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 Trump406
Joe Biden308
Jo Jorgensen195
Howie Hawkins40
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar19
Bernie Sanders241
Andrew Yang56
Elizabeth Warren39
John Kasich17
Jeb Bush9
Rand Paul41
Ted Cruz31
TOTAL:1508

The winner is Donald Trump with 26.9% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump533
Joe Biden552
Jo Jorgensen446
Howie Hawkins252
Tulsi Gabbard388
Dan Crenshaw185
Justin Amash342
Amy Klobuchar241
Bernie Sanders617
Andrew Yang527
Elizabeth Warren441
John Kasich180
Jeb Bush161
Rand Paul408
Ted Cruz336
Ballots Cast:1508

The winner is Bernie Sanders with 40.9% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump356
Joe Biden147
Jo Jorgensen172
Howie Hawkins55
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar21
Bernie Sanders291
Andrew Yang100
Elizabeth Warren76
John Kasich22
Jeb Bush12
Rand Paul63
Ted Cruz43

Jeb Bush eliminated in this round.

Round 2:

Donald Trump357
Joe Biden147
Jo Jorgensen172
Howie Hawkins55
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar22
Bernie Sanders292
Andrew Yang100
Elizabeth Warren76
John Kasich25
Rand Paul63
Ted Cruz47

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump357
Joe Biden156
Jo Jorgensen174
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders295
Andrew Yang102
Elizabeth Warren79
John Kasich26
Rand Paul63
Ted Cruz47

John Kasich eliminated in this round.

Round 4:

Donald Trump358
Joe Biden160
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard44
Dan Crenshaw28
Justin Amash87
Bernie Sanders297
Andrew Yang104
Elizabeth Warren82
Rand Paul67
Ted Cruz49

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump361
Joe Biden161
Jo Jorgensen179
Howie Hawkins57
Tulsi Gabbard50
Justin Amash88
Bernie Sanders297
Andrew Yang105
Elizabeth Warren83
Rand Paul71
Ted Cruz56

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump364
Joe Biden167
Jo Jorgensen189
Howie Hawkins61
Justin Amash97
Bernie Sanders304
Andrew Yang111
Elizabeth Warren85
Rand Paul74
Ted Cruz56

Ted Cruz eliminated in this round.

Round 7:

Donald Trump390
Joe Biden169
Jo Jorgensen192
Howie Hawkins62
Justin Amash99
Bernie Sanders306
Andrew Yang113
Elizabeth Warren85
Rand Paul92

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump395
Joe Biden176
Jo Jorgensen196
Justin Amash99
Bernie Sanders346
Andrew Yang116
Elizabeth Warren88
Rand Paul92

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump395
Joe Biden194
Jo Jorgensen204
Justin Amash101
Bernie Sanders391
Andrew Yang131
Rand Paul92

Rand Paul eliminated in this round.

Round 10:

Donald Trump431
Joe Biden195
Jo Jorgensen220
Justin Amash127
Bernie Sanders393
Andrew Yang142

Justin Amash eliminated in this round.

Round 11:

Donald Trump442
Joe Biden199
Jo Jorgensen318
Bernie Sanders398
Andrew Yang151

Andrew Yang eliminated in this round.

Round 12:

Donald Trump454
Joe Biden229
Jo Jorgensen351
Bernie Sanders474

Joe Biden eliminated in this round.

Round 13:

Donald Trump473
Jo Jorgensen412
Bernie Sanders623

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump682
Bernie Sanders826

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 Trump0/14/0 709 to
798		533 to
974		682 to
825		585 to
923		640 to
868		559 to
949		689 to
819		682 to
826		614 to
894		723 to
785		676 to
832		674 to
834		537 to
971		635 to
873
Joe Biden5/9/0798 to
709		 668 to
839		715 to
792		650 to
858		787 to
721		725 to
783		752 to
756		596 to
912		505 to
1003		670 to
838		775 to
733		786 to
722		743 to
765		805 to
703
Jo Jorgensen13/1/0974 to
533		839 to
668		 921 to
586		834 to
674		1010 to
498		914 to
594		887 to
621		757 to
751		753 to
755		842 to
666		1019 to
489		1039 to
469		990 to
518		1012 to
496
Howie Hawkins10/4/0825 to
682		792 to
715		586 to
921		 676 to
832		859 to
649		799 to
709		830 to
678		667 to
841		623 to
885		821 to
687		865 to
643		871 to
637		820 to
688		855 to
653
Tulsi Gabbard13/1/0922 to
585		857 to
650		673 to
834		831 to
676		 1023 to
485		931 to
577		1010 to
498		783 to
725		804 to
704		920 to
588		1079 to
429		1076 to
432		934 to
574		988 to
520
Dan Crenshaw7/7/0867 to
640		720 to
787		497 to
1010		648 to
859		485 to
1023		 690 to
818		784 to
724		671 to
837		646 to
862		789 to
719		852 to
656		874 to
634		759 to
749		892 to
616
Justin Amash9/5/0948 to
559		782 to
725		593 to
914		708 to
799		577 to
931		818 to
690		 834 to
674		720 to
788		721 to
787		821 to
687		1012 to
496		1035 to
473		980 to
528		1016 to
492
Amy Klobuchar7/7/0818 to
689		755 to
752		620 to
887		677 to
830		498 to
1010		724 to
784		674 to
834		 682 to
826		577 to
931		819 to
689		946 to
562		948 to
560		854 to
654		893 to
615
Bernie Sanders11/3/0825 to
682		911 to
596		750 to
757		840 to
667		725 to
783		837 to
671		788 to
720		826 to
682		 747 to
761		921 to
587		933 to
575		936 to
572		884 to
624		889 to
619
Andrew Yang13/1/0893 to
614		1002 to
505		754 to
753		884 to
623		704 to
804		862 to
646		787 to
721		931 to
577		761 to
747		 996 to
512		1097 to
411		1082 to
426		953 to
555		973 to
535
Elizabeth Warren6/8/0784 to
723		837 to
670		665 to
842		686 to
821		588 to
920		719 to
789		687 to
821		689 to
819		587 to
921		512 to
996		 856 to
652		889 to
619		830 to
678		851 to
657
John Kasich4/10/0831 to
676		732 to
775		488 to
1019		642 to
865		429 to
1079		656 to
852		496 to
1012		562 to
946		575 to
933		411 to
1097		652 to
856		 951 to
557		803 to
705		909 to
599
Jeb Bush2/12/0833 to
674		721 to
786		468 to
1039		636 to
871		432 to
1076		634 to
874		473 to
1035		560 to
948		572 to
936		426 to
1082		619 to
889		557 to
951		 737 to
771		890 to
618
Rand Paul4/10/0970 to
537		764 to
743		517 to
990		687 to
820		574 to
934		749 to
759		528 to
980		654 to
854		624 to
884		555 to
953		678 to
830		705 to
803		771 to
737		 1045 to
463
Ted Cruz1/13/0872 to
635		702 to
805		495 to
1012		652 to
855		520 to
988		616 to
892		492 to
1016		615 to
893		619 to
889		535 to
973		657 to
851		599 to
909		618 to
890		463 to
1045

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 Trump5290 3.5
Joe Biden5068 3.4
Jo Jorgensen5655 3.8
Howie Hawkins4026 2.7
Tulsi Gabbard5219 3.5
Dan Crenshaw3708 2.5
Justin Amash4978 3.3
Amy Klobuchar4043 2.7
Bernie Sanders6550 4.3
Andrew Yang6296 4.2
Elizabeth Warren5140 3.4
John Kasich3552 2.4
Jeb Bush3487 2.3
Rand Paul5160 3.4
Ted Cruz4285 2.8

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 Trump5290
Joe Biden5068
Jo Jorgensen5655
Howie Hawkins4026
Tulsi Gabbard5219
Dan Crenshaw3708
Justin Amash4978
Amy Klobuchar4043
Bernie Sanders6550
Andrew Yang6296
Elizabeth Warren5140
John Kasich3552
Jeb Bush3487
Rand Paul5160
Ted Cruz4285

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 Sanders987
Andrew Yang957

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 Trump7/7/0 633 to
700		504 to
766		650 to
578		542 to
686		569 to
437		532 to
674		649 to
619		623 to
750		566 to
799		671 to
653		636 to
520		620 to
509		467 to
605		517 to
371
Joe Biden10/4/0700 to
633		 633 to
615		639 to
475		580 to
673		730 to
477		658 to
541		602 to
363		361 to
667		385 to
750		459 to
516		688 to
409		716 to
425		696 to
628		739 to
555
Jo Jorgensen11/3/0766 to
504		615 to
633		 626 to
332		539 to
499		703 to
303		498 to
381		608 to
455		537 to
716		458 to
675		596 to
576		671 to
360		694 to
366		615 to
412		754 to
384
Howie Hawkins2/11/1578 to
650		475 to
639		332 to
626		 322 to
643		481 to
441		382 to
541		420 to
471		289 to
724		276 to
759		407 to
517		465 to
446		488 to
488		451 to
608		542 to
572
Tulsi Gabbard11/3/0686 to
542		673 to
580		499 to
539		643 to
322		 657 to
306		524 to
449		641 to
380		529 to
682		460 to
634		598 to
521		665 to
304		692 to
344		551 to
479		687 to
437
Dan Crenshaw0/14/0437 to
569		477 to
730		303 to
703		441 to
481		306 to
657		 290 to
560		422 to
542		435 to
777		349 to
784		470 to
619		407 to
432		422 to
461		300 to
569		405 to
447
Justin Amash8/6/0674 to
532		541 to
658		381 to
498		541 to
382		449 to
524		560 to
290		 495 to
477		487 to
717		404 to
687		511 to
593		542 to
348		587 to
368		513 to
404		646 to
404
Amy Klobuchar5/9/0619 to
649		363 to
602		455 to
608		471 to
420		380 to
641		542 to
422		477 to
495		 313 to
733		242 to
770		337 to
530		497 to
350		539 to
409		510 to
602		591 to
551
Bernie Sanders14/0/0750 to
623		667 to
361		716 to
537		724 to
289		682 to
529		777 to
435		717 to
487		733 to
313		 551 to
521		640 to
272		751 to
370		764 to
401		724 to
568		763 to
533
Andrew Yang13/1/0799 to
566		750 to
385		675 to
458		759 to
276		634 to
460		784 to
349		687 to
404		770 to
242		521 to
551		 652 to
361		802 to
268		812 to
315		694 to
484		785 to
471
Elizabeth Warren9/5/0653 to
671		516 to
459		576 to
596		517 to
407		521 to
598		619 to
470		593 to
511		530 to
337		272 to
640		361 to
652		 592 to
375		614 to
444		610 to
605		652 to
581
John Kasich2/12/0520 to
636		409 to
688		360 to
671		446 to
465		304 to
665		432 to
407		348 to
542		350 to
497		370 to
751		268 to
802		375 to
592		 391 to
329		389 to
559		486 to
505
Jeb Bush1/12/1509 to
620		425 to
716		366 to
694		488 to
488		344 to
692		461 to
422		368 to
587		409 to
539		401 to
764		315 to
812		444 to
614		329 to
391		 356 to
556		449 to
478
Rand Paul7/7/0605 to
467		628 to
696		412 to
615		608 to
451		479 to
551		569 to
300		404 to
513		602 to
510		568 to
724		484 to
694		605 to
610		559 to
389		556 to
356		 576 to
296
Ted Cruz4/10/0371 to
517		555 to
739		384 to
754		572 to
542		437 to
687		447 to
405		404 to
646		551 to
591		533 to
763		471 to
785		581 to
652		505 to
486		478 to
449		296 to
576

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
0803035.50%
118188.04%
216377.24%
318328.10%
416097.11%
519678.70%
612415.49%
712355.46%
810894.81%
98253.65%
1013375.91%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump680576972607664747357226
Joe Biden50411891115127117111127794772
Jo Jorgensen41713011914211914963766668159
Howie Hawkins600151112129981427455533163
Tulsi Gabbard414101115150150186123112694642
Dan Crenshaw631142124144871336568503331
Justin Amash52112311312910514863546564123
Amy Klobuchar56112311516211615610582531817
Bernie Sanders46488938479865999108113235
Andrew Yang35610010111812215812112111983109
Elizabeth Warren549117108831008891851019195
John Kasich6151301261491311628152351116
Jeb Bush5821641491621321356850321816
Rand Paul4981361071138812488971017680
Ted Cruz6381389580951076583856953

Number of bullet votes: 45 (2.98%).
Number of "approval" votes: 19 (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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