 to
979		684 to
805		568 to
922		744 to
746		523 to
967		649 to
841		619 to
871		548 to
942		673 to
817		698 to
792		766 to
724		 1036 to
454
Ted Cruz1/13/0867 to
622		691 to
798		486 to
1003		645 to
844		511 to
979		609 to
881		482 to
1008		607 to
883		611 to
879		526 to
964		649 to
841		591 to
899		608 to
882		454 to
1036

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 Trump5170 3.5
Joe Biden5012 3.4
Jo Jorgensen5603 3.8
Howie Hawkins3961 2.7
Tulsi Gabbard5177 3.5
Dan Crenshaw3664 2.5
Justin Amash4927 3.3
Amy Klobuchar3994 2.7
Bernie Sanders6492 4.4
Andrew Yang6234 4.2
Elizabeth Warren5073 3.4
John Kasich3501 2.3
Jeb Bush3434 2.3
Rand Paul5115 3.4
Ted Cruz4227 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 Trump5170
Joe Biden5012
Jo Jorgensen5603
Howie Hawkins3961
Tulsi Gabbard5177
Dan Crenshaw3664
Justin Amash4927
Amy Klobuchar3994
Bernie Sanders6492
Andrew Yang6234
Elizabeth Warren5073
John Kasich3501
Jeb Bush3434
Rand Paul5115
Ted Cruz4227

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 Sanders978
Andrew Yang943

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 Trump7/7/0 620 to
696		490 to
764		637 to
573		528 to
685		556 to
435		519 to
671		636 to
617		610 to
746		552 to
796		659 to
650		623 to
517		608 to
506		454 to
602		504 to
370
Joe Biden10/4/0696 to
620		 626 to
608		633 to
466		573 to
667		723 to
471		651 to
535		595 to
358		355 to
661		379 to
742		454 to
508		683 to
402		710 to
417		689 to
621		732 to
548
Jo Jorgensen11/3/0764 to
490		608 to
626		 621 to
327		534 to
496		696 to
300		494 to
377		603 to
450		530 to
711		454 to
669		592 to
567		666 to
356		691 to
361		609 to
408		749 to
377
Howie Hawkins2/12/0573 to
637		466 to
633		327 to
621		 314 to
639		473 to
438		377 to
535		413 to
466		280 to
720		271 to
752		400 to
511		457 to
444		482 to
483		442 to
605		536 to
564
Tulsi Gabbard11/3/0685 to
528		667 to
573		496 to
534		639 to
314		 651 to
302		521 to
445		635 to
376		524 to
677		458 to
626		594 to
512		662 to
298		688 to
340		546 to
476		681 to
432
Dan Crenshaw0/14/0435 to
556		471 to
723		300 to
696		438 to
473		302 to
651		 287 to
551		416 to
537		428 to
773		346 to
774		465 to
611		405 to
426		420 to
453		297 to
563		400 to
440
Justin Amash8/6/0671 to
519		535 to
651		377 to
494		535 to
377		445 to
521		551 to
287		 489 to
473		480 to
712		401 to
680		506 to
585		536 to
344		583 to
364		505 to
402		641 to
399
Amy Klobuchar5/9/0617 to
636		358 to
595		450 to
603		466 to
413		376 to
635		537 to
416		473 to
489		 308 to
724		239 to
763		333 to
525		492 to
345		535 to
403		505 to
596		587 to
545
Bernie Sanders14/0/0746 to
610		661 to
355		711 to
530		720 to
280		677 to
524		773 to
428		712 to
480		724 to
308		 547 to
512		635 to
264		746 to
363		758 to
394		719 to
563		757 to
525
Andrew Yang13/1/0796 to
552		742 to
379		669 to
454		752 to
271		626 to
458		774 to
346		680 to
401		763 to
239		512 to
547		 645 to
355		796 to
265		805 to
311		684 to
483		778 to
466
Elizabeth Warren8/5/1650 to
659		508 to
454		567 to
592		511 to
400		512 to
594		611 to
465		585 to
506		525 to
333		264 to
635		355 to
645		 585 to
370		608 to
439		601 to
601		645 to
575
John Kasich2/12/0517 to
623		402 to
683		356 to
666		444 to
457		298 to
662		426 to
405		344 to
536		345 to
492		363 to
746		265 to
796		370 to
585		 387 to
325		382 to
556		480 to
498
Jeb Bush2/12/0506 to
608		417 to
710		361 to
691		483 to
482		340 to
688		453 to
420		364 to
583		403 to
535		394 to
758		311 to
805		439 to
608		325 to
387		 349 to
553		443 to
472
Rand Paul7/6/1602 to
454		621 to
689		408 to
609		605 to
442		476 to
546		563 to
297		402 to
505		596 to
505		563 to
719		483 to
684		601 to
601		556 to
382		553 to
349		 569 to
289
Ted Cruz4/10/0370 to
504		548 to
732		377 to
749		564 to
536		432 to
681		440 to
400		399 to
641		545 to
587		525 to
757		466 to
778		575 to
645		498 to
480		472 to
443		289 to
569

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
0795435.59%
118058.08%
215987.15%
317988.04%
415837.08%
519448.70%
612315.51%
712175.45%
810764.81%
98163.65%
1013285.94%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump677576872607563736955221
Joe Biden49711789113127117110124784771
Jo Jorgensen41112911714111614763746568159
Howie Hawkins596151111124971397255523063
Tulsi Gabbard407101113146148185122111694642
Dan Crenshaw626140122139871306568493331
Justin Amash51412311112810214662536563123
Amy Klobuchar55612211115911415610581511817
Bernie Sanders46086898378845997107112235
Andrew Yang3521009811711815512111911883109
Elizabeth Warren54611710381988889831009095
John Kasich6101291231471281608052351115
Jeb Bush5771631451601301346849321616
Rand Paul4931341041108612288971017679
Ted Cruz6321369478941066481856852

Number of bullet votes: 44 (2.95%).
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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