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 Trump481
Joe Biden344
Jo Jorgensen199
Howie Hawkins45
Tulsi Gabbard39
Dan Crenshaw17
Justin Amash56
Amy Klobuchar21
Bernie Sanders266
Andrew Yang59
Elizabeth Warren42
John Kasich17
Jeb Bush10
Rand Paul48
Ted Cruz34
TOTAL:1678

The winner is Donald Trump with 28.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump609
Joe Biden611
Jo Jorgensen457
Howie Hawkins271
Tulsi Gabbard412
Dan Crenshaw200
Justin Amash357
Amy Klobuchar265
Bernie Sanders681
Andrew Yang549
Elizabeth Warren477
John Kasich189
Jeb Bush185
Rand Paul436
Ted Cruz392
Ballots Cast:1678

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump420
Joe Biden170
Jo Jorgensen178
Howie Hawkins58
Tulsi Gabbard41
Dan Crenshaw28
Justin Amash86
Amy Klobuchar23
Bernie Sanders326
Andrew Yang104
Elizabeth Warren81
John Kasich26
Jeb Bush14
Rand Paul72
Ted Cruz51

Jeb Bush eliminated in this round.

Round 2:

Donald Trump422
Joe Biden170
Jo Jorgensen178
Howie Hawkins58
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash87
Amy Klobuchar24
Bernie Sanders327
Andrew Yang104
Elizabeth Warren81
John Kasich29
Rand Paul73
Ted Cruz55

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump422
Joe Biden179
Jo Jorgensen180
Howie Hawkins60
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash87
Bernie Sanders331
Andrew Yang106
Elizabeth Warren85
John Kasich30
Rand Paul73
Ted Cruz55

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump426
Joe Biden180
Jo Jorgensen184
Howie Hawkins60
Tulsi Gabbard47
Justin Amash88
Bernie Sanders331
Andrew Yang107
Elizabeth Warren86
John Kasich32
Rand Paul76
Ted Cruz61

John Kasich eliminated in this round.

Round 5:

Donald Trump427
Joe Biden185
Jo Jorgensen185
Howie Hawkins61
Tulsi Gabbard53
Justin Amash90
Bernie Sanders333
Andrew Yang110
Elizabeth Warren89
Rand Paul81
Ted Cruz64

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump430
Joe Biden191
Jo Jorgensen196
Howie Hawkins65
Justin Amash99
Bernie Sanders340
Andrew Yang116
Elizabeth Warren91
Rand Paul85
Ted Cruz65

Eliminated in this round:

Round 7:

Donald Trump463
Joe Biden201
Jo Jorgensen205
Justin Amash102
Bernie Sanders383
Andrew Yang123
Elizabeth Warren96
Rand Paul105

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump464
Joe Biden222
Jo Jorgensen213
Justin Amash104
Bernie Sanders428
Andrew Yang142
Rand Paul105

Justin Amash eliminated in this round.

Round 9:

Donald Trump467
Joe Biden227
Jo Jorgensen264
Bernie Sanders433
Andrew Yang150
Rand Paul137

Rand Paul eliminated in this round.

Round 10:

Donald Trump516
Joe Biden230
Jo Jorgensen332
Bernie Sanders435
Andrew Yang165

Andrew Yang eliminated in this round.

Round 11:

Donald Trump528
Joe Biden262
Jo Jorgensen368
Bernie Sanders520

Joe Biden eliminated in this round.

Round 12:

Donald Trump554
Jo Jorgensen440
Bernie Sanders684

Jo Jorgensen eliminated in this round.

Round 13:

Donald Trump775
Bernie Sanders903

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 Trump0/14/0 803 to
874		622 to
1055		779 to
898		675 to
1003		733 to
945		649 to
1029		783 to
895		775 to
903		709 to
969		818 to
860		771 to
907		772 to
906		623 to
1055		729 to
949
Joe Biden5/9/0874 to
803		 741 to
936		790 to
887		724 to
954		870 to
808		802 to
876		830 to
848		658 to
1020		578 to
1100		748 to
930		857 to
821		869 to
809		828 to
850		886 to
792
Jo Jorgensen13/1/01055 to
622		936 to
741		 1015 to
662		927 to
751		1109 to
569		1014 to
664		979 to
699		832 to
846		851 to
827		941 to
737		1125 to
553		1143 to
535		1090 to
588		1105 to
573
Howie Hawkins10/4/0898 to
779		887 to
790		662 to
1015		 774 to
904		965 to
713		913 to
765		936 to
742		747 to
931		731 to
947		923 to
755		981 to
697		978 to
700		927 to
751		944 to
734
Tulsi Gabbard13/1/01002 to
675		953 to
724		750 to
927		903 to
774		 1127 to
551		1045 to
633		1120 to
558		867 to
811		909 to
769		1032 to
646		1201 to
477		1184 to
494		1038 to
640		1080 to
598
Dan Crenshaw7/7/0944 to
733		807 to
870		568 to
1109		712 to
965		551 to
1127		 792 to
886		888 to
790		755 to
923		747 to
931		892 to
786		965 to
713		981 to
697		868 to
810		984 to
694
Justin Amash9/5/01028 to
649		875 to
802		663 to
1014		764 to
913		633 to
1045		886 to
792		 926 to
752		795 to
883		818 to
860		922 to
756		1126 to
552		1147 to
531		1084 to
594		1106 to
572
Amy Klobuchar7/7/0894 to
783		847 to
830		698 to
979		741 to
936		558 to
1120		790 to
888		752 to
926		 759 to
919		670 to
1008		913 to
765		1054 to
624		1051 to
627		955 to
723		981 to
697
Bernie Sanders13/1/0902 to
775		1019 to
658		845 to
832		930 to
747		811 to
867		923 to
755		883 to
795		919 to
759		 852 to
826		1042 to
636		1047 to
631		1044 to
634		994 to
684		985 to
693
Andrew Yang11/3/0968 to
709		1099 to
578		826 to
851		946 to
731		769 to
909		931 to
747		860 to
818		1008 to
670		826 to
852		 1098 to
580		1210 to
468		1192 to
486		1056 to
622		1064 to
614
Elizabeth Warren6/8/0859 to
818		929 to
748		736 to
941		754 to
923		646 to
1032		786 to
892		756 to
922		765 to
913		636 to
1042		580 to
1098		 961 to
717		991 to
687		937 to
741		937 to
741
John Kasich4/10/0906 to
771		820 to
857		552 to
1125		696 to
981		477 to
1201		713 to
965		552 to
1126		624 to
1054		631 to
1047		468 to
1210		717 to
961		 1057 to
621		905 to
773		993 to
685
Jeb Bush2/12/0905 to
772		808 to
869		534 to
1143		699 to
978		494 to
1184		697 to
981		531 to
1147		627 to
1051		634 to
1044		486 to
1192		687 to
991		621 to
1057		 837 to
841		975 to
703
Rand Paul4/10/01054 to
623		849 to
828		587 to
1090		750 to
927		640 to
1038		810 to
868		594 to
1084		723 to
955		684 to
994		622 to
1056		741 to
937		773 to
905		841 to
837		 1128 to
550
Ted Cruz1/13/0948 to
729		791 to
886		572 to
1105		733 to
944		598 to
1080		694 to
984		572 to
1106		697 to
981		693 to
985		614 to
1064		741 to
937		685 to
993		703 to
975		550 to
1128

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 Trump6067 3.6
Joe Biden5667 3.4
Jo Jorgensen6093 3.6
Howie Hawkins4499 2.7
Tulsi Gabbard5755 3.4
Dan Crenshaw4176 2.5
Justin Amash5444 3.2
Amy Klobuchar4514 2.7
Bernie Sanders7267 4.3
Andrew Yang6843 4.1
Elizabeth Warren5693 3.4
John Kasich4020 2.4
Jeb Bush3992 2.4
Rand Paul5681 3.4
Ted Cruz4900 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 Trump6067
Joe Biden5667
Jo Jorgensen6093
Howie Hawkins4499
Tulsi Gabbard5755
Dan Crenshaw4176
Justin Amash5444
Amy Klobuchar4514
Bernie Sanders7267
Andrew Yang6843
Elizabeth Warren5693
John Kasich4020
Jeb Bush3992
Rand Paul5681
Ted Cruz4900

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 Sanders1107
Andrew Yang1058

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 Trump7/7/0 718 to
765		595 to
816		740 to
631		622 to
737		652 to
479		621 to
726		736 to
673		704 to
817		651 to
861		755 to
715		723 to
570		704 to
554		549 to
659		587 to
409
Joe Biden10/4/0765 to
718		 706 to
676		709 to
529		647 to
736		808 to
534		729 to
595		670 to
413		403 to
741		444 to
811		518 to
572		759 to
467		791 to
485		774 to
685		813 to
629
Jo Jorgensen10/4/0816 to
595		676 to
706		 652 to
377		576 to
548		744 to
349		527 to
425		648 to
503		575 to
800		485 to
730		635 to
640		704 to
409		733 to
427		656 to
465		797 to
463
Howie Hawkins2/12/0631 to
740		529 to
709		377 to
652		 364 to
693		529 to
485		421 to
580		461 to
512		325 to
806		310 to
814		446 to
573		505 to
490		530 to
547		497 to
658		591 to
649
Tulsi Gabbard11/3/0737 to
622		736 to
647		548 to
576		693 to
364		 709 to
339		569 to
485		694 to
420		580 to
756		504 to
688		651 to
574		712 to
341		742 to
393		599 to
521		734 to
500
Dan Crenshaw0/14/0479 to
652		534 to
808		349 to
744		485 to
529		339 to
709		 331 to
604		461 to
587		480 to
861		380 to
844		514 to
681		442 to
474		460 to
517		337 to
622		446 to
520
Justin Amash8/6/0726 to
621		595 to
729		425 to
527		580 to
421		485 to
569		604 to
331		 538 to
517		525 to
795		435 to
746		553 to
646		581 to
387		630 to
424		553 to
446		692 to
479
Amy Klobuchar5/9/0673 to
736		413 to
670		503 to
648		512 to
461		420 to
694		587 to
461		517 to
538		 345 to
813		279 to
825		377 to
586		540 to
395		584 to
466		554 to
650		637 to
628
Bernie Sanders14/0/0817 to
704		741 to
403		800 to
575		806 to
325		756 to
580		861 to
480		795 to
525		813 to
345		 620 to
571		715 to
310		831 to
414		840 to
453		800 to
614		836 to
595
Andrew Yang13/1/0861 to
651		811 to
444		730 to
485		814 to
310		688 to
504		844 to
380		746 to
435		825 to
279		571 to
620		 709 to
406		863 to
304		866 to
362		753 to
526		845 to
542
Elizabeth Warren10/4/0715 to
755		572 to
518		640 to
635		573 to
446		574 to
651		681 to
514		646 to
553		586 to
377		310 to
715		406 to
709		 646 to
423		669 to
504		665 to
657		709 to
658
John Kasich2/12/0570 to
723		467 to
759		409 to
704		490 to
505		341 to
712		474 to
442		387 to
581		395 to
540		414 to
831		304 to
863		423 to
646		 426 to
376		431 to
605		531 to
581
Jeb Bush2/12/0554 to
704		485 to
791		427 to
733		547 to
530		393 to
742		517 to
460		424 to
630		466 to
584		453 to
840		362 to
866		504 to
669		376 to
426		 404 to
603		495 to
545
Rand Paul7/7/0659 to
549		685 to
774		465 to
656		658 to
497		521 to
599		622 to
337		446 to
553		650 to
554		614 to
800		526 to
753		657 to
665		605 to
431		603 to
404		 622 to
364
Ted Cruz4/10/0409 to
587		629 to
813		463 to
797		649 to
591		500 to
734		520 to
446		479 to
692		628 to
637		595 to
836		542 to
845		658 to
709		581 to
531		545 to
495		364 to
622

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
0876134.81%
120067.97%
219267.65%
321148.40%
418507.35%
522749.03%
613725.45%
713365.31%
811884.72%
98773.48%
1014665.82%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump732667677758574828369259
Joe Biden551133108127141138123134874987
Jo Jorgensen46814714416213916967807169162
Howie Hawkins6491651341531151658061573168
Tulsi Gabbard462113128176167210134117724950
Dan Crenshaw6811571451701011557373533337
Justin Amash57213513814612617664606965127
Amy Klobuchar61213913618612617312190552020
Bernie Sanders50497114959210268109119124254
Andrew Yang40111611813714117812912713087114
Elizabeth Warren59812912998117106999510997101
John Kasich6641431451751491888956391218
Jeb Bush6311751661901491547759382019
Rand Paul546147130135106142981001077988
Ted Cruz690144115871061337693997362

Number of bullet votes: 51 (3.04%).
Number of "approval" votes: 25 (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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