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 Trump469
Joe Biden336
Jo Jorgensen197
Howie Hawkins43
Tulsi Gabbard38
Dan Crenshaw17
Justin Amash55
Amy Klobuchar21
Bernie Sanders262
Andrew Yang58
Elizabeth Warren41
John Kasich17
Jeb Bush10
Rand Paul47
Ted Cruz32
TOTAL:1643

The winner is Donald Trump with 28.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump598
Joe Biden593
Jo Jorgensen454
Howie Hawkins266
Tulsi Gabbard409
Dan Crenshaw198
Justin Amash351
Amy Klobuchar260
Bernie Sanders666
Andrew Yang546
Elizabeth Warren465
John Kasich188
Jeb Bush182
Rand Paul431
Ted Cruz382
Ballots Cast:1643

The winner is Bernie Sanders with 40.5% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump412
Joe Biden167
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard41
Dan Crenshaw28
Justin Amash85
Amy Klobuchar22
Bernie Sanders318
Andrew Yang103
Elizabeth Warren79
John Kasich24
Jeb Bush14
Rand Paul71
Ted Cruz47

Jeb Bush eliminated in this round.

Round 2:

Donald Trump414
Joe Biden167
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash86
Amy Klobuchar23
Bernie Sanders319
Andrew Yang103
Elizabeth Warren79
John Kasich27
Rand Paul72
Ted Cruz51

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump414
Joe Biden176
Jo Jorgensen177
Howie Hawkins59
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash86
Bernie Sanders322
Andrew Yang105
Elizabeth Warren83
John Kasich28
Rand Paul72
Ted Cruz51

Eliminated in this round:

Round 4:

Donald Trump419
Joe Biden182
Jo Jorgensen182
Howie Hawkins59
Tulsi Gabbard53
Justin Amash89
Bernie Sanders324
Andrew Yang108
Elizabeth Warren87
Rand Paul80
Ted Cruz60

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump422
Joe Biden188
Jo Jorgensen193
Howie Hawkins63
Justin Amash98
Bernie Sanders331
Andrew Yang114
Elizabeth Warren89
Rand Paul84
Ted Cruz61

Ted Cruz eliminated in this round.

Round 6:

Donald Trump450
Joe Biden190
Jo Jorgensen197
Howie Hawkins64
Justin Amash100
Bernie Sanders333
Andrew Yang116
Elizabeth Warren89
Rand Paul104

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump455
Joe Biden197
Jo Jorgensen202
Justin Amash100
Bernie Sanders373
Andrew Yang120
Elizabeth Warren92
Rand Paul104

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump455
Joe Biden216
Jo Jorgensen210
Justin Amash102
Bernie Sanders418
Andrew Yang138
Rand Paul104

Justin Amash eliminated in this round.

Round 9:

Donald Trump458
Joe Biden219
Jo Jorgensen261
Bernie Sanders423
Andrew Yang146
Rand Paul136

Rand Paul eliminated in this round.

Round 10:

Donald Trump507
Joe Biden222
Jo Jorgensen328
Bernie Sanders425
Andrew Yang161

Andrew Yang eliminated in this round.

Round 11:

Donald Trump519
Joe Biden254
Jo Jorgensen362
Bernie Sanders508

Joe Biden eliminated in this round.

Round 12:

Donald Trump544
Jo Jorgensen430
Bernie Sanders669

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump763
Bernie Sanders880

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
852		611 to
1031		766 to
876		663 to
980		721 to
922		637 to
1006		771 to
872		763 to
880		696 to
947		806 to
837		758 to
885		758 to
885		610 to
1033		716 to
927
Joe Biden5/9/0852 to
790		 724 to
918		776 to
866		707 to
936		851 to
792		787 to
856		813 to
830		647 to
996		560 to
1083		734 to
909		838 to
805		847 to
796		807 to
836		867 to
776
Jo Jorgensen13/1/01031 to
611		918 to
724		 997 to
645		905 to
738		1083 to
560		992 to
651		959 to
684		815 to
828		827 to
816		918 to
725		1101 to
542		1118 to
525		1063 to
580		1082 to
561
Howie Hawkins10/4/0876 to
766		866 to
776		645 to
997		 748 to
895		937 to
706		887 to
756		909 to
734		728 to
915		700 to
943		899 to
744		952 to
691		950 to
693		898 to
745		922 to
721
Tulsi Gabbard13/1/0979 to
663		935 to
707		737 to
905		894 to
748		 1104 to
539		1023 to
620		1096 to
547		850 to
793		885 to
758		1008 to
635		1174 to
469		1158 to
485		1012 to
631		1058 to
585
Dan Crenshaw7/7/0921 to
721		791 to
851		559 to
1083		705 to
937		539 to
1104		 774 to
869		869 to
774		739 to
904		723 to
920		871 to
772		940 to
703		957 to
686		841 to
802		962 to
681
Justin Amash9/5/01005 to
637		855 to
787		650 to
992		755 to
887		620 to
1023		869 to
774		 906 to
737		780 to
863		794 to
849		899 to
744		1100 to
543		1121 to
522		1055 to
588		1085 to
558
Amy Klobuchar7/7/0871 to
771		829 to
813		683 to
959		733 to
909		547 to
1096		774 to
869		737 to
906		 741 to
902		644 to
999		891 to
752		1027 to
616		1024 to
619		926 to
717		960 to
683
Bernie Sanders13/1/0879 to
763		995 to
647		827 to
815		914 to
728		793 to
850		904 to
739		863 to
780		902 to
741		 826 to
817		1015 to
628		1021 to
622		1016 to
627		966 to
677		964 to
679
Andrew Yang11/3/0946 to
696		1082 to
560		815 to
827		942 to
700		758 to
885		920 to
723		849 to
794		999 to
644		817 to
826		 1081 to
562		1186 to
457		1167 to
476		1030 to
613		1043 to
600
Elizabeth Warren6/8/0836 to
806		908 to
734		724 to
918		743 to
899		635 to
1008		772 to
871		744 to
899		752 to
891		628 to
1015		562 to
1081		 936 to
707		966 to
677		908 to
735		915 to
728
John Kasich4/10/0884 to
758		804 to
838		541 to
1101		690 to
952		469 to
1174		703 to
940		543 to
1100		616 to
1027		622 to
1021		457 to
1186		707 to
936		 1032 to
611		880 to
763		971 to
672
Jeb Bush2/12/0884 to
758		795 to
847		524 to
1118		692 to
950		485 to
1158		686 to
957		522 to
1121		619 to
1024		627 to
1016		476 to
1167		677 to
966		611 to
1032		 815 to
828		956 to
687
Rand Paul4/10/01032 to
610		835 to
807		579 to
1063		744 to
898		631 to
1012		802 to
841		588 to
1055		717 to
926		677 to
966		613 to
1030		735 to
908		763 to
880		828 to
815		 1111 to
532
Ted Cruz1/13/0926 to
716		775 to
867		560 to
1082		720 to
922		585 to
1058		681 to
962		558 to
1085		683 to
960		679 to
964		600 to
1043		728 to
915		672 to
971		687 to
956		532 to
1111

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 Trump5956 3.6
Joe Biden5522 3.4
Jo Jorgensen5979 3.6
Howie Hawkins4368 2.7
Tulsi Gabbard5648 3.4
Dan Crenshaw4085 2.5
Justin Amash5319 3.2
Amy Klobuchar4376 2.7
Bernie Sanders7088 4.3
Andrew Yang6726 4.1
Elizabeth Warren5552 3.4
John Kasich3903 2.4
Jeb Bush3877 2.4
Rand Paul5552 3.4
Ted Cruz4784 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 Trump5956
Joe Biden5522
Jo Jorgensen5979
Howie Hawkins4368
Tulsi Gabbard5648
Dan Crenshaw4085
Justin Amash5319
Amy Klobuchar4376
Bernie Sanders7088
Andrew Yang6726
Elizabeth Warren5552
John Kasich3903
Jeb Bush3877
Rand Paul5552
Ted Cruz4784

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 Sanders1084
Andrew Yang1037

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
748		584 to
803		730 to
614		612 to
725		641 to
469		609 to
712		726 to
656		691 to
801		642 to
846		746 to
697		713 to
555		694 to
543		538 to
644		579 to
400
Joe Biden10/4/0748 to
707		 688 to
664		694 to
518		631 to
726		789 to
527		712 to
585		655 to
403		394 to
723		431 to
801		506 to
558		741 to
458		772 to
476		756 to
676		796 to
618
Jo Jorgensen11/3/0803 to
584		664 to
688		 645 to
365		566 to
540		735 to
340		520 to
409		641 to
489		567 to
782		480 to
717		628 to
623		697 to
397		726 to
414		650 to
450		785 to
451
Howie Hawkins2/12/0614 to
730		518 to
694		365 to
645		 350 to
684		517 to
476		411 to
568		452 to
498		316 to
789		300 to
801		438 to
560		494 to
481		520 to
536		488 to
645		577 to
638
Tulsi Gabbard11/3/0725 to
612		726 to
631		540 to
566		684 to
350		 699 to
331		562 to
472		688 to
407		573 to
737		499 to
673		646 to
557		705 to
330		733 to
383		594 to
508		726 to
491
Dan Crenshaw0/14/0469 to
641		527 to
789		340 to
735		476 to
517		331 to
699		 324 to
590		457 to
572		472 to
842		376 to
830		510 to
665		438 to
462		457 to
504		333 to
607		440 to
511
Justin Amash8/6/0712 to
609		585 to
712		409 to
520		568 to
411		472 to
562		590 to
324		 527 to
506		515 to
778		425 to
732		545 to
632		568 to
380		617 to
413		543 to
435		680 to
468
Amy Klobuchar5/9/0656 to
726		403 to
655		489 to
641		498 to
452		407 to
688		572 to
457		506 to
527		 335 to
796		267 to
814		369 to
572		528 to
386		571 to
458		544 to
640		624 to
618
Bernie Sanders14/0/0801 to
691		723 to
394		782 to
567		789 to
316		737 to
573		842 to
472		778 to
515		796 to
335		 606 to
559		698 to
298		813 to
404		823 to
442		783 to
602		820 to
584
Andrew Yang13/1/0846 to
642		801 to
431		717 to
480		801 to
300		673 to
499		830 to
376		732 to
425		814 to
267		559 to
606		 701 to
395		849 to
294		853 to
352		741 to
515		832 to
533
Elizabeth Warren9/5/0697 to
746		558 to
506		623 to
628		560 to
438		557 to
646		665 to
510		632 to
545		572 to
369		298 to
698		395 to
701		 633 to
415		654 to
494		652 to
645		696 to
647
John Kasich2/12/0555 to
713		458 to
741		397 to
697		481 to
494		330 to
705		462 to
438		380 to
568		386 to
528		404 to
813		294 to
849		415 to
633		 419 to
368		423 to
596		519 to
573
Jeb Bush2/12/0543 to
694		476 to
772		414 to
726		536 to
520		383 to
733		504 to
457		413 to
617		458 to
571		442 to
823		352 to
853		494 to
654		368 to
419		 394 to
593		485 to
537
Rand Paul7/7/0644 to
538		676 to
756		450 to
650		645 to
488		508 to
594		607 to
333		435 to
543		640 to
544		602 to
783		515 to
741		645 to
652		596 to
423		593 to
394		 611 to
355
Ted Cruz4/10/0400 to
579		618 to
796		451 to
785		638 to
577		491 to
726		511 to
440		468 to
680		618 to
624		584 to
820		533 to
832		647 to
696		573 to
519		537 to
485		355 to
611

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
0864035.06%
119707.99%
218807.63%
320478.31%
417947.28%
521988.92%
613355.42%
713105.32%
811634.72%
98663.51%
1014425.85%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump717657476708273808367256
Joe Biden545131103125139133117132844985
Jo Jorgensen46214314115313616566777069161
Howie Hawkins6441621321451111577961563165
Tulsi Gabbard453112124169163205131117714949
Dan Crenshaw670153141167971507172533336
Justin Amash56513113714312016863586765126
Amy Klobuchar60713713218112416611687551919
Bernie Sanders5029511092879765108115122250
Andrew Yang39411111513213717512612612886113
Elizabeth Warren59212712595113100979210696100
John Kasich6551411431671471838755371117
Jeb Bush6211731641851451497557371918
Rand Paul53814512613110313894991057787
Ted Cruz675144113861021307589967360

Number of bullet votes: 50 (3.04%).
Number of "approval" votes: 24 (1%).

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