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 Trump341
Joe Biden292
Jo Jorgensen195
Howie Hawkins35
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders228
Andrew Yang55
Elizabeth Warren35
John Kasich15
Jeb Bush8
Rand Paul39
Ted Cruz27
TOTAL:1391

The winner is Donald Trump with 24.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump464
Joe Biden524
Jo Jorgensen437
Howie Hawkins237
Tulsi Gabbard375
Dan Crenshaw173
Justin Amash333
Amy Klobuchar223
Bernie Sanders585
Andrew Yang511
Elizabeth Warren418
John Kasich168
Jeb Bush140
Rand Paul392
Ted Cruz301
Ballots Cast:1391

The winner is Bernie Sanders with 42.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump303
Joe Biden134
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash83
Amy Klobuchar20
Bernie Sanders274
Andrew Yang97
Elizabeth Warren72
John Kasich20
Jeb Bush9
Rand Paul59
Ted Cruz39

Jeb Bush eliminated in this round.

Round 2:

Donald Trump304
Joe Biden134
Jo Jorgensen171
Howie Hawkins49
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Amy Klobuchar20
Bernie Sanders275
Andrew Yang97
Elizabeth Warren72
John Kasich22
Rand Paul59
Ted Cruz43

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump304
Joe Biden142
Jo Jorgensen173
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw22
Justin Amash84
Bernie Sanders278
Andrew Yang98
Elizabeth Warren75
John Kasich23
Rand Paul59
Ted Cruz43

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump305
Joe Biden143
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard44
Justin Amash85
Bernie Sanders278
Andrew Yang99
Elizabeth Warren75
John Kasich25
Rand Paul61
Ted Cruz48

John Kasich eliminated in this round.

Round 5:

Donald Trump306
Joe Biden147
Jo Jorgensen177
Howie Hawkins51
Tulsi Gabbard48
Justin Amash87
Bernie Sanders280
Andrew Yang101
Elizabeth Warren77
Rand Paul66
Ted Cruz51

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump309
Joe Biden153
Jo Jorgensen187
Howie Hawkins54
Justin Amash96
Bernie Sanders287
Andrew Yang106
Elizabeth Warren79
Rand Paul69
Ted Cruz51

Ted Cruz eliminated in this round.

Round 7:

Donald Trump333
Joe Biden155
Jo Jorgensen190
Howie Hawkins55
Justin Amash97
Bernie Sanders289
Andrew Yang107
Elizabeth Warren79
Rand Paul86

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump336
Joe Biden161
Jo Jorgensen192
Justin Amash97
Bernie Sanders327
Andrew Yang110
Elizabeth Warren82
Rand Paul86

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump336
Joe Biden179
Jo Jorgensen199
Justin Amash98
Bernie Sanders370
Andrew Yang123
Rand Paul86

Rand Paul eliminated in this round.

Round 10:

Donald Trump369
Joe Biden180
Jo Jorgensen215
Justin Amash123
Bernie Sanders371
Andrew Yang133

Justin Amash eliminated in this round.

Round 11:

Donald Trump378
Joe Biden184
Jo Jorgensen312
Bernie Sanders375
Andrew Yang142

Andrew Yang eliminated in this round.

Round 12:

Donald Trump389
Joe Biden213
Jo Jorgensen344
Bernie Sanders445

Joe Biden eliminated in this round.

Round 13:

Donald Trump406
Jo Jorgensen403
Bernie Sanders582

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump611
Bernie Sanders780

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 Trump0/14/0 636 to
755		459 to
932		610 to
781		513 to
878		569 to
822		484 to
907		613 to
778		611 to
780		542 to
849		646 to
745		600 to
791		598 to
793		465 to
926		558 to
833
Joe Biden6/8/0755 to
636		 623 to
768		677 to
714		605 to
786		738 to
653		678 to
713		707 to
684		558 to
833		463 to
928		623 to
768		726 to
665		739 to
652		694 to
697		752 to
639
Jo Jorgensen13/1/0932 to
459		768 to
623		 865 to
526		775 to
616		951 to
440		849 to
542		824 to
567		701 to
690		694 to
697		781 to
610		945 to
446		974 to
417		925 to
466		956 to
435
Howie Hawkins10/4/0781 to
610		714 to
677		526 to
865		 600 to
791		789 to
602		720 to
671		759 to
632		604 to
787		555 to
836		749 to
642		787 to
604		803 to
588		746 to
645		794 to
597
Tulsi Gabbard13/1/0878 to
513		786 to
605		616 to
775		791 to
600		 959 to
432		856 to
535		942 to
449		717 to
674		732 to
659		845 to
546		1000 to
391		1005 to
386		860 to
531		922 to
469
Dan Crenshaw6/8/0822 to
569		653 to
738		440 to
951		602 to
789		432 to
959		 614 to
777		716 to
675		605 to
786		575 to
816		716 to
675		771 to
620		803 to
588		680 to
711		823 to
568
Justin Amash9/5/0907 to
484		713 to
678		542 to
849		671 to
720		535 to
856		777 to
614		 773 to
618		662 to
729		655 to
736		753 to
638		930 to
461		963 to
428		906 to
485		955 to
436
Amy Klobuchar6/8/0778 to
613		684 to
707		567 to
824		632 to
759		449 to
942		675 to
716		618 to
773		 615 to
776		506 to
885		737 to
654		864 to
527		871 to
520		775 to
616		825 to
566
Bernie Sanders11/3/0780 to
611		833 to
558		690 to
701		787 to
604		674 to
717		786 to
605		729 to
662		776 to
615		 676 to
715		850 to
541		861 to
530		863 to
528		806 to
585		822 to
569
Andrew Yang13/1/0849 to
542		928 to
463		697 to
694		836 to
555		659 to
732		816 to
575		736 to
655		885 to
506		715 to
676		 925 to
466		1012 to
379		1001 to
390		875 to
516		907 to
484
Elizabeth Warren6/8/0745 to
646		768 to
623		610 to
781		642 to
749		546 to
845		675 to
716		638 to
753		654 to
737		541 to
850		466 to
925		 783 to
608		814 to
577		753 to
638		785 to
606
John Kasich4/10/0791 to
600		665 to
726		446 to
945		604 to
787		391 to
1000		620 to
771		461 to
930		527 to
864		530 to
861		379 to
1012		608 to
783		 884 to
507		729 to
662		845 to
546
Jeb Bush2/12/0793 to
598		652 to
739		417 to
974		588 to
803		386 to
1005		588 to
803		428 to
963		520 to
871		528 to
863		390 to
1001		577 to
814		507 to
884		 655 to
736		824 to
567
Rand Paul5/9/0926 to
465		697 to
694		466 to
925		645 to
746		531 to
860		711 to
680		485 to
906		616 to
775		585 to
806		516 to
875		638 to
753		662 to
729		736 to
655		 985 to
406
Ted Cruz1/13/0833 to
558		639 to
752		435 to
956		597 to
794		469 to
922		568 to
823		436 to
955		566 to
825		569 to
822		484 to
907		606 to
785		546 to
845		567 to
824		406 to
985

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 Trump4638 3.3
Joe Biden4723 3.4
Jo Jorgensen5383 3.9
Howie Hawkins3708 2.7
Tulsi Gabbard4908 3.5
Dan Crenshaw3401 2.4
Justin Amash4723 3.4
Amy Klobuchar3721 2.7
Bernie Sanders6123 4.4
Andrew Yang5910 4.2
Elizabeth Warren4781 3.4
John Kasich3242 2.3
Jeb Bush3140 2.3
Rand Paul4831 3.5
Ted Cruz3890 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 Trump4638
Joe Biden4723
Jo Jorgensen5383
Howie Hawkins3708
Tulsi Gabbard4908
Dan Crenshaw3401
Justin Amash4723
Amy Klobuchar3721
Bernie Sanders6123
Andrew Yang5910
Elizabeth Warren4781
John Kasich3242
Jeb Bush3140
Rand Paul4831
Ted Cruz3890

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 Sanders909
Andrew Yang878

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 Trump5/9/0 562 to
669		429 to
738		580 to
547		470 to
660		498 to
415		456 to
650		577 to
586		555 to
709		499 to
760		600 to
621		563 to
493		550 to
479		399 to
577		452 to
355
Joe Biden10/4/0669 to
562		 589 to
577		598 to
432		537 to
630		687 to
436		613 to
506		561 to
326		334 to
620		353 to
700		422 to
475		646 to
366		677 to
376		651 to
584		692 to
505
Jo Jorgensen11/3/0738 to
429		577 to
589		 597 to
301		515 to
468		668 to
270		466 to
362		581 to
418		514 to
662		440 to
630		573 to
536		646 to
326		673 to
324		586 to
376		724 to
332
Howie Hawkins3/11/0547 to
580		432 to
598		301 to
597		 295 to
617		452 to
413		350 to
517		390 to
441		265 to
677		256 to
713		376 to
484		438 to
419		466 to
450		419 to
577		511 to
522
Tulsi Gabbard11/3/0660 to
470		630 to
537		468 to
515		617 to
295		 627 to
280		491 to
429		611 to
347		504 to
632		438 to
588		569 to
481		640 to
274		664 to
309		517 to
451		653 to
395
Dan Crenshaw0/14/0415 to
498		436 to
687		270 to
668		413 to
452		280 to
627		 259 to
534		388 to
505		403 to
728		328 to
732		437 to
580		383 to
400		398 to
421		274 to
538		377 to
402
Justin Amash8/6/0650 to
456		506 to
613		362 to
466		517 to
350		429 to
491		534 to
259		 472 to
440		464 to
667		390 to
640		487 to
550		521 to
311		568 to
326		489 to
371		620 to
355
Amy Klobuchar6/8/0586 to
577		326 to
561		418 to
581		441 to
390		347 to
611		505 to
388		440 to
472		 285 to
683		222 to
726		311 to
504		470 to
321		514 to
372		476 to
567		556 to
503
Bernie Sanders14/0/0709 to
555		620 to
334		662 to
514		677 to
265		632 to
504		728 to
403		667 to
464		683 to
285		 513 to
482		598 to
246		706 to
342		717 to
367		675 to
540		719 to
490
Andrew Yang13/1/0760 to
499		700 to
353		630 to
440		713 to
256		588 to
438		732 to
328		640 to
390		726 to
222		482 to
513		 611 to
332		763 to
246		769 to
284		646 to
459		741 to
431
Elizabeth Warren9/5/0621 to
600		475 to
422		536 to
573		484 to
376		481 to
569		580 to
437		550 to
487		504 to
311		246 to
598		332 to
611		 557 to
345		580 to
405		570 to
575		613 to
535
John Kasich2/12/0493 to
563		366 to
646		326 to
646		419 to
438		274 to
640		400 to
383		311 to
521		321 to
470		342 to
706		246 to
763		345 to
557		 365 to
299		357 to
532		455 to
459
Jeb Bush1/13/0479 to
550		376 to
677		324 to
673		450 to
466		309 to
664		421 to
398		326 to
568		372 to
514		367 to
717		284 to
769		405 to
580		299 to
365		 319 to
530		415 to
436
Rand Paul8/6/0577 to
399		584 to
651		376 to
586		577 to
419		451 to
517		538 to
274		371 to
489		567 to
476		540 to
675		459 to
646		575 to
570		532 to
357		530 to
319		 545 to
254
Ted Cruz4/10/0355 to
452		505 to
692		332 to
724		522 to
511		395 to
653		402 to
377		355 to
620		503 to
556		490 to
719		431 to
741		535 to
613		459 to
455		436 to
415		254 to
545

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
0745935.75%
116698.00%
214596.99%
316728.01%
414667.03%
517898.57%
611535.53%
711245.39%
810154.86%
97863.77%
1012736.10%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump650556471547254656249195
Joe Biden45910881108120107105118734666
Jo Jorgensen37511810413310513559726467159
Howie Hawkins561138102115901276949512960
Tulsi Gabbard37692100135141173116107644542
Dan Crenshaw595128108128811216163463129
Justin Amash474112991209213559516561123
Amy Klobuchar52511110014910814310073491716
Bernie Sanders43082817471725688100109228
Andrew Yang323899210711314411310911381107
Elizabeth Warren511108947490778775968792
John Kasich5751201151361181487647311114
Jeb Bush5481541331531221215843281516
Rand Paul45912310098791118192967577
Ted Cruz5981318671821035972776349

Number of bullet votes: 38 (2.73%).
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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