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 Trump431
Joe Biden321
Jo Jorgensen197
Howie Hawkins43
Tulsi Gabbard37
Dan Crenshaw16
Justin Amash54
Amy Klobuchar21
Bernie Sanders248
Andrew Yang57
Elizabeth Warren40
John Kasich17
Jeb Bush9
Rand Paul46
Ted Cruz31
TOTAL:1568

The winner is Donald Trump with 27.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump562
Joe Biden571
Jo Jorgensen452
Howie Hawkins262
Tulsi Gabbard400
Dan Crenshaw187
Justin Amash347
Amy Klobuchar253
Bernie Sanders634
Andrew Yang536
Elizabeth Warren453
John Kasich183
Jeb Bush169
Rand Paul423
Ted Cruz357
Ballots Cast:1568

The winner is Bernie Sanders with 40.4% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump379
Joe Biden158
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash84
Amy Klobuchar22
Bernie Sanders298
Andrew Yang102
Elizabeth Warren77
John Kasich23
Jeb Bush13
Rand Paul69
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump380
Joe Biden158
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard41
Dan Crenshaw27
Justin Amash85
Amy Klobuchar23
Bernie Sanders299
Andrew Yang102
Elizabeth Warren77
John Kasich26
Rand Paul70
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump380
Joe Biden167
Jo Jorgensen177
Howie Hawkins59
Tulsi Gabbard41
Dan Crenshaw27
Justin Amash85
Bernie Sanders302
Andrew Yang104
Elizabeth Warren81
John Kasich27
Rand Paul70
Ted Cruz48

Eliminated in this round:

Round 4:

Donald Trump384
Joe Biden173
Jo Jorgensen182
Howie Hawkins59
Tulsi Gabbard51
Justin Amash88
Bernie Sanders304
Andrew Yang107
Elizabeth Warren85
Rand Paul78
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump387
Joe Biden179
Jo Jorgensen192
Howie Hawkins63
Justin Amash97
Bernie Sanders311
Andrew Yang113
Elizabeth Warren87
Rand Paul81
Ted Cruz58

Ted Cruz eliminated in this round.

Round 6:

Donald Trump414
Joe Biden181
Jo Jorgensen196
Howie Hawkins64
Justin Amash99
Bernie Sanders313
Andrew Yang115
Elizabeth Warren87
Rand Paul99

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump419
Joe Biden188
Jo Jorgensen201
Justin Amash99
Bernie Sanders353
Andrew Yang119
Elizabeth Warren90
Rand Paul99

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump419
Joe Biden206
Jo Jorgensen209
Justin Amash101
Bernie Sanders398
Andrew Yang136
Rand Paul99

Rand Paul eliminated in this round.

Round 9:

Donald Trump457
Joe Biden208
Jo Jorgensen226
Justin Amash130
Bernie Sanders400
Andrew Yang147

Justin Amash eliminated in this round.

Round 10:

Donald Trump468
Joe Biden212
Jo Jorgensen327
Bernie Sanders405
Andrew Yang156

Andrew Yang eliminated in this round.

Round 11:

Donald Trump480
Joe Biden244
Jo Jorgensen360
Bernie Sanders484

Joe Biden eliminated in this round.

Round 12:

Donald Trump503
Jo Jorgensen425
Bernie Sanders640

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump719
Bernie Sanders849

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 Trump0/14/0 744 to
823		566 to
1001		719 to
848		620 to
948		677 to
891		593 to
975		727 to
841		719 to
849		651 to
917		761 to
807		710 to
858		710 to
858		567 to
1001		670 to
898
Joe Biden5/9/0823 to
744		 693 to
874		741 to
826		675 to
893		815 to
753		752 to
816		780 to
788		626 to
942		531 to
1037		702 to
866		802 to
766		812 to
756		769 to
799		833 to
735
Jo Jorgensen14/0/01001 to
566		874 to
693		 955 to
612		866 to
702		1045 to
523		949 to
619		923 to
645		789 to
779		790 to
778		879 to
689		1055 to
513		1072 to
496		1019 to
549		1043 to
525
Howie Hawkins10/4/0848 to
719		826 to
741		612 to
955		 710 to
858		896 to
672		839 to
729		869 to
699		698 to
870		657 to
911		858 to
710		902 to
666		903 to
665		853 to
715		882 to
686
Tulsi Gabbard13/1/0947 to
620		892 to
675		701 to
866		857 to
710		 1057 to
511		971 to
597		1049 to
519		819 to
749		840 to
728		959 to
609		1121 to
447		1108 to
460		962 to
606		1018 to
550
Dan Crenshaw7/7/0890 to
677		752 to
815		522 to
1045		671 to
896		511 to
1057		 727 to
841		824 to
744		706 to
862		678 to
890		824 to
744		886 to
682		906 to
662		790 to
778		920 to
648
Justin Amash9/5/0974 to
593		815 to
752		618 to
949		728 to
839		597 to
971		841 to
727		 867 to
701		752 to
816		751 to
817		856 to
712		1048 to
520		1072 to
496		1007 to
561		1046 to
522
Amy Klobuchar7/7/0840 to
727		787 to
780		644 to
923		698 to
869		519 to
1049		744 to
824		701 to
867		 712 to
856		606 to
962		851 to
717		979 to
589		979 to
589		882 to
686		922 to
646
Bernie Sanders11/3/0848 to
719		941 to
626		778 to
789		869 to
698		749 to
819		862 to
706		816 to
752		856 to
712		 775 to
793		957 to
611		966 to
602		964 to
604		915 to
653		917 to
651
Andrew Yang12/2/0916 to
651		1036 to
531		777 to
790		910 to
657		728 to
840		890 to
678		817 to
751		962 to
606		793 to
775		 1035 to
533		1134 to
434		1118 to
450		983 to
585		1002 to
566
Elizabeth Warren6/8/0806 to
761		865 to
702		688 to
879		709 to
858		609 to
959		744 to
824		712 to
856		717 to
851		611 to
957		533 to
1035		 887 to
681		919 to
649		860 to
708		877 to
691
John Kasich4/10/0857 to
710		765 to
802		512 to
1055		665 to
902		447 to
1121		682 to
886		520 to
1048		589 to
979		602 to
966		434 to
1134		681 to
887		 982 to
586		836 to
732		937 to
631
Jeb Bush2/12/0857 to
710		755 to
812		495 to
1072		664 to
903		460 to
1108		662 to
906		496 to
1072		589 to
979		604 to
964		450 to
1118		649 to
919		586 to
982		 770 to
798		919 to
649
Rand Paul4/10/01000 to
567		798 to
769		548 to
1019		714 to
853		606 to
962		778 to
790		561 to
1007		686 to
882		653 to
915		585 to
983		708 to
860		732 to
836		798 to
770		 1078 to
490
Ted Cruz1/13/0897 to
670		734 to
833		524 to
1043		685 to
882		550 to
1018		648 to
920		522 to
1046		646 to
922		651 to
917		566 to
1002		691 to
877		631 to
937		649 to
919		490 to
1078

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 Trump5576 3.6
Joe Biden5260 3.4
Jo Jorgensen5826 3.7
Howie Hawkins4202 2.7
Tulsi Gabbard5403 3.4
Dan Crenshaw3875 2.5
Justin Amash5154 3.3
Amy Klobuchar4229 2.7
Bernie Sanders6767 4.3
Andrew Yang6482 4.1
Elizabeth Warren5322 3.4
John Kasich3707 2.4
Jeb Bush3649 2.3
Rand Paul5360 3.4
Ted Cruz4501 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 Trump5576
Joe Biden5260
Jo Jorgensen5826
Howie Hawkins4202
Tulsi Gabbard5403
Dan Crenshaw3875
Justin Amash5154
Amy Klobuchar4229
Bernie Sanders6767
Andrew Yang6482
Elizabeth Warren5322
John Kasich3707
Jeb Bush3649
Rand Paul5360
Ted Cruz4501

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 Sanders1028
Andrew Yang1000

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 Trump7/7/0 665 to
721		536 to
784		684 to
595		571 to
703		598 to
452		563 to
691		679 to
640		653 to
773		597 to
819		704 to
672		666 to
538		650 to
523		494 to
624		544 to
384
Joe Biden10/4/0721 to
665		 653 to
642		659 to
501		603 to
700		753 to
503		678 to
567		620 to
387		377 to
688		401 to
775		475 to
534		708 to
434		739 to
449		720 to
654		763 to
583
Jo Jorgensen11/3/0784 to
536		642 to
653		 635 to
350		555 to
517		721 to
320		511 to
396		623 to
476		556 to
738		471 to
691		618 to
595		687 to
376		715 to
386		635 to
429		771 to
410
Howie Hawkins2/11/1595 to
684		501 to
659		350 to
635		 342 to
662		499 to
457		396 to
555		433 to
486		304 to
746		288 to
777		426 to
535		481 to
461		508 to
508		474 to
625		561 to
598
Tulsi Gabbard11/3/0703 to
571		700 to
603		517 to
555		662 to
342		 676 to
319		541 to
463		661 to
398		549 to
704		478 to
653		624 to
541		684 to
316		711 to
362		569 to
497		701 to
461
Dan Crenshaw0/14/0452 to
598		503 to
753		320 to
721		457 to
499		319 to
676		 305 to
575		435 to
561		453 to
801		361 to
805		491 to
639		422 to
448		440 to
481		316 to
589		420 to
475
Justin Amash8/6/0691 to
563		567 to
678		396 to
511		555 to
396		463 to
541		575 to
305		 509 to
496		504 to
739		418 to
705		532 to
609		558 to
362		605 to
387		529 to
419		664 to
430
Amy Klobuchar5/9/0640 to
679		387 to
620		476 to
623		486 to
433		398 to
661		561 to
435		496 to
509		 329 to
751		259 to
786		361 to
543		518 to
364		560 to
428		533 to
617		610 to
577
Bernie Sanders14/0/0773 to
653		688 to
377		738 to
556		746 to
304		704 to
549		801 to
453		739 to
504		751 to
329		 568 to
540		661 to
282		772 to
386		786 to
421		746 to
585		787 to
558
Andrew Yang13/1/0819 to
597		775 to
401		691 to
471		777 to
288		653 to
478		805 to
361		705 to
418		786 to
259		540 to
568		 675 to
374		823 to
279		836 to
329		716 to
497		804 to
498
Elizabeth Warren9/5/0672 to
704		534 to
475		595 to
618		535 to
426		541 to
624		639 to
491		609 to
532		543 to
361		282 to
661		374 to
675		 613 to
395		632 to
468		630 to
628		673 to
611
John Kasich2/12/0538 to
666		434 to
708		376 to
687		461 to
481		316 to
684		448 to
422		362 to
558		364 to
518		386 to
772		279 to
823		395 to
613		 406 to
346		405 to
576		501 to
535
Jeb Bush1/12/1523 to
650		449 to
739		386 to
715		508 to
508		362 to
711		481 to
440		387 to
605		428 to
560		421 to
786		329 to
836		468 to
632		346 to
406		 371 to
574		462 to
504
Rand Paul7/7/0624 to
494		654 to
720		429 to
635		625 to
474		497 to
569		589 to
316		419 to
529		617 to
533		585 to
746		497 to
716		628 to
630		576 to
405		574 to
371		 593 to
318
Ted Cruz4/10/0384 to
544		583 to
763		410 to
771		598 to
561		461 to
701		475 to
420		430 to
664		577 to
610		558 to
787		498 to
804		611 to
673		535 to
501		504 to
462		318 to
593

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
0827035.16%
118978.07%
217757.55%
319218.17%
416757.12%
520778.83%
612835.45%
712705.40%
811224.77%
98463.60%
1013845.88%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump698597373657868777663238
Joe Biden52412498119130123113130814878
Jo Jorgensen43113713114712615863776869161
Howie Hawkins6161551251351021497658563165
Tulsi Gabbard429108119162152198125114694745
Dan Crenshaw645148134153921426871503332
Justin Amash53512812613611115663566764126
Amy Klobuchar57612812217311816311284551918
Bernie Sanders4819410188829062101111118240
Andrew Yang37010711012212916712412312283111
Elizabeth Warren568122119841049495881049496
John Kasich6291381351571381718454351116
Jeb Bush5991691581721351417353341816
Rand Paul5141401181199412989981047687
Ted Cruz65514010681971186886907255

Number of bullet votes: 48 (3.06%).
Number of "approval" votes: 20 (1%).

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