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 Trump470
Joe Biden337
Jo Jorgensen198
Howie Hawkins43
Tulsi Gabbard38
Dan Crenshaw17
Justin Amash55
Amy Klobuchar21
Bernie Sanders263
Andrew Yang58
Elizabeth Warren41
John Kasich17
Jeb Bush10
Rand Paul47
Ted Cruz32
TOTAL:1647

The winner is Donald Trump with 28.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump599
Joe Biden596
Jo Jorgensen455
Howie Hawkins266
Tulsi Gabbard410
Dan Crenshaw198
Justin Amash352
Amy Klobuchar260
Bernie Sanders668
Andrew Yang546
Elizabeth Warren466
John Kasich188
Jeb Bush182
Rand Paul432
Ted Cruz383
Ballots Cast:1647

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump412
Joe Biden168
Jo Jorgensen176
Howie Hawkins57
Tulsi Gabbard41
Dan Crenshaw28
Justin Amash85
Amy Klobuchar23
Bernie Sanders318
Andrew Yang103
Elizabeth Warren79
John Kasich25
Jeb Bush14
Rand Paul71
Ted Cruz47

Jeb Bush eliminated in this round.

Round 2:

Donald Trump414
Joe Biden168
Jo Jorgensen176
Howie Hawkins57
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash86
Amy Klobuchar24
Bernie Sanders319
Andrew Yang103
Elizabeth Warren79
John Kasich28
Rand Paul72
Ted Cruz51

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump414
Joe Biden177
Jo Jorgensen178
Howie Hawkins59
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash86
Bernie Sanders323
Andrew Yang105
Elizabeth Warren83
John Kasich29
Rand Paul72
Ted Cruz51

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump418
Joe Biden178
Jo Jorgensen182
Howie Hawkins59
Tulsi Gabbard47
Justin Amash87
Bernie Sanders323
Andrew Yang106
Elizabeth Warren84
John Kasich31
Rand Paul75
Ted Cruz57

John Kasich eliminated in this round.

Round 5:

Donald Trump419
Joe Biden183
Jo Jorgensen183
Howie Hawkins59
Tulsi Gabbard53
Justin Amash89
Bernie Sanders325
Andrew Yang109
Elizabeth Warren87
Rand Paul80
Ted Cruz60

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump422
Joe Biden189
Jo Jorgensen194
Howie Hawkins63
Justin Amash98
Bernie Sanders332
Andrew Yang115
Elizabeth Warren89
Rand Paul84
Ted Cruz61

Ted Cruz eliminated in this round.

Round 7:

Donald Trump450
Joe Biden191
Jo Jorgensen198
Howie Hawkins64
Justin Amash100
Bernie Sanders334
Andrew Yang117
Elizabeth Warren89
Rand Paul104

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump455
Joe Biden198
Jo Jorgensen203
Justin Amash100
Bernie Sanders374
Andrew Yang121
Elizabeth Warren92
Rand Paul104

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump455
Joe Biden217
Jo Jorgensen211
Justin Amash102
Bernie Sanders419
Andrew Yang139
Rand Paul104

Justin Amash eliminated in this round.

Round 10:

Donald Trump458
Joe Biden220
Jo Jorgensen262
Bernie Sanders424
Andrew Yang147
Rand Paul136

Rand Paul eliminated in this round.

Round 11:

Donald Trump507
Joe Biden223
Jo Jorgensen329
Bernie Sanders426
Andrew Yang162

Andrew Yang eliminated in this round.

Round 12:

Donald Trump519
Joe Biden255
Jo Jorgensen364
Bernie Sanders509

Joe Biden eliminated in this round.

Round 13:

Donald Trump544
Jo Jorgensen432
Bernie Sanders671

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump764
Bernie Sanders883

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 Trump0/14/0 790 to
856		611 to
1035		767 to
879		663 to
984		721 to
926		637 to
1010		771 to
876		764 to
883		696 to
951		807 to
840		758 to
889		758 to
889		610 to
1037		716 to
931
Joe Biden5/9/0856 to
790		 726 to
920		779 to
867		709 to
938		853 to
794		789 to
858		814 to
833		649 to
998		562 to
1085		737 to
910		840 to
807		850 to
797		810 to
837		869 to
778
Jo Jorgensen13/1/01035 to
611		920 to
726		 1000 to
646		907 to
740		1086 to
561		995 to
652		961 to
686		817 to
830		829 to
818		921 to
726		1103 to
544		1121 to
526		1066 to
581		1085 to
562
Howie Hawkins10/4/0879 to
767		867 to
779		646 to
1000		 750 to
897		939 to
708		889 to
758		910 to
737		729 to
918		702 to
945		901 to
746		954 to
693		952 to
695		900 to
747		924 to
723
Tulsi Gabbard13/1/0983 to
663		937 to
709		739 to
907		896 to
750		 1107 to
540		1025 to
622		1098 to
549		852 to
795		887 to
760		1011 to
636		1176 to
471		1161 to
486		1014 to
633		1061 to
586
Dan Crenshaw7/7/0925 to
721		793 to
853		560 to
1086		707 to
939		540 to
1107		 776 to
871		872 to
775		742 to
905		726 to
921		875 to
772		942 to
705		960 to
687		844 to
803		965 to
682
Justin Amash9/5/01009 to
637		857 to
789		651 to
995		757 to
889		622 to
1025		871 to
776		 908 to
739		782 to
865		796 to
851		902 to
745		1102 to
545		1124 to
523		1058 to
589		1087 to
560
Amy Klobuchar7/7/0875 to
771		832 to
814		685 to
961		736 to
910		549 to
1098		775 to
872		739 to
908		 744 to
903		645 to
1002		894 to
753		1028 to
619		1026 to
621		928 to
719		961 to
686
Bernie Sanders13/1/0882 to
764		997 to
649		829 to
817		917 to
729		795 to
852		905 to
742		865 to
782		903 to
744		 828 to
819		1019 to
628		1023 to
624		1018 to
629		968 to
679		966 to
681
Andrew Yang11/3/0950 to
696		1084 to
562		817 to
829		944 to
702		760 to
887		921 to
726		851 to
796		1002 to
645		819 to
828		 1083 to
564		1187 to
460		1169 to
478		1032 to
615		1045 to
602
Elizabeth Warren6/8/0839 to
807		909 to
737		725 to
921		745 to
901		636 to
1011		772 to
875		745 to
902		753 to
894		628 to
1019		564 to
1083		 938 to
709		968 to
679		910 to
737		917 to
730
John Kasich4/10/0888 to
758		806 to
840		543 to
1103		692 to
954		471 to
1176		705 to
942		545 to
1102		619 to
1028		624 to
1023		460 to
1187		709 to
938		 1036 to
611		883 to
764		975 to
672
Jeb Bush2/12/0888 to
758		796 to
850		525 to
1121		694 to
952		486 to
1161		687 to
960		523 to
1124		621 to
1026		629 to
1018		478 to
1169		679 to
968		611 to
1036		 817 to
830		958 to
689
Rand Paul4/10/01036 to
610		836 to
810		580 to
1066		746 to
900		633 to
1014		803 to
844		589 to
1058		719 to
928		679 to
968		615 to
1032		737 to
910		764 to
883		830 to
817		 1114 to
533
Ted Cruz1/13/0930 to
716		777 to
869		561 to
1085		722 to
924		586 to
1061		682 to
965		560 to
1087		686 to
961		681 to
966		602 to
1045		730 to
917		672 to
975		689 to
958		533 to
1114

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 Trump5962 3.6
Joe Biden5535 3.4
Jo Jorgensen5998 3.6
Howie Hawkins4380 2.7
Tulsi Gabbard5662 3.4
Dan Crenshaw4090 2.5
Justin Amash5332 3.2
Amy Klobuchar4386 2.7
Bernie Sanders7106 4.3
Andrew Yang6735 4.1
Elizabeth Warren5563 3.4
John Kasich3910 2.4
Jeb Bush3884 2.4
Rand Paul5566 3.4
Ted Cruz4789 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 Trump5962
Joe Biden5535
Jo Jorgensen5998
Howie Hawkins4380
Tulsi Gabbard5662
Dan Crenshaw4090
Justin Amash5332
Amy Klobuchar4386
Bernie Sanders7106
Andrew Yang6735
Elizabeth Warren5563
John Kasich3910
Jeb Bush3884
Rand Paul5566
Ted Cruz4789

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 Sanders1087
Andrew Yang1039

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 Trump7/7/0 707 to
750		584 to
805		730 to
615		613 to
727		642 to
469		610 to
713		727 to
657		692 to
803		642 to
847		746 to
698		714 to
556		695 to
544		539 to
646		580 to
400
Joe Biden10/4/0750 to
707		 689 to
666		695 to
518		634 to
727		792 to
527		715 to
586		658 to
403		395 to
725		433 to
801		508 to
558		744 to
458		775 to
476		759 to
677		799 to
618
Jo Jorgensen11/3/0805 to
584		666 to
689		 647 to
365		568 to
540		738 to
340		522 to
410		644 to
489		569 to
783		482 to
717		630 to
623		700 to
397		729 to
414		652 to
451		788 to
451
Howie Hawkins2/12/0615 to
730		518 to
695		365 to
647		 352 to
685		519 to
476		413 to
569		454 to
498		317 to
791		301 to
801		439 to
560		496 to
481		522 to
536		490 to
646		579 to
638
Tulsi Gabbard11/3/0727 to
613		727 to
634		540 to
568		685 to
352		 701 to
331		563 to
473		689 to
408		575 to
739		500 to
674		647 to
559		707 to
330		735 to
383		595 to
509		728 to
491
Dan Crenshaw0/14/0469 to
642		527 to
792		340 to
738		476 to
519		331 to
701		 324 to
591		457 to
573		473 to
845		376 to
832		510 to
667		438 to
463		457 to
505		333 to
609		440 to
511
Justin Amash8/6/0713 to
610		586 to
715		410 to
522		569 to
413		473 to
563		591 to
324		 528 to
507		517 to
780		426 to
734		546 to
634		569 to
381		618 to
414		543 to
436		681 to
468
Amy Klobuchar5/9/0657 to
727		403 to
658		489 to
644		498 to
454		408 to
689		573 to
457		507 to
528		 336 to
799		268 to
815		369 to
573		529 to
386		572 to
458		545 to
641		625 to
618
Bernie Sanders14/0/0803 to
692		725 to
395		783 to
569		791 to
317		739 to
575		845 to
473		780 to
517		799 to
336		 608 to
560		700 to
299		816 to
405		826 to
443		785 to
604		823 to
585
Andrew Yang13/1/0847 to
642		801 to
433		717 to
482		801 to
301		674 to
500		832 to
376		734 to
426		815 to
268		560 to
608		 701 to
396		851 to
294		855 to
352		743 to
516		834 to
533
Elizabeth Warren9/5/0698 to
746		558 to
508		623 to
630		560 to
439		559 to
647		667 to
510		634 to
546		573 to
369		299 to
700		396 to
701		 635 to
415		656 to
494		654 to
646		698 to
647
John Kasich2/12/0556 to
714		458 to
744		397 to
700		481 to
496		330 to
707		463 to
438		381 to
569		386 to
529		405 to
816		294 to
851		415 to
635		 419 to
368		424 to
597		520 to
573
Jeb Bush2/12/0544 to
695		476 to
775		414 to
729		536 to
522		383 to
735		505 to
457		414 to
618		458 to
572		443 to
826		352 to
855		494 to
656		368 to
419		 395 to
594		486 to
537
Rand Paul7/7/0646 to
539		677 to
759		451 to
652		646 to
490		509 to
595		609 to
333		436 to
543		641 to
545		604 to
785		516 to
743		646 to
654		597 to
424		594 to
395		 613 to
355
Ted Cruz4/10/0400 to
580		618 to
799		451 to
788		638 to
579		491 to
728		511 to
440		468 to
681		618 to
625		585 to
823		533 to
834		647 to
698		573 to
520		537 to
486		355 to
613

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
0866235.06%
119788.01%
218827.62%
320498.29%
417967.27%
522138.96%
613405.42%
713115.31%
811654.72%
98673.51%
1014425.84%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump719667476708373808367256
Joe Biden546132103125139133119132844985
Jo Jorgensen46214414115313616667787069161
Howie Hawkins6451631321451111588061563165
Tulsi Gabbard454112124170163206132117714949
Dan Crenshaw673153141167971517172533336
Justin Amash56713113714312016963586865126
Amy Klobuchar60913713218112416811687551919
Bernie Sanders5029611092899765108115123250
Andrew Yang39511211513313717612612612886113
Elizabeth Warren59312812595113102979210696100
John Kasich6571411441671471848755371117
Jeb Bush6231731651851451507557371918
Rand Paul53914612613110313994991067787
Ted Cruz678144113861021317589967360

Number of bullet votes: 50 (3.04%).
Number of "approval" votes: 24 (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