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 Trump408
Joe Biden309
Jo Jorgensen196
Howie Hawkins40
Tulsi Gabbard36
Dan Crenshaw16
Justin Amash54
Amy Klobuchar19
Bernie Sanders242
Andrew Yang56
Elizabeth Warren39
John Kasich17
Jeb Bush9
Rand Paul41
Ted Cruz31
TOTAL:1513

The winner is Donald Trump with 27.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump535
Joe Biden553
Jo Jorgensen448
Howie Hawkins253
Tulsi Gabbard391
Dan Crenshaw185
Justin Amash344
Amy Klobuchar241
Bernie Sanders618
Andrew Yang528
Elizabeth Warren442
John Kasich181
Jeb Bush162
Rand Paul410
Ted Cruz336
Ballots Cast:1513

The winner is Bernie Sanders with 40.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump357
Joe Biden148
Jo Jorgensen173
Howie Hawkins55
Tulsi Gabbard39
Dan Crenshaw27
Justin Amash84
Amy Klobuchar21
Bernie Sanders292
Andrew Yang100
Elizabeth Warren76
John Kasich22
Jeb Bush12
Rand Paul63
Ted Cruz44

Jeb Bush eliminated in this round.

Round 2:

Donald Trump358
Joe Biden148
Jo Jorgensen173
Howie Hawkins55
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Amy Klobuchar22
Bernie Sanders293
Andrew Yang100
Elizabeth Warren76
John Kasich25
Rand Paul63
Ted Cruz48

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump358
Joe Biden157
Jo Jorgensen175
Howie Hawkins57
Tulsi Gabbard40
Dan Crenshaw27
Justin Amash85
Bernie Sanders296
Andrew Yang102
Elizabeth Warren79
John Kasich26
Rand Paul63
Ted Cruz48

John Kasich eliminated in this round.

Round 4:

Donald Trump359
Joe Biden161
Jo Jorgensen176
Howie Hawkins57
Tulsi Gabbard44
Dan Crenshaw28
Justin Amash87
Bernie Sanders298
Andrew Yang104
Elizabeth Warren82
Rand Paul67
Ted Cruz50

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump362
Joe Biden162
Jo Jorgensen180
Howie Hawkins57
Tulsi Gabbard50
Justin Amash88
Bernie Sanders298
Andrew Yang105
Elizabeth Warren83
Rand Paul71
Ted Cruz57

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump365
Joe Biden168
Jo Jorgensen190
Howie Hawkins61
Justin Amash97
Bernie Sanders305
Andrew Yang111
Elizabeth Warren85
Rand Paul74
Ted Cruz57

Ted Cruz eliminated in this round.

Round 7:

Donald Trump392
Joe Biden170
Jo Jorgensen193
Howie Hawkins62
Justin Amash99
Bernie Sanders307
Andrew Yang113
Elizabeth Warren85
Rand Paul92

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump397
Joe Biden177
Jo Jorgensen197
Justin Amash99
Bernie Sanders347
Andrew Yang116
Elizabeth Warren88
Rand Paul92

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump397
Joe Biden195
Jo Jorgensen205
Justin Amash101
Bernie Sanders392
Andrew Yang131
Rand Paul92

Rand Paul eliminated in this round.

Round 10:

Donald Trump433
Joe Biden196
Jo Jorgensen221
Justin Amash127
Bernie Sanders394
Andrew Yang142

Justin Amash eliminated in this round.

Round 11:

Donald Trump444
Joe Biden200
Jo Jorgensen319
Bernie Sanders399
Andrew Yang151

Andrew Yang eliminated in this round.

Round 12:

Donald Trump456
Joe Biden230
Jo Jorgensen352
Bernie Sanders475

Joe Biden eliminated in this round.

Round 13:

Donald Trump475
Jo Jorgensen414
Bernie Sanders624

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump684
Bernie Sanders829

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 Trump0/14/0 711 to
801		535 to
977		685 to
827		587 to
926		642 to
871		561 to
952		691 to
822		684 to
829		616 to
897		726 to
787		678 to
835		675 to
838		539 to
974		636 to
877
Joe Biden5/9/0801 to
711		 669 to
843		718 to
794		651 to
862		790 to
723		727 to
786		755 to
758		598 to
915		507 to
1006		672 to
841		777 to
736		788 to
725		745 to
768		807 to
706
Jo Jorgensen14/0/0977 to
535		843 to
669		 926 to
586		837 to
676		1014 to
499		918 to
595		891 to
622		760 to
753		757 to
756		845 to
668		1022 to
491		1041 to
472		994 to
519		1015 to
498
Howie Hawkins10/4/0827 to
685		794 to
718		586 to
926		 678 to
835		862 to
651		802 to
711		832 to
681		669 to
844		625 to
888		823 to
690		867 to
646		872 to
641		823 to
690		857 to
656
Tulsi Gabbard13/1/0925 to
587		861 to
651		675 to
837		834 to
678		 1027 to
486		935 to
578		1014 to
499		787 to
726		808 to
705		923 to
590		1083 to
430		1078 to
435		935 to
578		991 to
522
Dan Crenshaw7/7/0870 to
642		722 to
790		498 to
1014		650 to
862		486 to
1027		 692 to
821		786 to
727		674 to
839		648 to
865		791 to
722		853 to
660		876 to
637		761 to
752		896 to
617
Justin Amash9/5/0951 to
561		785 to
727		594 to
918		710 to
802		578 to
935		821 to
692		 836 to
677		722 to
791		722 to
791		823 to
690		1014 to
499		1037 to
476		981 to
532		1019 to
494
Amy Klobuchar7/7/0821 to
691		757 to
755		621 to
891		680 to
832		499 to
1014		727 to
786		677 to
836		 684 to
829		578 to
935		820 to
693		948 to
565		949 to
564		855 to
658		895 to
618
Bernie Sanders11/3/0828 to
684		914 to
598		752 to
760		843 to
669		726 to
787		839 to
674		791 to
722		829 to
684		 748 to
765		923 to
590		934 to
579		937 to
576		886 to
627		892 to
621
Andrew Yang12/2/0896 to
616		1005 to
507		755 to
757		887 to
625		705 to
808		865 to
648		791 to
722		935 to
578		765 to
748		 998 to
515		1098 to
415		1083 to
430		955 to
558		976 to
537
Elizabeth Warren6/8/0786 to
726		840 to
672		667 to
845		689 to
823		590 to
923		722 to
791		690 to
823		693 to
820		590 to
923		515 to
998		 858 to
655		890 to
623		832 to
681		853 to
660
John Kasich4/10/0834 to
678		735 to
777		490 to
1022		645 to
867		430 to
1083		660 to
853		499 to
1014		565 to
948		579 to
934		415 to
1098		655 to
858		 953 to
560		804 to
709		912 to
601
Jeb Bush2/12/0837 to
675		724 to
788		471 to
1041		640 to
872		435 to
1078		637 to
876		476 to
1037		564 to
949		576 to
937		430 to
1083		623 to
890		560 to
953		 739 to
774		893 to
620
Rand Paul4/10/0973 to
539		767 to
745		518 to
994		689 to
823		578 to
935		752 to
761		532 to
981		658 to
855		627 to
886		558 to
955		681 to
832		709 to
804		774 to
739		 1048 to
465
Ted Cruz1/13/0876 to
636		705 to
807		497 to
1015		655 to
857		522 to
991		617 to
896		494 to
1019		618 to
895		621 to
892		537 to
976		660 to
853		601 to
912		620 to
893		465 to
1048

And the Condorcet winner is: Jo Jorgensen.

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 Trump5312 3.5
Joe Biden5083 3.4
Jo Jorgensen5687 3.8
Howie Hawkins4044 2.7
Tulsi Gabbard5244 3.5
Dan Crenshaw3727 2.5
Justin Amash5004 3.3
Amy Klobuchar4056 2.7
Bernie Sanders6570 4.3
Andrew Yang6319 4.2
Elizabeth Warren5156 3.4
John Kasich3572 2.4
Jeb Bush3510 2.3
Rand Paul5184 3.4
Ted Cruz4296 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 Trump5312
Joe Biden5083
Jo Jorgensen5687
Howie Hawkins4044
Tulsi Gabbard5244
Dan Crenshaw3727
Justin Amash5004
Amy Klobuchar4056
Bernie Sanders6570
Andrew Yang6319
Elizabeth Warren5156
John Kasich3572
Jeb Bush3510
Rand Paul5184
Ted Cruz4296

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 Sanders989
Andrew Yang962

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 Trump7/7/0 635 to
702		506 to
769		653 to
580		544 to
689		571 to
440		534 to
677		651 to
622		625 to
753		568 to
802		674 to
655		638 to
523		622 to
512		469 to
608		519 to
372
Joe Biden10/4/0702 to
635		 633 to
619		641 to
478		581 to
677		731 to
480		659 to
545		604 to
365		362 to
670		386 to
754		461 to
517		689 to
413		717 to
428		697 to
632		741 to
557
Jo Jorgensen11/3/0769 to
506		619 to
633		 628 to
333		541 to
500		706 to
304		500 to
382		612 to
456		540 to
717		460 to
676		600 to
577		674 to
360		697 to
367		618 to
413		757 to
386
Howie Hawkins2/12/0580 to
653		478 to
641		333 to
628		 323 to
646		482 to
443		383 to
543		422 to
473		290 to
726		277 to
761		409 to
520		467 to
448		490 to
491		453 to
610		543 to
574
Tulsi Gabbard11/3/0689 to
544		677 to
581		500 to
541		646 to
323		 661 to
307		525 to
450		645 to
380		532 to
682		462 to
635		601 to
522		668 to
304		693 to
346		553 to
480		690 to
438
Dan Crenshaw0/14/0440 to
571		480 to
731		304 to
706		443 to
482		307 to
661		 291 to
563		425 to
543		437 to
779		350 to
786		472 to
621		408 to
435		423 to
464		301 to
572		408 to
448
Justin Amash8/6/0677 to
534		545 to
659		382 to
500		543 to
383		450 to
525		563 to
291		 498 to
477		489 to
717		405 to
688		514 to
594		545 to
349		589 to
369		514 to
404		648 to
405
Amy Klobuchar5/9/0622 to
651		365 to
604		456 to
612		473 to
422		380 to
645		543 to
425		477 to
498		 313 to
734		242 to
774		338 to
532		498 to
354		539 to
413		510 to
605		593 to
552
Bernie Sanders14/0/0753 to
625		670 to
362		717 to
540		726 to
290		682 to
532		779 to
437		717 to
489		734 to
313		 551 to
524		642 to
273		753 to
373		765 to
404		725 to
570		765 to
534
Andrew Yang13/1/0802 to
568		754 to
386		676 to
460		761 to
277		635 to
462		786 to
350		688 to
405		774 to
242		524 to
551		 656 to
362		804 to
270		814 to
317		696 to
485		788 to
472
Elizabeth Warren9/5/0655 to
674		517 to
461		577 to
600		520 to
409		522 to
601		621 to
472		594 to
514		532 to
338		273 to
642		362 to
656		 594 to
378		614 to
447		611 to
608		654 to
583
John Kasich2/12/0523 to
638		413 to
689		360 to
674		448 to
467		304 to
668		435 to
408		349 to
545		354 to
498		373 to
753		270 to
804		378 to
594		 392 to
332		390 to
562		489 to
507
Jeb Bush2/12/0512 to
622		428 to
717		367 to
697		491 to
490		346 to
693		464 to
423		369 to
589		413 to
539		404 to
765		317 to
814		447 to
614		332 to
392		 357 to
558		452 to
479
Rand Paul7/7/0608 to
469		632 to
697		413 to
618		610 to
453		480 to
553		572 to
301		404 to
514		605 to
510		570 to
725		485 to
696		608 to
611		562 to
390		558 to
357		 578 to
297
Ted Cruz4/10/0372 to
519		557 to
741		386 to
757		574 to
543		438 to
690		448 to
408		405 to
648		552 to
593		534 to
765		472 to
788		583 to
654		507 to
489		479 to
452		297 to
578

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
0803935.42%
118268.05%
216507.27%
318368.09%
416177.12%
519828.73%
612445.48%
712365.45%
810944.82%
98263.64%
1013455.93%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump682577072607664747357228
Joe Biden50611892115127118111127804772
Jo Jorgensen41713111914212014963766769160
Howie Hawkins601151114129991427455533164
Tulsi Gabbard414102115150151188123112694643
Dan Crenshaw631142125144901346568503331
Justin Amash52112411412910514963546664124
Amy Klobuchar56212311616411615710582531817
Bernie Sanders46588948579875999108113236
Andrew Yang35610110211812315812212111983110
Elizabeth Warren550118108831009191851019195
John Kasich6151311261501321638153351116
Jeb Bush5821651491621321377050321816
Rand Paul4981371081138812588971037680
Ted Cruz6391389880951086583856953

Number of bullet votes: 45 (2.97%).
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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