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 Trump337
Joe Biden290
Jo Jorgensen195
Howie Hawkins35
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash52
Amy Klobuchar17
Bernie Sanders228
Andrew Yang55
Elizabeth Warren35
John Kasich15
Jeb Bush8
Rand Paul39
Ted Cruz27
TOTAL:1384

The winner is Donald Trump with 24.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump459
Joe Biden522
Jo Jorgensen437
Howie Hawkins237
Tulsi Gabbard374
Dan Crenshaw172
Justin Amash331
Amy Klobuchar222
Bernie Sanders584
Andrew Yang510
Elizabeth Warren417
John Kasich166
Jeb Bush139
Rand Paul391
Ted Cruz300
Ballots Cast:1384

The winner is Bernie Sanders with 42.2% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump299
Joe Biden133
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash82
Amy Klobuchar20
Bernie Sanders274
Andrew Yang97
Elizabeth Warren71
John Kasich20
Jeb Bush9
Rand Paul59
Ted Cruz39

Jeb Bush eliminated in this round.

Round 2:

Donald Trump300
Joe Biden133
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders275
Andrew Yang97
Elizabeth Warren71
John Kasich22
Rand Paul59
Ted Cruz43

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump300
Joe Biden141
Jo Jorgensen173
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Bernie Sanders278
Andrew Yang98
Elizabeth Warren74
John Kasich23
Rand Paul59
Ted Cruz43

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump301
Joe Biden142
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard44
Justin Amash84
Bernie Sanders278
Andrew Yang99
Elizabeth Warren74
John Kasich25
Rand Paul61
Ted Cruz48

John Kasich eliminated in this round.

Round 5:

Donald Trump302
Joe Biden146
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard48
Justin Amash86
Bernie Sanders280
Andrew Yang101
Elizabeth Warren76
Rand Paul66
Ted Cruz51

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump305
Joe Biden152
Jo Jorgensen187
Howie Hawkins54
Justin Amash95
Bernie Sanders287
Andrew Yang106
Elizabeth Warren78
Rand Paul69
Ted Cruz51

Ted Cruz eliminated in this round.

Round 7:

Donald Trump329
Joe Biden154
Jo Jorgensen190
Howie Hawkins55
Justin Amash96
Bernie Sanders289
Andrew Yang107
Elizabeth Warren78
Rand Paul86

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump332
Joe Biden160
Jo Jorgensen192
Justin Amash96
Bernie Sanders327
Andrew Yang110
Elizabeth Warren81
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump332
Joe Biden178
Jo Jorgensen199
Justin Amash97
Bernie Sanders369
Andrew Yang123
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump365
Joe Biden179
Jo Jorgensen215
Justin Amash122
Bernie Sanders370
Andrew Yang133

Justin Amash eliminated in this round.

Round 11:

Donald Trump373
Joe Biden183
Jo Jorgensen312
Bernie Sanders374
Andrew Yang142

Andrew Yang eliminated in this round.

Round 12:

Donald Trump384
Joe Biden212
Jo Jorgensen344
Bernie Sanders444

Joe Biden eliminated in this round.

Round 13:

Donald Trump401
Jo Jorgensen402
Bernie Sanders581

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen695
Bernie Sanders689

And the winner is: Jo Jorgensen

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 Trump0/14/0 631 to
753		454 to
930		605 to
779		508 to
876		565 to
819		480 to
904		608 to
776		606 to
778		537 to
847		641 to
743		595 to
789		593 to
791		460 to
924		553 to
831
Joe Biden6/7/1753 to
631		 621 to
763		674 to
710		603 to
781		736 to
648		676 to
708		705 to
679		555 to
829		461 to
923		622 to
762		724 to
660		737 to
647		692 to
692		750 to
634
Jo Jorgensen13/1/0930 to
454		763 to
621		 858 to
526		770 to
614		948 to
436		845 to
539		818 to
566		695 to
689		689 to
695		775 to
609		940 to
444		969 to
415		920 to
464		951 to
433
Howie Hawkins10/4/0779 to
605		710 to
674		526 to
858		 596 to
788		787 to
597		717 to
667		756 to
628		599 to
785		552 to
832		745 to
639		784 to
600		800 to
584		742 to
642		790 to
594
Tulsi Gabbard13/1/0876 to
508		781 to
603		614 to
770		788 to
596		 956 to
428		852 to
532		937 to
447		712 to
672		727 to
657		839 to
545		996 to
388		1001 to
383		856 to
528		918 to
466
Dan Crenshaw6/8/0819 to
565		648 to
736		436 to
948		597 to
787		428 to
956		 609 to
775		710 to
674		599 to
785		569 to
815		710 to
674		765 to
619		797 to
587		674 to
710		817 to
567
Justin Amash9/5/0904 to
480		708 to
676		539 to
845		667 to
717		532 to
852		775 to
609		 767 to
617		657 to
727		649 to
735		747 to
637		925 to
459		958 to
426		901 to
483		950 to
434
Amy Klobuchar6/8/0776 to
608		679 to
705		566 to
818		628 to
756		447 to
937		674 to
710		617 to
767		 611 to
773		502 to
882		732 to
652		859 to
525		866 to
518		771 to
613		821 to
563
Bernie Sanders11/3/0778 to
606		829 to
555		689 to
695		785 to
599		672 to
712		785 to
599		727 to
657		773 to
611		 671 to
713		846 to
538		857 to
527		859 to
525		802 to
582		818 to
566
Andrew Yang13/1/0847 to
537		923 to
461		695 to
689		832 to
552		657 to
727		815 to
569		735 to
649		882 to
502		713 to
671		 920 to
464		1007 to
377		995 to
389		870 to
514		903 to
481
Elizabeth Warren6/8/0743 to
641		762 to
622		609 to
775		639 to
745		545 to
839		674 to
710		637 to
747		652 to
732		538 to
846		464 to
920		 779 to
605		810 to
574		749 to
635		781 to
603
John Kasich4/10/0789 to
595		660 to
724		444 to
940		600 to
784		388 to
996		619 to
765		459 to
925		525 to
859		527 to
857		377 to
1007		605 to
779		 878 to
506		724 to
660		841 to
543
Jeb Bush2/12/0791 to
593		647 to
737		415 to
969		584 to
800		383 to
1001		587 to
797		426 to
958		518 to
866		525 to
859		389 to
995		574 to
810		506 to
878		 651 to
733		821 to
563
Rand Paul4/9/1924 to
460		692 to
692		464 to
920		642 to
742		528 to
856		710 to
674		483 to
901		613 to
771		582 to
802		514 to
870		635 to
749		660 to
724		733 to
651		 982 to
402
Ted Cruz1/13/0831 to
553		634 to
750		433 to
951		594 to
790		466 to
918		567 to
817		434 to
950		563 to
821		566 to
818		481 to
903		603 to
781		543 to
841		563 to
821		402 to
982

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 Trump4593 3.3
Joe Biden4705 3.4
Jo Jorgensen5367 3.9
Howie Hawkins3697 2.7
Tulsi Gabbard4893 3.5
Dan Crenshaw3374 2.4
Justin Amash4697 3.4
Amy Klobuchar3699 2.7
Bernie Sanders6106 4.4
Andrew Yang5887 4.3
Elizabeth Warren4759 3.4
John Kasich3214 2.3
Jeb Bush3124 2.3
Rand Paul4810 3.5
Ted Cruz3867 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 Trump4593
Joe Biden4705
Jo Jorgensen5367
Howie Hawkins3697
Tulsi Gabbard4893
Dan Crenshaw3374
Justin Amash4697
Amy Klobuchar3699
Bernie Sanders6106
Andrew Yang5887
Elizabeth Warren4759
John Kasich3214
Jeb Bush3124
Rand Paul4810
Ted Cruz3867

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 Sanders904
Andrew Yang872

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 Trump5/9/0 557 to
667		424 to
738		575 to
547		465 to
660		495 to
414		452 to
649		572 to
585		550 to
708		494 to
759		595 to
620		558 to
492		545 to
479		395 to
577		447 to
355
Joe Biden10/4/0667 to
557		 587 to
574		596 to
429		535 to
626		685 to
432		611 to
502		559 to
323		332 to
618		351 to
697		421 to
472		644 to
362		675 to
372		649 to
580		690 to
501
Jo Jorgensen11/3/0738 to
424		574 to
587		 595 to
301		513 to
467		668 to
267		466 to
360		580 to
416		512 to
661		439 to
628		572 to
534		645 to
323		671 to
323		585 to
374		723 to
330
Howie Hawkins3/11/0547 to
575		429 to
596		301 to
595		 294 to
616		452 to
410		350 to
514		390 to
438		263 to
676		256 to
710		375 to
482		438 to
415		465 to
449		419 to
574		511 to
519
Tulsi Gabbard11/3/0660 to
465		626 to
535		467 to
513		616 to
294		 627 to
277		491 to
426		610 to
344		501 to
631		437 to
585		567 to
479		640 to
270		664 to
308		516 to
449		653 to
392
Dan Crenshaw0/14/0414 to
495		432 to
685		267 to
668		410 to
452		277 to
627		 257 to
533		386 to
504		400 to
727		326 to
731		435 to
579		381 to
398		395 to
421		272 to
537		375 to
401
Justin Amash8/6/0649 to
452		502 to
611		360 to
466		514 to
350		426 to
491		533 to
257		 470 to
438		461 to
666		388 to
638		485 to
548		520 to
309		566 to
326		487 to
370		619 to
354
Amy Klobuchar6/8/0585 to
572		323 to
559		416 to
580		438 to
390		344 to
610		504 to
386		438 to
470		 283 to
682		222 to
725		310 to
503		469 to
319		511 to
371		475 to
565		555 to
501
Bernie Sanders14/0/0708 to
550		618 to
332		661 to
512		676 to
263		631 to
501		727 to
400		666 to
461		682 to
283		 512 to
480		598 to
245		705 to
339		716 to
364		674 to
537		718 to
487
Andrew Yang13/1/0759 to
494		697 to
351		628 to
439		710 to
256		585 to
437		731 to
326		638 to
388		725 to
222		480 to
512		 610 to
331		761 to
244		766 to
283		644 to
457		739 to
429
Elizabeth Warren9/5/0620 to
595		472 to
421		534 to
572		482 to
375		479 to
567		579 to
435		548 to
485		503 to
310		245 to
598		331 to
610		 556 to
342		578 to
403		569 to
572		612 to
532
John Kasich2/12/0492 to
558		362 to
644		323 to
645		415 to
438		270 to
640		398 to
381		309 to
520		319 to
469		339 to
705		244 to
761		342 to
556		 362 to
299		355 to
531		454 to
458
Jeb Bush1/13/0479 to
545		372 to
675		323 to
671		449 to
465		308 to
664		421 to
395		326 to
566		371 to
511		364 to
716		283 to
766		403 to
578		299 to
362		 318 to
528		415 to
434
Rand Paul8/6/0577 to
395		580 to
649		374 to
585		574 to
419		449 to
516		537 to
272		370 to
487		565 to
475		537 to
674		457 to
644		572 to
569		531 to
355		528 to
318		 544 to
253
Ted Cruz4/10/0355 to
447		501 to
690		330 to
723		519 to
511		392 to
653		401 to
375		354 to
619		501 to
555		487 to
718		429 to
739		532 to
612		458 to
454		434 to
415		253 to
544

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
0742635.77%
116648.02%
214547.00%
316417.90%
414657.06%
517858.60%
611435.51%
711215.40%
810104.87%
97833.77%
1012686.11%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump649556470547253656049193
Joe Biden45610780108120107104118734566
Jo Jorgensen37211810413110513359726467159
Howie Hawkins558137102113891276949512960
Tulsi Gabbard37491100132141172116107644542
Dan Crenshaw593128108126811216062453129
Justin Amash472112991189213458516560123
Amy Klobuchar523111991471081439973481716
Bernie Sanders42781817271725688100109227
Andrew Yang321899210411314411210911281107
Elizabeth Warren508108947290778675968791
John Kasich5741201141341181487545311114
Jeb Bush5461531331501221215743281516
Rand Paul4571239995791118192967576
Ted Cruz5961318569821035872776249

Number of bullet votes: 37 (2.67%).
Number of "approval" votes: 18 (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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