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 Hawkins36
Tulsi Gabbard36
Dan Crenshaw15
Justin Amash53
Amy Klobuchar17
Bernie Sanders233
Andrew Yang56
Elizabeth Warren38
John Kasich16
Jeb Bush8
Rand Paul39
Ted Cruz29
TOTAL:1435

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 Hawkins242
Tulsi Gabbard382
Dan Crenshaw178
Justin Amash337
Amy Klobuchar230
Bernie Sanders600
Andrew Yang521
Elizabeth Warren428
John Kasich175
Jeb Bush153
Rand Paul402
Ted Cruz313
Ballots Cast:1435

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 Hawkins50
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash83
Amy Klobuchar20
Bernie Sanders281
Andrew Yang98
Elizabeth Warren74
John Kasich21
Jeb Bush10
Rand Paul62
Ted Cruz41

Jeb Bush eliminated in this round.

Round 2:

Donald Trump320
Joe Biden141
Jo Jorgensen172
Howie Hawkins50
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Amy Klobuchar20
Bernie Sanders282
Andrew Yang98
Elizabeth Warren74
John Kasich24
Rand Paul62
Ted Cruz45

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump320
Joe Biden149
Jo Jorgensen174
Howie Hawkins52
Tulsi Gabbard39
Dan Crenshaw24
Justin Amash84
Bernie Sanders285
Andrew Yang99
Elizabeth Warren77
John Kasich25
Rand Paul62
Ted Cruz45

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump322
Joe Biden150
Jo Jorgensen178
Howie Hawkins52
Tulsi Gabbard44
Justin Amash85
Bernie Sanders285
Andrew Yang100
Elizabeth Warren77
John Kasich27
Rand Paul65
Ted Cruz50

John Kasich eliminated in this round.

Round 5:

Donald Trump323
Joe Biden154
Jo Jorgensen179
Howie Hawkins52
Tulsi Gabbard48
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 Hawkins55
Justin Amash96
Bernie Sanders294
Andrew Yang107
Elizabeth Warren82
Rand Paul73
Ted Cruz53

Ted Cruz eliminated in this round.

Round 7:

Donald Trump351
Joe Biden162
Jo Jorgensen192
Howie Hawkins56
Justin Amash97
Bernie Sanders296
Andrew Yang109
Elizabeth Warren82
Rand Paul90

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump354
Joe Biden168
Jo Jorgensen194
Justin Amash97
Bernie Sanders335
Andrew Yang112
Elizabeth Warren85
Rand Paul90

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump354
Joe Biden186
Jo Jorgensen201
Justin Amash98
Bernie Sanders380
Andrew Yang126
Rand Paul90

Rand Paul eliminated in this round.

Round 10:

Donald Trump390
Joe Biden187
Jo Jorgensen217
Justin Amash124
Bernie Sanders381
Andrew Yang136

Justin Amash eliminated in this round.

Round 11:

Donald Trump400
Joe Biden191
Jo Jorgensen314
Bernie Sanders385
Andrew Yang145

Andrew Yang eliminated in this round.

Round 12:

Donald Trump411
Joe Biden220
Jo Jorgensen346
Bernie Sanders458

Joe Biden eliminated in this round.

Round 13:

Donald Trump429
Jo Jorgensen406
Bernie Sanders600

Jo Jorgensen eliminated in this round.

Round 14:

Donald Trump634
Bernie Sanders801

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
775		484 to
951		634 to
801		538 to
897		593 to
842		509 to
926		638 to
797		634 to
801		566 to
869		671 to
764		625 to
810		623 to
812		486 to
949		585 to
850
Joe Biden6/8/0775 to
660		 640 to
795		693 to
742		622 to
813		755 to
680		693 to
742		725 to
710		574 to
861		479 to
956		640 to
795		743 to
692		756 to
679		710 to
725		772 to
663
Jo Jorgensen13/1/0951 to
484		795 to
640		 885 to
550		796 to
639		971 to
464		874 to
561		847 to
588		719 to
716		714 to
721		803 to
632		969 to
466		995 to
440		946 to
489		979 to
456
Howie Hawkins10/4/0801 to
634		742 to
693		550 to
885		 626 to
809		812 to
623		746 to
689		783 to
652		623 to
812		578 to
857		774 to
661		812 to
623		822 to
613		770 to
665		818 to
617
Tulsi Gabbard13/1/0897 to
538		813 to
622		639 to
796		809 to
626		 977 to
458		881 to
554		963 to
472		738 to
697		754 to
681		870 to
565		1024 to
411		1025 to
410		880 to
555		947 to
488
Dan Crenshaw6/8/0842 to
593		680 to
755		464 to
971		623 to
812		458 to
977		 643 to
792		741 to
694		625 to
810		599 to
836		742 to
693		801 to
634		826 to
609		707 to
728		850 to
585
Justin Amash9/5/0926 to
509		742 to
693		561 to
874		689 to
746		554 to
881		792 to
643		 795 to
640		680 to
755		677 to
758		779 to
656		958 to
477		986 to
449		930 to
505		980 to
455
Amy Klobuchar6/8/0797 to
638		710 to
725		588 to
847		652 to
783		472 to
963		694 to
741		640 to
795		 634 to
801		527 to
908		767 to
668		889 to
546		894 to
541		800 to
635		851 to
584
Bernie Sanders11/3/0801 to
634		861 to
574		716 to
719		812 to
623		697 to
738		810 to
625		755 to
680		801 to
634		 700 to
735		876 to
559		885 to
550		886 to
549		831 to
604		846 to
589
Andrew Yang13/1/0869 to
566		956 to
479		721 to
714		857 to
578		681 to
754		836 to
599		758 to
677		908 to
527		735 to
700		 953 to
482		1042 to
393		1025 to
410		900 to
535		930 to
505
Elizabeth Warren6/8/0764 to
671		795 to
640		632 to
803		661 to
774		565 to
870		693 to
742		656 to
779		668 to
767		559 to
876		482 to
953		 805 to
630		836 to
599		776 to
659		810 to
625
John Kasich4/10/0810 to
625		692 to
743		466 to
969		623 to
812		411 to
1024		634 to
801		477 to
958		546 to
889		550 to
885		393 to
1042		630 to
805		 905 to
530		755 to
680		869 to
566
Jeb Bush2/12/0812 to
623		679 to
756		440 to
995		613 to
822		410 to
1025		609 to
826		449 to
986		541 to
894		549 to
886		410 to
1025		599 to
836		530 to
905		 685 to
750		850 to
585
Rand Paul5/9/0949 to
486		725 to
710		489 to
946		665 to
770		555 to
880		728 to
707		505 to
930		635 to
800		604 to
831		535 to
900		659 to
776		680 to
755		750 to
685		 1008 to
427
Ted Cruz1/13/0850 to
585		663 to
772		456 to
979		617 to
818		488 to
947		585 to
850		455 to
980		584 to
851		589 to
846		505 to
930		625 to
810		566 to
869		585 to
850		427 to
1008

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 Biden4855 3.4
Jo Jorgensen5495 3.8
Howie Hawkins3819 2.7
Tulsi Gabbard5044 3.5
Dan Crenshaw3532 2.5
Justin Amash4817 3.4
Amy Klobuchar3846 2.7
Bernie Sanders6298 4.4
Andrew Yang6059 4.2
Elizabeth Warren4921 3.4
John Kasich3375 2.4
Jeb Bush3307 2.3
Rand Paul4994 3.5
Ted Cruz4052 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 Biden4855
Jo Jorgensen5495
Howie Hawkins3819
Tulsi Gabbard5044
Dan Crenshaw3532
Justin Amash4817
Amy Klobuchar3846
Bernie Sanders6298
Andrew Yang6059
Elizabeth Warren4921
John Kasich3375
Jeb Bush3307
Rand Paul4994
Ted Cruz4052

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 Sanders941
Andrew Yang905

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
685		454 to
751		603 to
559		492 to
672		520 to
424		481 to
661		600 to
604		578 to
728		519 to
778		624 to
637		587 to
507		574 to
494		419 to
592		473 to
361
Joe Biden10/4/0685 to
586		 605 to
592		613 to
447		552 to
648		703 to
452		628 to
518		576 to
338		342 to
639		363 to
720		436 to
490		661 to
384		689 to
397		667 to
604		711 to
525
Jo Jorgensen11/3/0751 to
454		592 to
605		 607 to
310		522 to
481		681 to
282		479 to
365		590 to
431		521 to
684		446 to
646		582 to
552		653 to
340		679 to
344		593 to
391		735 to
354
Howie Hawkins3/11/0559 to
603		447 to
613		310 to
607		 302 to
629		459 to
424		363 to
523		401 to
451		271 to
698		262 to
732		385 to
497		442 to
432		471 to
470		428 to
592		521 to
543
Tulsi Gabbard11/3/0672 to
492		648 to
552		481 to
522		629 to
302		 638 to
290		507 to
434		622 to
358		512 to
653		448 to
606		578 to
497		649 to
285		674 to
326		528 to
464		665 to
413
Dan Crenshaw0/14/0424 to
520		452 to
703		282 to
681		424 to
459		290 to
638		 273 to
541		401 to
520		413 to
749		335 to
753		449 to
595		392 to
414		405 to
442		282 to
553		388 to
419
Justin Amash8/6/0661 to
481		518 to
628		365 to
479		523 to
363		434 to
507		541 to
273		 479 to
455		470 to
688		394 to
658		495 to
567		526 to
329		572 to
348		492 to
389		629 to
376
Amy Klobuchar6/8/0604 to
600		338 to
576		431 to
590		451 to
401		358 to
622		520 to
401		455 to
479		 293 to
704		230 to
742		318 to
514		478 to
334		522 to
389		488 to
582		572 to
523
Bernie Sanders14/0/0728 to
578		639 to
342		684 to
521		698 to
271		653 to
512		749 to
413		688 to
470		704 to
293		 530 to
494		616 to
253		725 to
351		735 to
381		696 to
553		737 to
506
Andrew Yang13/1/0778 to
519		720 to
363		646 to
446		732 to
262		606 to
448		753 to
335		658 to
394		742 to
230		494 to
530		 627 to
344		777 to
255		786 to
297		662 to
473		758 to
448
Elizabeth Warren9/5/0637 to
624		490 to
436		552 to
582		497 to
385		497 to
578		595 to
449		567 to
495		514 to
318		253 to
616		344 to
627		 570 to
357		592 to
423		584 to
587		629 to
553
John Kasich2/12/0507 to
587		384 to
661		340 to
653		432 to
442		285 to
649		414 to
392		329 to
526		334 to
478		351 to
725		255 to
777		357 to
570		 375 to
313		369 to
542		469 to
478
Jeb Bush1/13/0494 to
574		397 to
689		344 to
679		470 to
471		326 to
674		442 to
405		348 to
572		389 to
522		381 to
735		297 to
786		423 to
592		313 to
375		 335 to
539		431 to
452
Rand Paul8/6/0592 to
419		604 to
667		391 to
593		592 to
428		464 to
528		553 to
282		389 to
492		582 to
488		553 to
696		473 to
662		587 to
584		542 to
369		539 to
335		 558 to
269
Ted Cruz4/10/0361 to
473		525 to
711		354 to
735		543 to
521		413 to
665		419 to
388		376 to
629		523 to
572		506 to
737		448 to
758		553 to
629		478 to
469		452 to
431		269 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
0767435.65%
117127.95%
215046.99%
317248.01%
415287.10%
518748.71%
611945.55%
711735.45%
810434.85%
98013.72%
1012986.03%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump664566472577258696453206
Joe Biden47711282110123112108121764668
Jo Jorgensen39112210813610914362726568159
Howie Hawkins578143105117951337052523060
Tulsi Gabbard39094104139145180120109664642
Dan Crenshaw608131115132851266465463231
Justin Amash4941161011229914160526562123
Amy Klobuchar53911510515211015110279491716
Bernie Sanders44382847776785893103110231
Andrew Yang336929311311715011611311681108
Elizabeth Warren525111987895828780978894
John Kasich5891231161421221577850331114
Jeb Bush5571561381581231296546311616
Rand Paul471126101103841168595997679
Ted Cruz6121339073881046177816551

Number of bullet votes: 40 (2.79%).
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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