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 Trump263
Joe Biden248
Jo Jorgensen191
Howie Hawkins32
Tulsi Gabbard34
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders192
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1197

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump371
Joe Biden452
Jo Jorgensen418
Howie Hawkins204
Tulsi Gabbard347
Dan Crenshaw161
Justin Amash316
Amy Klobuchar197
Bernie Sanders511
Andrew Yang469
Elizabeth Warren371
John Kasich154
Jeb Bush121
Rand Paul364
Ted Cruz247
Ballots Cast:1197

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump232
Joe Biden103
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard32
Dan Crenshaw22
Justin Amash81
Amy Klobuchar15
Bernie Sanders234
Andrew Yang90
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul50
Ted Cruz32

Jeb Bush eliminated in this round.

Round 2:

Donald Trump233
Joe Biden103
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard32
Dan Crenshaw22
Justin Amash82
Amy Klobuchar15
Bernie Sanders235
Andrew Yang90
Elizabeth Warren68
John Kasich20
Rand Paul50
Ted Cruz35

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump233
Joe Biden110
Jo Jorgensen169
Howie Hawkins46
Tulsi Gabbard32
Dan Crenshaw22
Justin Amash82
Bernie Sanders237
Andrew Yang91
Elizabeth Warren69
John Kasich21
Rand Paul50
Ted Cruz35

John Kasich eliminated in this round.

Round 4:

Donald Trump234
Joe Biden114
Jo Jorgensen169
Howie Hawkins46
Tulsi Gabbard35
Dan Crenshaw23
Justin Amash84
Bernie Sanders239
Andrew Yang93
Elizabeth Warren71
Rand Paul53
Ted Cruz36

Dan Crenshaw eliminated in this round.

Round 5:

Donald Trump235
Joe Biden115
Jo Jorgensen173
Howie Hawkins46
Tulsi Gabbard41
Justin Amash85
Bernie Sanders239
Andrew Yang94
Elizabeth Warren71
Rand Paul56
Ted Cruz42

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump238
Joe Biden120
Jo Jorgensen182
Howie Hawkins49
Justin Amash93
Bernie Sanders244
Andrew Yang98
Elizabeth Warren72
Rand Paul59
Ted Cruz42

Ted Cruz eliminated in this round.

Round 7:

Donald Trump257
Joe Biden122
Jo Jorgensen185
Howie Hawkins50
Justin Amash94
Bernie Sanders246
Andrew Yang98
Elizabeth Warren72
Rand Paul73

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump260
Joe Biden128
Jo Jorgensen187
Justin Amash94
Bernie Sanders280
Andrew Yang101
Elizabeth Warren74
Rand Paul73

Rand Paul eliminated in this round.

Round 9:

Donald Trump286
Joe Biden129
Jo Jorgensen202
Justin Amash118
Bernie Sanders281
Andrew Yang105
Elizabeth Warren76

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump286
Joe Biden146
Jo Jorgensen207
Justin Amash119
Bernie Sanders320
Andrew Yang119

Eliminated in this round:

Round 11:

Donald Trump301
Joe Biden176
Jo Jorgensen331
Bernie Sanders389

Joe Biden eliminated in this round.

Round 12:

Donald Trump313
Jo Jorgensen376
Bernie Sanders508

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen613
Bernie Sanders584

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 Trump0/14/0 534 to
663		357 to
840		502 to
695		409 to
788		457 to
740		381 to
816		504 to
693		510 to
687		440 to
757		534 to
663		492 to
705		487 to
710		364 to
833		456 to
741
Joe Biden6/8/0663 to
534		 520 to
677		583 to
614		506 to
691		628 to
569		573 to
624		611 to
586		473 to
724		372 to
825		523 to
674		618 to
579		631 to
566		590 to
607		647 to
550
Jo Jorgensen14/0/0840 to
357		677 to
520		 762 to
435		669 to
528		825 to
372		730 to
467		716 to
481		613 to
584		599 to
598		673 to
524		818 to
379		845 to
352		810 to
387		845 to
352
Howie Hawkins9/5/0695 to
502		614 to
583		435 to
762		 494 to
703		667 to
530		592 to
605		636 to
561		512 to
685		450 to
747		630 to
567		657 to
540		678 to
519		623 to
574		681 to
516
Tulsi Gabbard13/1/0788 to
409		691 to
506		528 to
669		703 to
494		 825 to
372		722 to
475		813 to
384		618 to
579		617 to
580		717 to
480		862 to
335		866 to
331		734 to
463		805 to
392
Dan Crenshaw6/8/0740 to
457		569 to
628		372 to
825		530 to
667		372 to
825		 511 to
686		606 to
591		518 to
679		479 to
718		599 to
598		657 to
540		684 to
513		571 to
626		717 to
480
Justin Amash10/4/0816 to
381		624 to
573		467 to
730		605 to
592		475 to
722		686 to
511		 660 to
537		576 to
621		552 to
645		638 to
559		793 to
404		827 to
370		782 to
415		836 to
361
Amy Klobuchar6/8/0693 to
504		586 to
611		481 to
716		561 to
636		384 to
813		591 to
606		537 to
660		 528 to
669		413 to
784		617 to
580		732 to
465		738 to
459		652 to
545		713 to
484
Bernie Sanders11/3/0687 to
510		724 to
473		584 to
613		685 to
512		579 to
618		679 to
518		621 to
576		669 to
528		 560 to
637		720 to
477		729 to
468		730 to
467		677 to
520		709 to
488
Andrew Yang12/2/0757 to
440		825 to
372		598 to
599		747 to
450		580 to
617		718 to
479		645 to
552		784 to
413		637 to
560		 802 to
395		870 to
327		859 to
338		746 to
451		790 to
407
Elizabeth Warren6/8/0663 to
534		674 to
523		524 to
673		567 to
630		480 to
717		598 to
599		559 to
638		580 to
617		477 to
720		395 to
802		 672 to
525		697 to
500		641 to
556		684 to
513
John Kasich4/10/0705 to
492		579 to
618		379 to
818		540 to
657		335 to
862		540 to
657		404 to
793		465 to
732		468 to
729		327 to
870		525 to
672		 756 to
441		617 to
580		738 to
459
Jeb Bush2/12/0710 to
487		566 to
631		352 to
845		519 to
678		331 to
866		513 to
684		370 to
827		459 to
738		467 to
730		338 to
859		500 to
697		441 to
756		 550 to
647		712 to
485
Rand Paul5/9/0833 to
364		607 to
590		387 to
810		574 to
623		463 to
734		626 to
571		415 to
782		545 to
652		520 to
677		451 to
746		556 to
641		580 to
617		647 to
550		 867 to
330
Ted Cruz1/13/0741 to
456		550 to
647		352 to
845		516 to
681		392 to
805		480 to
717		361 to
836		484 to
713		488 to
709		407 to
790		513 to
684		459 to
738		485 to
712		330 to
867

And the Condorcet winner is: Jo Jorgensen.

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 Trump3733 3.1
Joe Biden4055 3.4
Jo Jorgensen4877 4.1
Howie Hawkins3172 2.6
Tulsi Gabbard4349 3.6
Dan Crenshaw2941 2.5
Justin Amash4226 3.5
Amy Klobuchar3202 2.7
Bernie Sanders5347 4.5
Andrew Yang5286 4.4
Elizabeth Warren4221 3.5
John Kasich2758 2.3
Jeb Bush2617 2.2
Rand Paul4221 3.5
Ted Cruz3226 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 Trump3733
Joe Biden4055
Jo Jorgensen4877
Howie Hawkins3172
Tulsi Gabbard4349
Dan Crenshaw2941
Justin Amash4226
Amy Klobuchar3202
Bernie Sanders5347
Andrew Yang5286
Elizabeth Warren4221
John Kasich2758
Jeb Bush2617
Rand Paul4221
Ted Cruz3226

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 Sanders763
Andrew Yang764

And the winner is: Andrew Yang

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 Trump4/10/0 462 to
589		328 to
675		475 to
484		373 to
599		393 to
371		354 to
592		467 to
518		459 to
625		397 to
687		490 to
553		459 to
440		447 to
427		309 to
525		365 to
315
Joe Biden9/5/0589 to
462		 500 to
529		512 to
378		441 to
569		589 to
384		518 to
451		476 to
277		275 to
540		279 to
627		344 to
417		553 to
314		578 to
318		555 to
517		598 to
430
Jo Jorgensen12/2/0675 to
328		529 to
500		 551 to
258		467 to
411		607 to
225		423 to
310		530 to
366		465 to
572		400 to
557		513 to
473		594 to
277		621 to
268		537 to
309		663 to
260
Howie Hawkins5/9/0484 to
475		378 to
512		258 to
551		 246 to
563		393 to
366		304 to
470		343 to
391		226 to
589		215 to
638		322 to
430		385 to
366		412 to
384		366 to
511		448 to
437
Tulsi Gabbard11/3/0599 to
373		569 to
441		411 to
467		563 to
246		 568 to
240		441 to
379		549 to
293		453 to
543		382 to
519		503 to
418		586 to
227		605 to
247		464 to
387		588 to
320
Dan Crenshaw1/13/0371 to
393		384 to
589		225 to
607		366 to
393		240 to
568		 227 to
483		341 to
443		358 to
636		289 to
653		387 to
518		346 to
351		359 to
365		239 to
474		338 to
323
Justin Amash8/6/0592 to
354		451 to
518		310 to
423		470 to
304		379 to
441		483 to
227		 421 to
390		415 to
579		353 to
564		432 to
490		470 to
267		514 to
274		443 to
316		560 to
280
Amy Klobuchar6/8/0518 to
467		277 to
476		366 to
530		391 to
343		293 to
549		443 to
341		390 to
421		 246 to
591		188 to
654		266 to
446		414 to
272		457 to
315		419 to
503		494 to
420
Bernie Sanders13/1/0625 to
459		540 to
275		572 to
465		589 to
226		543 to
453		636 to
358		579 to
415		591 to
246		 433 to
434		506 to
207		617 to
295		630 to
312		584 to
478		634 to
416
Andrew Yang14/0/0687 to
397		627 to
279		557 to
400		638 to
215		519 to
382		653 to
289		564 to
353		654 to
188		434 to
433		 543 to
279		684 to
205		693 to
232		578 to
406		663 to
356
Elizabeth Warren9/5/0553 to
490		417 to
344		473 to
513		430 to
322		418 to
503		518 to
387		490 to
432		446 to
266		207 to
506		279 to
543		 492 to
287		516 to
339		503 to
505		544 to
451
John Kasich3/11/0440 to
459		314 to
553		277 to
594		366 to
385		227 to
586		351 to
346		267 to
470		272 to
414		295 to
617		205 to
684		287 to
492		 326 to
248		314 to
477		406 to
382
Jeb Bush1/12/1427 to
447		318 to
578		268 to
621		384 to
412		247 to
605		365 to
359		274 to
514		315 to
457		312 to
630		232 to
693		339 to
516		248 to
326		 268 to
477		369 to
369
Rand Paul8/6/0525 to
309		517 to
555		309 to
537		511 to
366		387 to
464		474 to
239		316 to
443		503 to
419		478 to
584		406 to
578		505 to
503		477 to
314		477 to
268		 497 to
190
Ted Cruz0/13/1315 to
365		430 to
598		260 to
663		437 to
448		320 to
588		323 to
338		280 to
560		420 to
494		416 to
634		356 to
663		451 to
544		382 to
406		369 to
369		190 to
497

And the Condorcet winner is: Andrew Yang.

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
0649936.20%
114307.96%
212326.86%
313477.50%
412416.91%
514668.16%
69835.47%
79735.42%
89175.11%
97133.97%
1011546.43%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump589505266436143504740156
Joe Biden399957286101948797693958
Jo Jorgensen308101881098510952635967156
Howie Hawkins494119889180975547472653
Tulsi Gabbard3167685111118140112102603839
Dan Crenshaw521112909771995354442927
Justin Amash4049584967610748466260119
Amy Klobuchar4619181128941218265431714
Bernie Sanders377666957556050698699209
Andrew Yang27171788296120949910578103
Elizabeth Warren44689755279627364878288
John Kasich50410299114103122643927914
Jeb Bush479138116130110984334241114
Rand Paul397107827566897683866967
Ted Cruz533118735364875161714937

Number of bullet votes: 30 (2.51%).
Number of "approval" votes: 16 (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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