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 Trump362
Joe Biden302
Jo Jorgensen195
Howie Hawkins37
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders233
Andrew Yang56
Elizabeth Warren38
John Kasich17
Jeb Bush8
Rand Paul39
Ted Cruz29
TOTAL:1437

The winner is Donald Trump with 25.2% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump485
Joe Biden537
Jo Jorgensen443
Howie Hawkins243
Tulsi Gabbard383
Dan Crenshaw178
Justin Amash337
Amy Klobuchar230
Bernie Sanders601
Andrew Yang522
Elizabeth Warren428
John Kasich176
Jeb Bush153
Rand Paul402
Ted Cruz313
Ballots Cast:1437

The winner is Bernie Sanders with 41.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump319
Joe Biden141
Jo Jorgensen172
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash83
Amy Klobuchar20
Bernie Sanders281
Andrew Yang98
Elizabeth Warren74
John Kasich22
Jeb Bush10
Rand Paul62
Ted Cruz41

Jeb Bush eliminated in this round.

Round 2:

Donald Trump320
Joe Biden141
Jo Jorgensen172
Howie Hawkins51
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Amy Klobuchar20
Bernie Sanders282
Andrew Yang98
Elizabeth Warren74
John Kasich25
Rand Paul62
Ted Cruz45

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump320
Joe Biden149
Jo Jorgensen174
Howie Hawkins53
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Bernie Sanders285
Andrew Yang99
Elizabeth Warren77
John Kasich26
Rand Paul62
Ted Cruz45

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump322
Joe Biden150
Jo Jorgensen178
Howie Hawkins53
Tulsi Gabbard44
Justin Amash85
Bernie Sanders285
Andrew Yang100
Elizabeth Warren77
John Kasich28
Rand Paul65
Ted Cruz50

John Kasich eliminated in this round.

Round 5:

Donald Trump323
Joe Biden154
Jo Jorgensen179
Howie Hawkins53
Tulsi Gabbard49
Justin Amash87
Bernie Sanders287
Andrew Yang102
Elizabeth Warren80
Rand Paul70
Ted Cruz53

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump326
Joe Biden160
Jo Jorgensen189
Howie Hawkins56
Justin Amash96
Bernie Sanders294
Andrew Yang108
Elizabeth Warren82
Rand Paul73
Ted Cruz53

Ted Cruz eliminated in this round.

Round 7:

Donald Trump351
Joe Biden162
Jo Jorgensen192
Howie Hawkins57
Justin Amash97
Bernie Sanders296
Andrew Yang110
Elizabeth Warren82
Rand Paul90

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump354
Joe Biden168
Jo Jorgensen194
Justin Amash97
Bernie Sanders336
Andrew Yang113
Elizabeth Warren85
Rand Paul90

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump354
Joe Biden186
Jo Jorgensen201
Justin Amash98
Bernie Sanders381
Andrew Yang127
Rand Paul90

Rand Paul eliminated in this round.

Round 10:

Donald Trump390
Joe Biden187
Jo Jorgensen217
Justin Amash124
Bernie Sanders382
Andrew Yang137

Justin Amash eliminated in this round.

Round 11:

Donald Trump400
Joe Biden191
Jo Jorgensen314
Bernie Sanders386
Andrew Yang146

Andrew Yang eliminated in this round.

Round 12:

Donald Trump411
Joe Biden220
Jo Jorgensen346
Bernie Sanders460

Joe Biden eliminated in this round.

Round 13:

Donald Trump429
Jo Jorgensen406
Bernie Sanders602

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump634
Bernie Sanders803

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 Trump0/14/0 660 to
777		485 to
952		635 to
802		538 to
899		594 to
843		510 to
927		638 to
799		634 to
803		566 to
871		672 to
765		625 to
812		623 to
814		487 to
950		586 to
851
Joe Biden6/8/0777 to
660		 641 to
796		694 to
743		622 to
815		757 to
680		695 to
742		727 to
710		574 to
863		480 to
957		641 to
796		744 to
693		757 to
680		712 to
725		774 to
663
Jo Jorgensen13/1/0952 to
485		796 to
641		 886 to
551		796 to
641		972 to
465		875 to
562		848 to
589		719 to
718		715 to
722		803 to
634		970 to
467		996 to
441		947 to
490		980 to
457
Howie Hawkins10/4/0802 to
635		743 to
694		551 to
886		 627 to
810		813 to
624		747 to
690		784 to
653		624 to
813		579 to
858		775 to
662		813 to
624		823 to
614		771 to
666		819 to
618
Tulsi Gabbard13/1/0899 to
538		815 to
622		641 to
796		810 to
627		 979 to
458		883 to
554		965 to
472		739 to
698		756 to
681		871 to
566		1025 to
412		1027 to
410		882 to
555		949 to
488
Dan Crenshaw6/8/0843 to
594		680 to
757		465 to
972		624 to
813		458 to
979		 645 to
792		742 to
695		625 to
812		600 to
837		743 to
694		802 to
635		827 to
610		709 to
728		852 to
585
Justin Amash9/5/0927 to
510		742 to
695		562 to
875		690 to
747		554 to
883		792 to
645		 796 to
641		680 to
757		678 to
759		779 to
658		959 to
478		987 to
450		931 to
506		981 to
456
Amy Klobuchar6/8/0799 to
638		710 to
727		589 to
848		653 to
784		472 to
965		695 to
742		641 to
796		 634 to
803		528 to
909		768 to
669		890 to
547		895 to
542		802 to
635		853 to
584
Bernie Sanders11/3/0803 to
634		863 to
574		718 to
719		813 to
624		698 to
739		812 to
625		757 to
680		803 to
634		 701 to
736		878 to
559		886 to
551		887 to
550		833 to
604		848 to
589
Andrew Yang13/1/0871 to
566		957 to
480		722 to
715		858 to
579		681 to
756		837 to
600		759 to
678		909 to
528		736 to
701		 954 to
483		1043 to
394		1027 to
410		902 to
535		932 to
505
Elizabeth Warren6/8/0765 to
672		796 to
641		634 to
803		662 to
775		566 to
871		694 to
743		658 to
779		669 to
768		559 to
878		483 to
954		 806 to
631		837 to
600		778 to
659		811 to
626
John Kasich4/10/0812 to
625		693 to
744		467 to
970		624 to
813		412 to
1025		635 to
802		478 to
959		547 to
890		551 to
886		394 to
1043		631 to
806		 907 to
530		757 to
680		871 to
566
Jeb Bush2/12/0814 to
623		680 to
757		441 to
996		614 to
823		410 to
1027		610 to
827		450 to
987		542 to
895		550 to
887		410 to
1027		600 to
837		530 to
907		 687 to
750		852 to
585
Rand Paul5/9/0950 to
487		725 to
712		490 to
947		666 to
771		555 to
882		728 to
709		506 to
931		635 to
802		604 to
833		535 to
902		659 to
778		680 to
757		750 to
687		 1009 to
428
Ted Cruz1/13/0851 to
586		663 to
774		457 to
980		618 to
819		488 to
949		585 to
852		456 to
981		584 to
853		589 to
848		505 to
932		626 to
811		566 to
871		585 to
852		428 to
1009

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 Trump4868 3.4
Joe Biden4861 3.4
Jo Jorgensen5497 3.8
Howie Hawkins3829 2.7
Tulsi Gabbard5055 3.5
Dan Crenshaw3535 2.5
Justin Amash4818 3.4
Amy Klobuchar3849 2.7
Bernie Sanders6310 4.4
Andrew Yang6067 4.2
Elizabeth Warren4927 3.4
John Kasich3388 2.4
Jeb Bush3313 2.3
Rand Paul4995 3.5
Ted Cruz4056 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 Trump4868
Joe Biden4861
Jo Jorgensen5497
Howie Hawkins3829
Tulsi Gabbard5055
Dan Crenshaw3535
Justin Amash4818
Amy Klobuchar3849
Bernie Sanders6310
Andrew Yang6067
Elizabeth Warren4927
John Kasich3388
Jeb Bush3313
Rand Paul4995
Ted Cruz4056

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 Sanders942
Andrew Yang906

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 Trump5/9/0 586 to
687		454 to
752		603 to
560		492 to
674		520 to
426		481 to
662		600 to
606		578 to
730		519 to
780		624 to
638		587 to
509		574 to
496		419 to
593		473 to
363
Joe Biden10/4/0687 to
586		 607 to
592		614 to
448		553 to
649		704 to
452		630 to
518		578 to
338		342 to
641		364 to
721		437 to
491		662 to
385		690 to
398		669 to
604		712 to
526
Jo Jorgensen11/3/0752 to
454		592 to
607		 607 to
311		522 to
483		682 to
283		480 to
365		590 to
432		521 to
686		447 to
647		582 to
553		653 to
342		679 to
345		594 to
391		736 to
355
Howie Hawkins3/11/0560 to
603		448 to
614		311 to
607		 303 to
630		460 to
425		364 to
523		402 to
452		272 to
699		263 to
733		386 to
497		443 to
433		472 to
471		429 to
592		522 to
544
Tulsi Gabbard11/3/0674 to
492		649 to
553		483 to
522		630 to
303		 640 to
290		509 to
434		624 to
358		513 to
654		450 to
606		579 to
498		649 to
286		676 to
326		530 to
464		667 to
413
Dan Crenshaw0/14/0426 to
520		452 to
704		283 to
682		425 to
460		290 to
640		 274 to
541		402 to
521		413 to
751		335 to
754		450 to
596		392 to
416		405 to
444		283 to
553		388 to
420
Justin Amash8/6/0662 to
481		518 to
630		365 to
480		523 to
364		434 to
509		541 to
274		 479 to
457		470 to
690		394 to
659		495 to
568		526 to
331		572 to
350		492 to
389		629 to
377
Amy Klobuchar6/8/0606 to
600		338 to
578		432 to
590		452 to
402		358 to
624		521 to
402		457 to
479		 293 to
706		231 to
743		319 to
515		478 to
336		522 to
390		490 to
582		573 to
524
Bernie Sanders14/0/0730 to
578		641 to
342		686 to
521		699 to
272		654 to
513		751 to
413		690 to
470		706 to
293		 531 to
495		618 to
253		726 to
352		736 to
382		698 to
553		738 to
506
Andrew Yang13/1/0780 to
519		721 to
364		647 to
447		733 to
263		606 to
450		754 to
335		659 to
394		743 to
231		495 to
531		 628 to
345		777 to
257		787 to
298		663 to
473		759 to
448
Elizabeth Warren9/5/0638 to
624		491 to
437		553 to
582		497 to
386		498 to
579		596 to
450		568 to
495		515 to
319		253 to
618		345 to
628		 571 to
358		593 to
424		585 to
587		630 to
554
John Kasich2/12/0509 to
587		385 to
662		342 to
653		433 to
443		286 to
649		416 to
392		331 to
526		336 to
478		352 to
726		257 to
777		358 to
571		 377 to
313		371 to
542		471 to
478
Jeb Bush1/13/0496 to
574		398 to
690		345 to
679		471 to
472		326 to
676		444 to
405		350 to
572		390 to
522		382 to
736		298 to
787		424 to
593		313 to
377		 337 to
539		433 to
452
Rand Paul8/6/0593 to
419		604 to
669		391 to
594		592 to
429		464 to
530		553 to
283		389 to
492		582 to
490		553 to
698		473 to
663		587 to
585		542 to
371		539 to
337		 558 to
270
Ted Cruz4/10/0363 to
473		526 to
712		355 to
736		544 to
522		413 to
667		420 to
388		377 to
629		524 to
573		506 to
738		448 to
759		554 to
630		478 to
471		452 to
433		270 to
558

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
0768135.63%
117187.97%
215097.00%
317288.02%
415307.10%
518748.69%
611955.54%
711745.45%
810444.84%
98023.72%
1013006.03%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump666566472577258696453206
Joe Biden47711283110124112108121764668
Jo Jorgensen39212210913610914362726568159
Howie Hawkins579143105117951337052523061
Tulsi Gabbard39094104140145180120109674642
Dan Crenshaw608132116132851266465463231
Justin Amash4951171011229914160526562123
Amy Klobuchar53911610615211015110279491716
Bernie Sanders44382847876785893103111231
Andrew Yang336939311311715011611411681108
Elizabeth Warren526111987895828880978894
John Kasich5891231161431221577850331115
Jeb Bush5571561391581241296546311616
Rand Paul472127101103841168595997679
Ted Cruz6121349074881046177816551

Number of bullet votes: 40 (2.78%).
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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