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 Trump288
Joe Biden261
Jo Jorgensen192
Howie Hawkins34
Tulsi Gabbard35
Dan Crenshaw15
Justin Amash51
Amy Klobuchar16
Bernie Sanders210
Andrew Yang52
Elizabeth Warren34
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1263

The winner is Donald Trump with 22.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump398
Joe Biden477
Jo Jorgensen425
Howie Hawkins217
Tulsi Gabbard360
Dan Crenshaw165
Justin Amash320
Amy Klobuchar210
Bernie Sanders539
Andrew Yang485
Elizabeth Warren388
John Kasich160
Jeb Bush125
Rand Paul370
Ted Cruz261
Ballots Cast:1263

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump255
Joe Biden114
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash81
Amy Klobuchar18
Bernie Sanders252
Andrew Yang92
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul50
Ted Cruz34

Jeb Bush eliminated in this round.

Round 2:

Donald Trump256
Joe Biden114
Jo Jorgensen168
Howie Hawkins46
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Amy Klobuchar18
Bernie Sanders253
Andrew Yang92
Elizabeth Warren68
John Kasich20
Rand Paul50
Ted Cruz37

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump256
Joe Biden122
Jo Jorgensen169
Howie Hawkins48
Tulsi Gabbard37
Dan Crenshaw22
Justin Amash82
Bernie Sanders256
Andrew Yang93
Elizabeth Warren70
John Kasich21
Rand Paul50
Ted Cruz37

John Kasich eliminated in this round.

Round 4:

Donald Trump257
Joe Biden126
Jo Jorgensen169
Howie Hawkins48
Tulsi Gabbard40
Dan Crenshaw23
Justin Amash84
Bernie Sanders258
Andrew Yang95
Elizabeth Warren72
Rand Paul53
Ted Cruz38

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump258
Joe Biden127
Jo Jorgensen173
Howie Hawkins48
Tulsi Gabbard46
Justin Amash85
Bernie Sanders258
Andrew Yang96
Elizabeth Warren72
Rand Paul56
Ted Cruz44

Ted Cruz eliminated in this round.

Round 6:

Donald Trump278
Joe Biden129
Jo Jorgensen176
Howie Hawkins49
Tulsi Gabbard48
Justin Amash86
Bernie Sanders260
Andrew Yang96
Elizabeth Warren72
Rand Paul69

Tulsi Gabbard eliminated in this round.

Round 7:

Donald Trump281
Joe Biden135
Jo Jorgensen185
Howie Hawkins52
Justin Amash95
Bernie Sanders266
Andrew Yang101
Elizabeth Warren74
Rand Paul74

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump284
Joe Biden141
Jo Jorgensen187
Justin Amash95
Bernie Sanders301
Andrew Yang104
Elizabeth Warren77
Rand Paul74

Rand Paul eliminated in this round.

Round 9:

Donald Trump310
Joe Biden142
Jo Jorgensen202
Justin Amash119
Bernie Sanders302
Andrew Yang109
Elizabeth Warren79

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump310
Joe Biden159
Jo Jorgensen208
Justin Amash120
Bernie Sanders342
Andrew Yang124

Justin Amash eliminated in this round.

Round 11:

Donald Trump318
Joe Biden163
Jo Jorgensen303
Bernie Sanders346
Andrew Yang133

Andrew Yang eliminated in this round.

Round 12:

Donald Trump326
Joe Biden192
Jo Jorgensen333
Bernie Sanders412

Joe Biden eliminated in this round.

Round 13:

Donald Trump342
Jo Jorgensen382
Bernie Sanders539

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen636
Bernie Sanders627

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 Trump0/14/0 563 to
700		389 to
874		532 to
731		443 to
820		494 to
769		414 to
849		538 to
725		539 to
724		473 to
790		567 to
696		527 to
736		521 to
742		399 to
864		489 to
774
Joe Biden6/8/0700 to
563		 557 to
706		612 to
651		542 to
721		668 to
595		610 to
653		643 to
620		498 to
765		403 to
860		558 to
705		656 to
607		671 to
592		627 to
636		686 to
577
Jo Jorgensen13/1/0874 to
389		706 to
557		 793 to
470		710 to
553		872 to
391		773 to
490		752 to
511		636 to
627		631 to
632		709 to
554		862 to
401		893 to
370		857 to
406		884 to
379
Howie Hawkins10/4/0731 to
532		651 to
612		470 to
793		 536 to
727		715 to
548		641 to
622		683 to
580		541 to
722		491 to
772		674 to
589		710 to
553		731 to
532		676 to
587		726 to
537
Tulsi Gabbard13/1/0820 to
443		721 to
542		553 to
710		727 to
536		 872 to
391		767 to
496		856 to
407		646 to
617		654 to
609		762 to
501		912 to
351		919 to
344		783 to
480		848 to
415
Dan Crenshaw6/8/0769 to
494		595 to
668		391 to
872		548 to
715		391 to
872		 543 to
720		640 to
623		543 to
720		509 to
754		638 to
625		699 to
564		728 to
535		615 to
648		756 to
507
Justin Amash9/5/0849 to
414		653 to
610		490 to
773		622 to
641		496 to
767		720 to
543		 695 to
568		601 to
662		585 to
678		675 to
588		843 to
420		879 to
384		831 to
432		878 to
385
Amy Klobuchar6/8/0725 to
538		620 to
643		511 to
752		580 to
683		407 to
856		623 to
640		568 to
695		 552 to
711		444 to
819		657 to
606		781 to
482		791 to
472		701 to
562		755 to
508
Bernie Sanders11/3/0724 to
539		765 to
498		627 to
636		722 to
541		617 to
646		720 to
543		662 to
601		711 to
552		 606 to
657		767 to
496		778 to
485		782 to
481		728 to
535		752 to
511
Andrew Yang13/1/0790 to
473		860 to
403		632 to
631		772 to
491		609 to
654		754 to
509		678 to
585		819 to
444		657 to
606		 840 to
423		923 to
340		914 to
349		795 to
468		832 to
431
Elizabeth Warren6/8/0696 to
567		705 to
558		554 to
709		589 to
674		501 to
762		625 to
638		588 to
675		606 to
657		496 to
767		423 to
840		 715 to
548		745 to
518		684 to
579		722 to
541
John Kasich4/10/0736 to
527		607 to
656		401 to
862		553 to
710		351 to
912		564 to
699		420 to
843		482 to
781		485 to
778		340 to
923		548 to
715		 802 to
461		659 to
604		778 to
485
Jeb Bush2/12/0742 to
521		592 to
671		370 to
893		532 to
731		344 to
919		535 to
728		384 to
879		472 to
791		481 to
782		349 to
914		518 to
745		461 to
802		 590 to
673		751 to
512
Rand Paul5/9/0864 to
399		636 to
627		406 to
857		587 to
676		480 to
783		648 to
615		432 to
831		562 to
701		535 to
728		468 to
795		579 to
684		604 to
659		673 to
590		 907 to
356
Ted Cruz1/13/0774 to
489		577 to
686		379 to
884		537 to
726		415 to
848		507 to
756		385 to
878		508 to
755		511 to
752		431 to
832		541 to
722		485 to
778		512 to
751		356 to
907

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 Trump4007 3.2
Joe Biden4308 3.4
Jo Jorgensen5056 4.0
Howie Hawkins3389 2.7
Tulsi Gabbard4539 3.6
Dan Crenshaw3072 2.4
Justin Amash4411 3.5
Amy Klobuchar3404 2.7
Bernie Sanders5648 4.5
Andrew Yang5511 4.4
Elizabeth Warren4427 3.5
John Kasich2915 2.3
Jeb Bush2788 2.2
Rand Paul4416 3.5
Ted Cruz3436 2.7

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 Trump4007
Joe Biden4308
Jo Jorgensen5056
Howie Hawkins3389
Tulsi Gabbard4539
Dan Crenshaw3072
Justin Amash4411
Amy Klobuchar3404
Bernie Sanders5648
Andrew Yang5511
Elizabeth Warren4427
John Kasich2915
Jeb Bush2788
Rand Paul4416
Ted Cruz3436

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 Sanders819
Andrew Yang796

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 Trump4/10/0 491 to
620		360 to
699		506 to
509		404 to
622		429 to
386		387 to
614		500 to
545		486 to
659		429 to
717		524 to
581		490 to
458		478 to
447		339 to
543		391 to
329
Joe Biden9/5/0620 to
491		 535 to
543		544 to
397		476 to
588		627 to
396		553 to
472		507 to
299		296 to
570		309 to
650		375 to
438		589 to
330		616 to
333		589 to
537		633 to
450
Jo Jorgensen12/2/0699 to
360		543 to
535		 565 to
275		482 to
430		629 to
239		440 to
331		547 to
385		475 to
607		412 to
581		532 to
496		612 to
292		640 to
288		554 to
333		684 to
284
Howie Hawkins5/9/0509 to
506		397 to
544		275 to
565		 268 to
581		417 to
379		322 to
489		360 to
407		238 to
622		233 to
663		338 to
448		409 to
383		435 to
405		387 to
533		474 to
463
Tulsi Gabbard11/3/0622 to
404		588 to
476		430 to
482		581 to
268		 592 to
251		457 to
399		573 to
311		468 to
577		402 to
546		522 to
440		608 to
238		630 to
268		486 to
407		614 to
344
Dan Crenshaw1/13/0386 to
429		396 to
627		239 to
629		379 to
417		251 to
592		 232 to
506		352 to
468		366 to
671		299 to
686		399 to
541		357 to
368		370 to
386		248 to
497		351 to
349
Justin Amash8/6/0614 to
387		472 to
553		331 to
440		489 to
322		399 to
457		506 to
232		 442 to
407		430 to
610		369 to
588		455 to
508		493 to
281		535 to
292		461 to
334		585 to
302
Amy Klobuchar6/8/0545 to
500		299 to
507		385 to
547		407 to
360		311 to
573		468 to
352		407 to
442		 258 to
625		201 to
677		280 to
466		438 to
288		480 to
333		439 to
524		518 to
445
Bernie Sanders14/0/0659 to
486		570 to
296		607 to
475		622 to
238		577 to
468		671 to
366		610 to
430		625 to
258		 467 to
444		544 to
219		653 to
306		666 to
325		616 to
494		668 to
435
Andrew Yang13/1/0717 to
429		650 to
309		581 to
412		663 to
233		546 to
402		686 to
299		588 to
369		677 to
201		444 to
467		 567 to
298		714 to
217		720 to
248		605 to
424		692 to
378
Elizabeth Warren9/4/1581 to
524		438 to
375		496 to
532		448 to
338		440 to
522		541 to
399		508 to
455		466 to
280		219 to
544		298 to
567		 518 to
303		542 to
358		526 to
526		572 to
478
John Kasich3/11/0458 to
490		330 to
589		292 to
612		383 to
409		238 to
608		368 to
357		281 to
493		288 to
438		306 to
653		217 to
714		303 to
518		 338 to
268		324 to
497		423 to
404
Jeb Bush1/12/1447 to
478		333 to
616		288 to
640		405 to
435		268 to
630		386 to
370		292 to
535		333 to
480		325 to
666		248 to
720		358 to
542		268 to
338		 284 to
494		387 to
387
Rand Paul7/6/1543 to
339		537 to
589		333 to
554		533 to
387		407 to
486		497 to
248		334 to
461		524 to
439		494 to
616		424 to
605		526 to
526		497 to
324		494 to
284		 515 to
209
Ted Cruz0/13/1329 to
391		450 to
633		284 to
684		463 to
474		344 to
614		349 to
351		302 to
585		445 to
518		435 to
668		378 to
692		478 to
572		404 to
423		387 to
387		209 to
515

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
0677535.76%
115188.01%
213307.02%
314747.78%
413287.01%
515818.35%
610405.49%
710325.45%
89464.99%
97323.86%
1011896.28%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump612535767476546555241168
Joe Biden41699749410610096107704061
Jo Jorgensen326109941179611852676067157
Howie Hawkins51012496101841056348492756
Tulsi Gabbard3338191123127152112104613940
Dan Crenshaw54512099109741055457442927
Justin Amash422100911068511554486260120
Amy Klobuchar47798891361011279068441716
Bernie Sanders3906974656063528291103214
Andrew Yang2847587901051319910110878105
Elizabeth Warren46098836481687967918488
John Kasich5291071061221071336543271014
Jeb Bush5011451231371151074835251215
Rand Paul416114918270987786897268
Ted Cruz554126756170945364735340

Number of bullet votes: 31 (2.45%).
Number of "approval" votes: 17 (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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