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 Trump424
Joe Biden316
Jo Jorgensen196
Howie Hawkins43
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders246
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul46
Ted Cruz31
TOTAL:1552

The winner is Donald Trump with 27.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump554
Joe Biden565
Jo Jorgensen451
Howie Hawkins259
Tulsi Gabbard399
Dan Crenshaw186
Justin Amash347
Amy Klobuchar250
Bernie Sanders630
Andrew Yang535
Elizabeth Warren451
John Kasich182
Jeb Bush167
Rand Paul421
Ted Cruz351
Ballots Cast:1552

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump372
Joe Biden154
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders295
Andrew Yang102
Elizabeth Warren77
John Kasich23
Jeb Bush13
Rand Paul69
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump373
Joe Biden154
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders296
Andrew Yang102
Elizabeth Warren77
John Kasich26
Rand Paul70
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump373
Joe Biden163
Jo Jorgensen176
Howie Hawkins59
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders299
Andrew Yang104
Elizabeth Warren81
John Kasich27
Rand Paul70
Ted Cruz48

Eliminated in this round:

Round 4:

Donald Trump377
Joe Biden169
Jo Jorgensen181
Howie Hawkins59
Tulsi Gabbard50
Justin Amash88
Bernie Sanders301
Andrew Yang107
Elizabeth Warren85
Rand Paul78
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump380
Joe Biden175
Jo Jorgensen191
Howie Hawkins63
Justin Amash97
Bernie Sanders308
Andrew Yang113
Elizabeth Warren87
Rand Paul81
Ted Cruz57

Ted Cruz eliminated in this round.

Round 6:

Donald Trump407
Joe Biden177
Jo Jorgensen194
Howie Hawkins64
Justin Amash99
Bernie Sanders310
Andrew Yang115
Elizabeth Warren87
Rand Paul99

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump412
Joe Biden184
Jo Jorgensen199
Justin Amash99
Bernie Sanders350
Andrew Yang119
Elizabeth Warren90
Rand Paul99

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump412
Joe Biden202
Jo Jorgensen207
Justin Amash101
Bernie Sanders395
Andrew Yang136
Rand Paul99

Rand Paul eliminated in this round.

Round 9:

Donald Trump450
Joe Biden204
Jo Jorgensen224
Justin Amash130
Bernie Sanders397
Andrew Yang147

Justin Amash eliminated in this round.

Round 10:

Donald Trump461
Joe Biden208
Jo Jorgensen325
Bernie Sanders402
Andrew Yang156

Andrew Yang eliminated in this round.

Round 11:

Donald Trump473
Joe Biden240
Jo Jorgensen358
Bernie Sanders481

Joe Biden eliminated in this round.

Round 12:

Donald Trump494
Jo Jorgensen422
Bernie Sanders636

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump708
Bernie Sanders844

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 Trump0/14/0 734 to
817		556 to
995		709 to
842		610 to
942		666 to
886		583 to
969		716 to
836		708 to
844		639 to
913		749 to
803		698 to
854		697 to
855		556 to
996		658 to
894
Joe Biden5/9/0817 to
734		 686 to
865		736 to
815		668 to
884		806 to
746		744 to
808		771 to
781		618 to
934		521 to
1031		692 to
860		791 to
761		803 to
749		760 to
792		824 to
728
Jo Jorgensen14/0/0995 to
556		865 to
686		 948 to
603		858 to
694		1035 to
517		939 to
613		914 to
638		781 to
771		780 to
772		870 to
682		1045 to
507		1062 to
490		1010 to
542		1034 to
518
Howie Hawkins10/4/0842 to
709		815 to
736		603 to
948		 701 to
851		886 to
666		829 to
723		859 to
693		689 to
863		646 to
906		846 to
706		892 to
660		894 to
658		844 to
708		874 to
678
Tulsi Gabbard13/1/0941 to
610		883 to
668		693 to
858		850 to
701		 1047 to
505		960 to
592		1039 to
513		811 to
741		829 to
723		948 to
604		1110 to
442		1099 to
453		954 to
598		1010 to
542
Dan Crenshaw7/7/0885 to
666		745 to
806		516 to
1035		665 to
886		505 to
1047		 717 to
835		814 to
738		697 to
855		669 to
883		814 to
738		876 to
676		899 to
653		782 to
770		912 to
640
Justin Amash9/5/0968 to
583		807 to
744		612 to
939		722 to
829		592 to
960		835 to
717		 859 to
693		744 to
808		743 to
809		846 to
706		1038 to
514		1062 to
490		999 to
553		1038 to
514
Amy Klobuchar7/7/0835 to
716		780 to
771		637 to
914		692 to
859		513 to
1039		738 to
814		693 to
859		 707 to
845		598 to
954		843 to
709		970 to
582		970 to
582		874 to
678		913 to
639
Bernie Sanders11/3/0843 to
708		933 to
618		770 to
781		862 to
689		741 to
811		855 to
697		808 to
744		845 to
707		 765 to
787		945 to
607		956 to
596		956 to
596		906 to
646		909 to
643
Andrew Yang12/2/0912 to
639		1030 to
521		771 to
780		905 to
646		723 to
829		883 to
669		809 to
743		954 to
598		787 to
765		 1024 to
528		1126 to
426		1107 to
445		977 to
575		994 to
558
Elizabeth Warren6/8/0802 to
749		859 to
692		681 to
870		705 to
846		604 to
948		738 to
814		706 to
846		709 to
843		607 to
945		528 to
1024		 880 to
672		911 to
641		853 to
699		870 to
682
John Kasich4/10/0853 to
698		760 to
791		506 to
1045		659 to
892		442 to
1110		676 to
876		514 to
1038		582 to
970		596 to
956		426 to
1126		672 to
880		 975 to
577		828 to
724		930 to
622
Jeb Bush2/12/0854 to
697		748 to
803		489 to
1062		657 to
894		453 to
1099		653 to
899		490 to
1062		582 to
970		596 to
956		445 to
1107		641 to
911		577 to
975		 761 to
791		911 to
641
Rand Paul4/10/0995 to
556		791 to
760		541 to
1010		707 to
844		598 to
954		770 to
782		553 to
999		678 to
874		646 to
906		575 to
977		699 to
853		724 to
828		791 to
761		 1072 to
480
Ted Cruz1/13/0893 to
658		727 to
824		517 to
1034		677 to
874		542 to
1010		640 to
912		514 to
1038		639 to
913		643 to
909		558 to
994		682 to
870		622 to
930		641 to
911		480 to
1072

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 Trump5485 3.5
Joe Biden5202 3.4
Jo Jorgensen5779 3.7
Howie Hawkins4155 2.7
Tulsi Gabbard5361 3.5
Dan Crenshaw3832 2.5
Justin Amash5119 3.3
Amy Klobuchar4183 2.7
Bernie Sanders6717 4.3
Andrew Yang6439 4.1
Elizabeth Warren5283 3.4
John Kasich3670 2.4
Jeb Bush3602 2.3
Rand Paul5325 3.4
Ted Cruz4441 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 Trump5485
Joe Biden5202
Jo Jorgensen5779
Howie Hawkins4155
Tulsi Gabbard5361
Dan Crenshaw3832
Justin Amash5119
Amy Klobuchar4183
Bernie Sanders6717
Andrew Yang6439
Elizabeth Warren5283
John Kasich3670
Jeb Bush3602
Rand Paul5325
Ted Cruz4441

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 Sanders1015
Andrew Yang989

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 Trump7/7/0 656 to
715		526 to
779		674 to
590		561 to
699		589 to
449		552 to
688		670 to
635		643 to
768		586 to
815		693 to
668		656 to
535		640 to
520		484 to
620		535 to
380
Joe Biden10/4/0715 to
656		 647 to
634		653 to
494		596 to
695		746 to
497		671 to
562		614 to
382		372 to
683		395 to
769		470 to
529		702 to
427		732 to
443		712 to
650		755 to
576
Jo Jorgensen11/3/0779 to
526		634 to
647		 634 to
344		551 to
512		718 to
315		508 to
393		620 to
470		551 to
734		468 to
687		612 to
591		685 to
372		711 to
380		630 to
427		766 to
403
Howie Hawkins3/11/0590 to
674		494 to
653		344 to
634		 337 to
658		495 to
453		392 to
554		430 to
483		300 to
742		284 to
775		419 to
532		478 to
459		503 to
502		467 to
624		556 to
591
Tulsi Gabbard11/3/0699 to
561		695 to
596		512 to
551		658 to
337		 673 to
316		536 to
460		657 to
394		546 to
699		473 to
649		618 to
537		681 to
313		707 to
356		564 to
494		697 to
453
Dan Crenshaw0/14/0449 to
589		497 to
746		315 to
718		453 to
495		316 to
673		 299 to
573		432 to
557		448 to
797		356 to
801		484 to
636		417 to
447		436 to
475		311 to
587		418 to
466
Justin Amash8/6/0688 to
552		562 to
671		393 to
508		554 to
392		460 to
536		573 to
299		 508 to
490		500 to
735		416 to
700		526 to
606		556 to
359		602 to
380		524 to
416		660 to
422
Amy Klobuchar5/9/0635 to
670		382 to
614		470 to
620		483 to
430		394 to
657		557 to
432		490 to
508		 325 to
746		254 to
784		354 to
541		512 to
362		555 to
421		526 to
616		606 to
570
Bernie Sanders14/0/0768 to
643		683 to
372		734 to
551		742 to
300		699 to
546		797 to
448		735 to
500		746 to
325		 563 to
537		654 to
281		768 to
382		782 to
415		742 to
583		782 to
551
Andrew Yang13/1/0815 to
586		769 to
395		687 to
468		775 to
284		649 to
473		801 to
356		700 to
416		784 to
254		537 to
563		 670 to
372		819 to
276		830 to
324		712 to
494		800 to
490
Elizabeth Warren9/5/0668 to
693		529 to
470		591 to
612		532 to
419		537 to
618		636 to
484		606 to
526		541 to
354		281 to
654		372 to
670		 609 to
389		629 to
460		626 to
623		669 to
602
John Kasich2/12/0535 to
656		427 to
702		372 to
685		459 to
478		313 to
681		447 to
417		359 to
556		362 to
512		382 to
768		276 to
819		389 to
609		 402 to
340		400 to
573		498 to
526
Jeb Bush1/13/0520 to
640		443 to
732		380 to
711		502 to
503		356 to
707		475 to
436		380 to
602		421 to
555		415 to
782		324 to
830		460 to
629		340 to
402		 364 to
571		458 to
498
Rand Paul7/7/0620 to
484		650 to
712		427 to
630		624 to
467		494 to
564		587 to
311		416 to
524		616 to
526		583 to
742		494 to
712		623 to
626		573 to
400		571 to
364		 589 to
310
Ted Cruz4/10/0380 to
535		576 to
755		403 to
766		591 to
556		453 to
697		466 to
418		422 to
660		570 to
606		551 to
782		490 to
800		602 to
669		526 to
498		498 to
458		310 to
589

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
0821035.27%
118728.04%
217237.40%
319078.19%
416567.11%
520518.81%
612725.46%
712605.41%
811144.79%
98393.60%
1013765.91%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump695597273627866777560235
Joe Biden51912397117129121112130814776
Jo Jorgensen42913412614612515663766869160
Howie Hawkins6131531201351011477557553165
Tulsi Gabbard425105117159152196124114694744
Dan Crenshaw640147131152911396869503332
Justin Amash53212612013510915463566764126
Amy Klobuchar57212611917211716111183541918
Bernie Sanders476929788828962100111116239
Andrew Yang36610510612212816412312312183111
Elizabeth Warren561121116841039394881039396
John Kasich6251361311561361698354351116
Jeb Bush5951691541701331407251341816
Rand Paul5101371151179212889971047687
Ted Cruz65213910281961166785877255

Number of bullet votes: 47 (3.03%).
Number of "approval" votes: 20 (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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