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 Paul43
Ted Cruz31
TOTAL:1549

The winner is Donald Trump with 27.4% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump553
Joe Biden565
Jo Jorgensen451
Howie Hawkins258
Tulsi Gabbard398
Dan Crenshaw186
Justin Amash346
Amy Klobuchar250
Bernie Sanders630
Andrew Yang535
Elizabeth Warren451
John Kasich182
Jeb Bush167
Rand Paul418
Ted Cruz350
Ballots Cast:1549

The winner is Bernie Sanders with 40.7% 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 Paul66
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 Paul67
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 Paul67
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 Paul75
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 Paul78
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 Paul96

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump412
Joe Biden184
Jo Jorgensen199
Justin Amash99
Bernie Sanders350
Andrew Yang119
Elizabeth Warren90
Rand Paul96

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump412
Joe Biden202
Jo Jorgensen207
Justin Amash101
Bernie Sanders395
Andrew Yang136
Rand Paul96

Rand Paul eliminated in this round.

Round 9:

Donald Trump450
Joe Biden203
Jo Jorgensen223
Justin Amash129
Bernie Sanders397
Andrew Yang147

Justin Amash eliminated in this round.

Round 10:

Donald Trump461
Joe Biden207
Jo Jorgensen323
Bernie Sanders402
Andrew Yang156

Andrew Yang eliminated in this round.

Round 11:

Donald Trump473
Joe Biden239
Jo Jorgensen356
Bernie Sanders481

Joe Biden eliminated in this round.

Round 12:

Donald Trump493
Jo Jorgensen420
Bernie Sanders636

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump705
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 Trump0/14/0 732 to
816		555 to
993		707 to
841		609 to
940		664 to
885		581 to
968		714 to
835		705 to
844		636 to
913		747 to
802		696 to
853		696 to
853		556 to
993		658 to
891
Joe Biden5/9/0816 to
732		 685 to
863		735 to
813		667 to
882		805 to
744		742 to
807		769 to
780		615 to
934		519 to
1030		691 to
858		790 to
759		803 to
746		760 to
789		824 to
725
Jo Jorgensen14/0/0993 to
555		863 to
685		 946 to
602		857 to
692		1032 to
517		937 to
612		911 to
638		778 to
771		777 to
772		867 to
682		1043 to
506		1061 to
488		1010 to
539		1033 to
516
Howie Hawkins10/4/0841 to
707		813 to
735		602 to
946		 700 to
849		883 to
666		827 to
722		856 to
693		686 to
863		643 to
906		843 to
706		889 to
660		893 to
656		844 to
705		874 to
675
Tulsi Gabbard13/1/0939 to
609		881 to
667		691 to
857		848 to
700		 1044 to
505		958 to
591		1036 to
513		808 to
741		826 to
723		945 to
604		1107 to
442		1098 to
451		954 to
595		1009 to
540
Dan Crenshaw7/7/0884 to
664		743 to
805		516 to
1032		665 to
883		505 to
1044		 715 to
834		811 to
738		694 to
855		667 to
882		811 to
738		875 to
674		899 to
650		782 to
767		912 to
637
Justin Amash9/5/0967 to
581		806 to
742		611 to
937		721 to
827		591 to
958		834 to
715		 857 to
692		741 to
808		740 to
809		844 to
705		1036 to
513		1061 to
488		999 to
550		1037 to
512
Amy Klobuchar7/7/0834 to
714		779 to
769		637 to
911		692 to
856		513 to
1036		738 to
811		692 to
857		 704 to
845		596 to
953		842 to
707		969 to
580		970 to
579		874 to
675		913 to
636
Bernie Sanders11/3/0843 to
705		933 to
615		770 to
778		862 to
686		741 to
808		855 to
694		808 to
741		845 to
704		 764 to
785		944 to
605		955 to
594		956 to
593		906 to
643		909 to
640
Andrew Yang12/2/0912 to
636		1029 to
519		771 to
777		905 to
643		723 to
826		882 to
667		809 to
740		953 to
596		785 to
764		 1022 to
527		1124 to
425		1106 to
443		977 to
572		994 to
555
Elizabeth Warren6/8/0801 to
747		857 to
691		681 to
867		705 to
843		604 to
945		738 to
811		705 to
844		707 to
842		605 to
944		527 to
1022		 879 to
670		911 to
638		853 to
696		870 to
679
John Kasich4/10/0852 to
696		758 to
790		505 to
1043		659 to
889		442 to
1107		674 to
875		513 to
1036		580 to
969		594 to
955		425 to
1124		670 to
879		 975 to
574		828 to
721		930 to
619
Jeb Bush2/12/0852 to
696		745 to
803		487 to
1061		655 to
893		451 to
1098		650 to
899		488 to
1061		579 to
970		593 to
956		443 to
1106		638 to
911		574 to
975		 761 to
788		911 to
638
Rand Paul4/10/0992 to
556		788 to
760		538 to
1010		704 to
844		595 to
954		767 to
782		550 to
999		675 to
874		643 to
906		572 to
977		696 to
853		721 to
828		788 to
761		 1069 to
480
Ted Cruz1/13/0890 to
658		724 to
824		515 to
1033		674 to
874		540 to
1009		637 to
912		512 to
1037		636 to
913		640 to
909		555 to
994		679 to
870		619 to
930		638 to
911		480 to
1069

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 Trump5478 3.5
Joe Biden5200 3.4
Jo Jorgensen5775 3.7
Howie Hawkins4150 2.7
Tulsi Gabbard5351 3.5
Dan Crenshaw3830 2.5
Justin Amash5110 3.3
Amy Klobuchar4181 2.7
Bernie Sanders6715 4.3
Andrew Yang6437 4.2
Elizabeth Warren5281 3.4
John Kasich3667 2.4
Jeb Bush3596 2.3
Rand Paul5295 3.4
Ted Cruz4430 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 Trump5478
Joe Biden5200
Jo Jorgensen5775
Howie Hawkins4150
Tulsi Gabbard5351
Dan Crenshaw3830
Justin Amash5110
Amy Klobuchar4181
Bernie Sanders6715
Andrew Yang6437
Elizabeth Warren5281
John Kasich3667
Jeb Bush3596
Rand Paul5295
Ted Cruz4430

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 Sanders1012
Andrew Yang986

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 Trump7/7/0 655 to
715		525 to
779		673 to
590		561 to
697		588 to
449		552 to
687		669 to
635		642 to
768		585 to
815		692 to
668		655 to
534		639 to
518		484 to
617		534 to
378
Joe Biden10/4/0715 to
655		 647 to
633		653 to
493		596 to
693		746 to
497		671 to
561		614 to
382		372 to
683		395 to
769		470 to
529		702 to
426		732 to
441		712 to
647		755 to
573
Jo Jorgensen11/3/0779 to
525		633 to
647		 634 to
343		551 to
510		717 to
315		508 to
392		619 to
470		550 to
734		467 to
687		611 to
591		684 to
371		710 to
378		630 to
424		765 to
401
Howie Hawkins3/11/0590 to
673		493 to
653		343 to
634		 337 to
656		494 to
453		392 to
553		429 to
483		299 to
742		283 to
775		418 to
532		477 to
458		502 to
500		467 to
621		555 to
589
Tulsi Gabbard11/3/0697 to
561		693 to
596		510 to
551		656 to
337		 671 to
316		535 to
459		655 to
394		544 to
699		471 to
649		616 to
537		679 to
312		706 to
355		564 to
491		696 to
452
Dan Crenshaw0/14/0449 to
588		497 to
746		315 to
717		453 to
494		316 to
671		 299 to
572		432 to
557		448 to
797		356 to
801		484 to
636		417 to
446		436 to
473		311 to
584		418 to
463
Justin Amash8/6/0687 to
552		561 to
671		392 to
508		553 to
392		459 to
535		572 to
299		 507 to
490		499 to
735		415 to
700		525 to
606		555 to
358		601 to
378		524 to
413		659 to
420
Amy Klobuchar5/9/0635 to
669		382 to
614		470 to
619		483 to
429		394 to
655		557 to
432		490 to
507		 325 to
746		254 to
784		354 to
541		512 to
361		555 to
419		526 to
613		606 to
567
Bernie Sanders14/0/0768 to
642		683 to
372		734 to
550		742 to
299		699 to
544		797 to
448		735 to
499		746 to
325		 563 to
537		654 to
281		768 to
381		782 to
413		742 to
580		782 to
548
Andrew Yang13/1/0815 to
585		769 to
395		687 to
467		775 to
283		649 to
471		801 to
356		700 to
415		784 to
254		537 to
563		 670 to
372		819 to
275		830 to
322		712 to
491		800 to
487
Elizabeth Warren9/5/0668 to
692		529 to
470		591 to
611		532 to
418		537 to
616		636 to
484		606 to
525		541 to
354		281 to
654		372 to
670		 609 to
388		629 to
458		626 to
620		669 to
599
John Kasich2/12/0534 to
655		426 to
702		371 to
684		458 to
477		312 to
679		446 to
417		358 to
555		361 to
512		381 to
768		275 to
819		388 to
609		 402 to
338		400 to
570		498 to
523
Jeb Bush1/13/0518 to
639		441 to
732		378 to
710		500 to
502		355 to
706		473 to
436		378 to
601		419 to
555		413 to
782		322 to
830		458 to
629		338 to
402		 364 to
568		458 to
496
Rand Paul7/7/0617 to
484		647 to
712		424 to
630		621 to
467		491 to
564		584 to
311		413 to
524		613 to
526		580 to
742		491 to
712		620 to
626		570 to
400		568 to
364		 586 to
310
Ted Cruz4/10/0378 to
534		573 to
755		401 to
765		589 to
555		452 to
696		463 to
418		420 to
659		567 to
606		548 to
782		487 to
800		599 to
669		523 to
498		496 to
458		310 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
0819935.29%
118527.97%
217217.41%
319038.19%
416557.12%
520518.83%
612705.47%
712595.42%
811134.79%
98393.61%
1013735.91%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump694587273627865777560235
Joe Biden51812197117129121112130814776
Jo Jorgensen42813312614512515663766869160
Howie Hawkins6121521201351001477557553165
Tulsi Gabbard424105117158152196124113694744
Dan Crenshaw639145131152911396869503332
Justin Amash53112512013510915463566664126
Amy Klobuchar57112411917211716111183541918
Bernie Sanders475909788828962100111116239
Andrew Yang36510310612212816412312312183111
Elizabeth Warren560119116841039394881039396
John Kasich6251331311561361698354351116
Jeb Bush5951681531691331407251341816
Rand Paul5101371151179212889971047684
Ted Cruz65213910180961166685877255

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.

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