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 Biden341
Jo Jorgensen198
Howie Hawkins45
Tulsi Gabbard39
Dan Crenshaw17
Justin Amash56
Amy Klobuchar21
Bernie Sanders266
Andrew Yang58
Elizabeth Warren42
John Kasich17
Jeb Bush10
Rand Paul47
Ted Cruz34
TOTAL:1672

The winner is Donald Trump with 28.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump609
Joe Biden607
Jo Jorgensen455
Howie Hawkins270
Tulsi Gabbard411
Dan Crenshaw200
Justin Amash354
Amy Klobuchar262
Bernie Sanders678
Andrew Yang547
Elizabeth Warren474
John Kasich188
Jeb Bush185
Rand Paul435
Ted Cruz392
Ballots Cast:1672

The winner is Bernie Sanders with 40.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump420
Joe Biden168
Jo Jorgensen177
Howie Hawkins58
Tulsi Gabbard41
Dan Crenshaw28
Justin Amash86
Amy Klobuchar23
Bernie Sanders325
Andrew Yang103
Elizabeth Warren81
John Kasich26
Jeb Bush14
Rand Paul71
Ted Cruz51

Jeb Bush eliminated in this round.

Round 2:

Donald Trump422
Joe Biden168
Jo Jorgensen177
Howie Hawkins58
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash87
Amy Klobuchar24
Bernie Sanders326
Andrew Yang103
Elizabeth Warren81
John Kasich29
Rand Paul72
Ted Cruz55

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump422
Joe Biden177
Jo Jorgensen179
Howie Hawkins60
Tulsi Gabbard42
Dan Crenshaw28
Justin Amash87
Bernie Sanders330
Andrew Yang105
Elizabeth Warren85
John Kasich30
Rand Paul72
Ted Cruz55

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump426
Joe Biden178
Jo Jorgensen183
Howie Hawkins60
Tulsi Gabbard47
Justin Amash88
Bernie Sanders330
Andrew Yang106
Elizabeth Warren86
John Kasich32
Rand Paul75
Ted Cruz61

John Kasich eliminated in this round.

Round 5:

Donald Trump427
Joe Biden183
Jo Jorgensen184
Howie Hawkins61
Tulsi Gabbard53
Justin Amash90
Bernie Sanders332
Andrew Yang109
Elizabeth Warren89
Rand Paul80
Ted Cruz64

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump430
Joe Biden189
Jo Jorgensen195
Howie Hawkins65
Justin Amash99
Bernie Sanders339
Andrew Yang115
Elizabeth Warren91
Rand Paul84
Ted Cruz65

Eliminated in this round:

Round 7:

Donald Trump463
Joe Biden199
Jo Jorgensen204
Justin Amash102
Bernie Sanders382
Andrew Yang122
Elizabeth Warren96
Rand Paul104

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump464
Joe Biden220
Jo Jorgensen212
Justin Amash104
Bernie Sanders427
Andrew Yang141
Rand Paul104

Eliminated in this round:

Round 9:

Donald Trump516
Joe Biden228
Jo Jorgensen330
Bernie Sanders434
Andrew Yang164

Andrew Yang eliminated in this round.

Round 10:

Donald Trump528
Joe Biden260
Jo Jorgensen366
Bernie Sanders518

Joe Biden eliminated in this round.

Round 11:

Donald Trump553
Jo Jorgensen437
Bernie Sanders682

Jo Jorgensen eliminated in this round.

Round 12:

Donald Trump774
Bernie Sanders898

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 Trump0/14/0 801 to
870		621 to
1050		778 to
893		674 to
998		731 to
941		648 to
1024		782 to
890		774 to
898		707 to
965		817 to
855		769 to
903		770 to
902		622 to
1050		727 to
945
Joe Biden5/9/0870 to
801		 737 to
934		787 to
884		721 to
951		866 to
806		799 to
873		826 to
846		656 to
1016		575 to
1097		746 to
926		853 to
819		865 to
807		824 to
848		882 to
790
Jo Jorgensen13/1/01050 to
621		934 to
737		 1011 to
660		924 to
748		1104 to
568		1012 to
660		977 to
695		829 to
843		848 to
824		937 to
735		1120 to
552		1137 to
535		1086 to
586		1099 to
573
Howie Hawkins10/4/0893 to
778		884 to
787		660 to
1011		 771 to
901		960 to
712		910 to
762		932 to
740		745 to
927		726 to
946		920 to
752		976 to
696		973 to
699		923 to
749		938 to
734
Tulsi Gabbard13/1/0997 to
674		950 to
721		747 to
924		900 to
771		 1122 to
550		1042 to
630		1116 to
556		865 to
807		905 to
767		1029 to
643		1195 to
477		1179 to
493		1034 to
638		1074 to
598
Dan Crenshaw7/7/0940 to
731		805 to
866		567 to
1104		711 to
960		550 to
1122		 791 to
881		887 to
785		755 to
917		745 to
927		891 to
781		962 to
710		978 to
694		865 to
807		979 to
693
Justin Amash9/5/01023 to
648		872 to
799		659 to
1012		761 to
910		630 to
1042		881 to
791		 922 to
750		792 to
880		814 to
858		918 to
754		1120 to
552		1142 to
530		1079 to
593		1100 to
572
Amy Klobuchar7/7/0889 to
782		845 to
826		694 to
977		739 to
932		556 to
1116		785 to
887		750 to
922		 756 to
916		666 to
1006		909 to
763		1049 to
623		1045 to
627		950 to
722		975 to
697
Bernie Sanders13/1/0897 to
774		1015 to
656		842 to
829		926 to
745		807 to
865		917 to
755		880 to
792		916 to
756		 848 to
824		1038 to
634		1042 to
630		1038 to
634		989 to
683		979 to
693
Andrew Yang11/3/0964 to
707		1096 to
575		823 to
848		945 to
726		767 to
905		927 to
745		858 to
814		1006 to
666		824 to
848		 1094 to
578		1205 to
467		1187 to
485		1052 to
620		1059 to
613
Elizabeth Warren6/8/0854 to
817		925 to
746		734 to
937		751 to
920		643 to
1029		781 to
891		754 to
918		763 to
909		634 to
1038		578 to
1094		 957 to
715		985 to
687		932 to
740		931 to
741
John Kasich4/10/0902 to
769		818 to
853		551 to
1120		695 to
976		477 to
1195		710 to
962		552 to
1120		623 to
1049		630 to
1042		467 to
1205		715 to
957		 1054 to
618		901 to
771		988 to
684
Jeb Bush2/12/0901 to
770		806 to
865		534 to
1137		698 to
973		493 to
1179		694 to
978		530 to
1142		627 to
1045		634 to
1038		485 to
1187		687 to
985		618 to
1054		 833 to
839		970 to
702
Rand Paul4/10/01049 to
622		847 to
824		585 to
1086		748 to
923		638 to
1034		807 to
865		593 to
1079		722 to
950		683 to
989		620 to
1052		740 to
932		771 to
901		839 to
833		 1123 to
549
Ted Cruz1/13/0944 to
727		789 to
882		572 to
1099		733 to
938		598 to
1074		693 to
979		572 to
1100		697 to
975		693 to
979		613 to
1059		741 to
931		684 to
988		702 to
970		549 to
1123

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 Trump6057 3.6
Joe Biden5638 3.4
Jo Jorgensen6070 3.6
Howie Hawkins4481 2.7
Tulsi Gabbard5737 3.4
Dan Crenshaw4163 2.5
Justin Amash5419 3.2
Amy Klobuchar4483 2.7
Bernie Sanders7233 4.3
Andrew Yang6818 4.1
Elizabeth Warren5668 3.4
John Kasich3994 2.4
Jeb Bush3979 2.4
Rand Paul5657 3.4
Ted Cruz4888 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 Trump6057
Joe Biden5638
Jo Jorgensen6070
Howie Hawkins4481
Tulsi Gabbard5737
Dan Crenshaw4163
Justin Amash5419
Amy Klobuchar4483
Bernie Sanders7233
Andrew Yang6818
Elizabeth Warren5668
John Kasich3994
Jeb Bush3979
Rand Paul5657
Ted Cruz4888

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 Sanders1104
Andrew Yang1054

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 Trump7/7/0 717 to
761		594 to
813		740 to
627		622 to
735		651 to
477		620 to
723		736 to
668		703 to
813		651 to
857		754 to
712		723 to
566		704 to
553		549 to
655		587 to
408
Joe Biden10/4/0761 to
717		 702 to
674		706 to
527		644 to
735		804 to
534		726 to
593		668 to
412		401 to
737		441 to
809		516 to
569		757 to
466		787 to
484		771 to
684		809 to
628
Jo Jorgensen10/4/0813 to
594		674 to
702		 649 to
375		575 to
546		742 to
348		526 to
423		646 to
499		574 to
797		484 to
727		633 to
638		703 to
406		731 to
426		655 to
461		794 to
462
Howie Hawkins2/12/0627 to
740		527 to
706		375 to
649		 362 to
691		527 to
483		419 to
577		460 to
508		324 to
803		309 to
811		445 to
570		504 to
486		527 to
546		496 to
654		588 to
649
Tulsi Gabbard11/3/0735 to
622		735 to
644		546 to
575		691 to
362		 707 to
338		568 to
483		693 to
417		578 to
753		504 to
685		650 to
572		712 to
339		740 to
393		599 to
518		732 to
500
Dan Crenshaw0/14/0477 to
651		534 to
804		348 to
742		483 to
527		338 to
707		 330 to
601		461 to
582		479 to
857		380 to
841		513 to
678		442 to
470		459 to
516		337 to
618		444 to
519
Justin Amash8/6/0723 to
620		593 to
726		423 to
526		577 to
419		483 to
568		601 to
330		 536 to
514		523 to
792		434 to
743		551 to
645		579 to
386		627 to
423		551 to
444		689 to
478
Amy Klobuchar5/9/0668 to
736		412 to
668		499 to
646		508 to
460		417 to
693		582 to
461		514 to
536		 342 to
810		276 to
823		375 to
583		538 to
393		579 to
466		552 to
649		632 to
628
Bernie Sanders14/0/0813 to
703		737 to
401		797 to
574		803 to
324		753 to
578		857 to
479		792 to
523		810 to
342		 618 to
568		711 to
309		828 to
411		836 to
452		797 to
611		832 to
594
Andrew Yang13/1/0857 to
651		809 to
441		727 to
484		811 to
309		685 to
504		841 to
380		743 to
434		823 to
276		568 to
618		 707 to
405		861 to
302		862 to
362		751 to
523		841 to
542
Elizabeth Warren10/4/0712 to
754		569 to
516		638 to
633		570 to
445		572 to
650		678 to
513		645 to
551		583 to
375		309 to
711		405 to
707		 644 to
421		666 to
503		663 to
654		706 to
657
John Kasich2/12/0566 to
723		466 to
757		406 to
703		486 to
504		339 to
712		470 to
442		386 to
579		393 to
538		411 to
828		302 to
861		421 to
644		 422 to
376		429 to
604		527 to
581
Jeb Bush2/12/0553 to
704		484 to
787		426 to
731		546 to
527		393 to
740		516 to
459		423 to
627		466 to
579		452 to
836		362 to
862		503 to
666		376 to
422		 404 to
599		494 to
545
Rand Paul7/7/0655 to
549		684 to
771		461 to
655		654 to
496		518 to
599		618 to
337		444 to
551		649 to
552		611 to
797		523 to
751		654 to
663		604 to
429		599 to
404		 618 to
364
Ted Cruz4/10/0408 to
587		628 to
809		462 to
794		649 to
588		500 to
732		519 to
444		478 to
689		628 to
632		594 to
832		542 to
841		657 to
706		581 to
527		545 to
494		364 to
618

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
0872934.80%
120068.00%
219207.66%
321098.41%
418397.33%
522689.04%
613645.44%
713305.30%
811774.69%
98743.48%
1014645.84%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump729667577738574828369259
Joe Biden550133107126141138122134864986
Jo Jorgensen46614714416113916867797069162
Howie Hawkins6471651341531131638061573168
Tulsi Gabbard459113128176166210133117714950
Dan Crenshaw6781571441701011547273533337
Justin Amash57013513814512617664586865127
Amy Klobuchar61113913618512617311989551920
Bernie Sanders50397114949210168109117124253
Andrew Yang39911611713714117812812712986114
Elizabeth Warren59612912898117106999410797101
John Kasich6621431451751481888856371218
Jeb Bush6281751661901471537759382019
Rand Paul54414712913510614297991077888
Ted Cruz687144115871031337693997362

Number of bullet votes: 51 (3.05%).
Number of "approval" votes: 25 (1%).

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