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 Hawkins31
Tulsi Gabbard33
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders191
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush8
Rand Paul33
Ted Cruz20
TOTAL:1194

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump370
Joe Biden452
Jo Jorgensen418
Howie Hawkins203
Tulsi Gabbard344
Dan Crenshaw160
Justin Amash315
Amy Klobuchar197
Bernie Sanders509
Andrew Yang467
Elizabeth Warren371
John Kasich153
Jeb Bush120
Rand Paul364
Ted Cruz247
Ballots Cast:1194

The winner is Bernie Sanders with 42.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump232
Joe Biden103
Jo Jorgensen168
Howie Hawkins44
Tulsi Gabbard31
Dan Crenshaw21
Justin Amash81
Amy Klobuchar15
Bernie Sanders233
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 Gabbard31
Dan Crenshaw21
Justin Amash82
Amy Klobuchar15
Bernie Sanders234
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 Gabbard31
Dan Crenshaw21
Justin Amash82
Bernie Sanders236
Andrew Yang91
Elizabeth Warren69
John Kasich21
Rand Paul50
Ted Cruz35

Eliminated in this round:

Round 4:

Donald Trump235
Joe Biden115
Jo Jorgensen173
Howie Hawkins46
Tulsi Gabbard39
Justin Amash85
Bernie Sanders238
Andrew Yang94
Elizabeth Warren71
Rand Paul56
Ted Cruz42

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump238
Joe Biden120
Jo Jorgensen182
Howie Hawkins48
Justin Amash93
Bernie Sanders242
Andrew Yang98
Elizabeth Warren72
Rand Paul59
Ted Cruz42

Ted Cruz eliminated in this round.

Round 6:

Donald Trump257
Joe Biden122
Jo Jorgensen185
Howie Hawkins49
Justin Amash94
Bernie Sanders244
Andrew Yang98
Elizabeth Warren72
Rand Paul73

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump260
Joe Biden128
Jo Jorgensen187
Justin Amash94
Bernie Sanders277
Andrew Yang101
Elizabeth Warren74
Rand Paul73

Rand Paul eliminated in this round.

Round 8:

Donald Trump286
Joe Biden129
Jo Jorgensen202
Justin Amash118
Bernie Sanders278
Andrew Yang105
Elizabeth Warren76

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump286
Joe Biden146
Jo Jorgensen207
Justin Amash119
Bernie Sanders317
Andrew Yang119

Eliminated in this round:

Round 10:

Donald Trump301
Joe Biden176
Jo Jorgensen331
Bernie Sanders386

Joe Biden eliminated in this round.

Round 11:

Donald Trump313
Jo Jorgensen376
Bernie Sanders505

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen613
Bernie Sanders581

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 Trump0/14/0 532 to
662		355 to
839		501 to
693		409 to
785		456 to
738		379 to
815		503 to
691		510 to
684		439 to
755		533 to
661		491 to
703		485 to
709		362 to
832		454 to
740
Joe Biden6/8/0662 to
532		 518 to
676		583 to
611		506 to
688		628 to
566		572 to
622		611 to
583		473 to
721		371 to
823		523 to
671		618 to
576		630 to
564		589 to
605		645 to
549
Jo Jorgensen14/0/0839 to
355		676 to
518		 761 to
433		669 to
525		824 to
370		729 to
465		715 to
479		613 to
581		598 to
596		673 to
521		817 to
377		844 to
350		809 to
385		844 to
350
Howie Hawkins9/5/0693 to
501		611 to
583		433 to
761		 494 to
700		666 to
528		590 to
604		634 to
560		511 to
683		449 to
745		628 to
566		655 to
539		675 to
519		621 to
573		679 to
515
Tulsi Gabbard13/1/0785 to
409		688 to
506		525 to
669		700 to
494		 823 to
371		719 to
475		810 to
384		616 to
578		614 to
580		714 to
480		859 to
335		863 to
331		731 to
463		802 to
392
Dan Crenshaw5/8/1738 to
456		566 to
628		370 to
824		528 to
666		371 to
823		 509 to
685		603 to
591		517 to
677		478 to
716		597 to
597		655 to
539		682 to
512		569 to
625		715 to
479
Justin Amash10/4/0815 to
379		622 to
572		465 to
729		604 to
590		475 to
719		685 to
509		 658 to
536		576 to
618		551 to
643		636 to
558		792 to
402		826 to
368		779 to
415		835 to
359
Amy Klobuchar6/8/0691 to
503		583 to
611		479 to
715		560 to
634		384 to
810		591 to
603		536 to
658		 527 to
667		412 to
782		615 to
579		731 to
463		736 to
458		651 to
543		711 to
483
Bernie Sanders11/3/0684 to
510		721 to
473		581 to
613		683 to
511		578 to
616		677 to
517		618 to
576		667 to
527		 557 to
637		717 to
477		727 to
467		727 to
467		674 to
520		706 to
488
Andrew Yang12/2/0755 to
439		823 to
371		596 to
598		745 to
449		580 to
614		716 to
478		643 to
551		782 to
412		637 to
557		 801 to
393		868 to
326		857 to
337		743 to
451		788 to
406
Elizabeth Warren6/7/1661 to
533		671 to
523		521 to
673		566 to
628		480 to
714		597 to
597		558 to
636		579 to
615		477 to
717		393 to
801		 671 to
523		695 to
499		639 to
555		682 to
512
John Kasich4/10/0703 to
491		576 to
618		377 to
817		539 to
655		335 to
859		539 to
655		402 to
792		463 to
731		467 to
727		326 to
868		523 to
671		 754 to
440		615 to
579		736 to
458
Jeb Bush2/12/0709 to
485		564 to
630		350 to
844		519 to
675		331 to
863		512 to
682		368 to
826		458 to
736		467 to
727		337 to
857		499 to
695		440 to
754		 548 to
646		710 to
484
Rand Paul5/9/0832 to
362		605 to
589		385 to
809		573 to
621		463 to
731		625 to
569		415 to
779		543 to
651		520 to
674		451 to
743		555 to
639		579 to
615		646 to
548		 866 to
328
Ted Cruz1/13/0740 to
454		549 to
645		350 to
844		515 to
679		392 to
802		479 to
715		359 to
835		483 to
711		488 to
706		406 to
788		512 to
682		458 to
736		484 to
710		328 to
866

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 Trump3720 3.1
Joe Biden4046 3.4
Jo Jorgensen4871 4.1
Howie Hawkins3158 2.6
Tulsi Gabbard4326 3.6
Dan Crenshaw2926 2.5
Justin Amash4216 3.5
Amy Klobuchar3189 2.7
Bernie Sanders5324 4.5
Andrew Yang5274 4.4
Elizabeth Warren4205 3.5
John Kasich2744 2.3
Jeb Bush2607 2.2
Rand Paul4210 3.5
Ted Cruz3219 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 Trump3720
Joe Biden4046
Jo Jorgensen4871
Howie Hawkins3158
Tulsi Gabbard4326
Dan Crenshaw2926
Justin Amash4216
Amy Klobuchar3189
Bernie Sanders5324
Andrew Yang5274
Elizabeth Warren4205
John Kasich2744
Jeb Bush2607
Rand Paul4210
Ted Cruz3219

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 Sanders760
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 Trump4/10/0 461 to
589		326 to
674		474 to
482		373 to
596		392 to
369		352 to
591		466 to
516		459 to
622		396 to
685		489 to
551		458 to
438		445 to
426		307 to
524		362 to
315
Joe Biden9/5/0589 to
461		 499 to
527		512 to
375		441 to
566		589 to
381		517 to
449		476 to
274		275 to
537		278 to
625		344 to
415		553 to
311		577 to
317		554 to
516		596 to
429
Jo Jorgensen12/2/0674 to
326		527 to
499		 551 to
257		467 to
408		607 to
224		423 to
309		530 to
364		465 to
569		400 to
555		512 to
471		594 to
275		619 to
267		536 to
307		662 to
259
Howie Hawkins5/9/0482 to
474		375 to
512		257 to
551		 245 to
561		393 to
365		303 to
469		342 to
390		225 to
587		214 to
636		320 to
429		384 to
365		410 to
384		364 to
510		446 to
437
Tulsi Gabbard11/3/0596 to
373		566 to
441		408 to
467		561 to
245		 566 to
239		438 to
379		547 to
293		452 to
542		380 to
519		501 to
418		584 to
226		603 to
246		461 to
387		585 to
320
Dan Crenshaw1/13/0369 to
392		381 to
589		224 to
607		365 to
393		239 to
566		 226 to
482		340 to
442		357 to
634		288 to
651		385 to
517		345 to
350		356 to
365		237 to
473		336 to
323
Justin Amash8/6/0591 to
352		449 to
517		309 to
423		469 to
303		379 to
438		482 to
226		 420 to
389		415 to
576		352 to
563		431 to
488		469 to
265		512 to
273		441 to
315		559 to
279
Amy Klobuchar6/8/0516 to
466		274 to
476		364 to
530		390 to
342		293 to
547		442 to
340		389 to
420		 246 to
589		187 to
652		265 to
445		413 to
270		455 to
314		417 to
502		492 to
420
Bernie Sanders13/1/0622 to
459		537 to
275		569 to
465		587 to
225		542 to
452		634 to
357		576 to
415		589 to
246		 430 to
434		504 to
207		615 to
294		628 to
311		581 to
478		631 to
416
Andrew Yang14/0/0685 to
396		625 to
278		555 to
400		636 to
214		519 to
380		651 to
288		563 to
352		652 to
187		434 to
430		 542 to
277		682 to
204		691 to
231		577 to
405		661 to
355
Elizabeth Warren9/5/0551 to
489		415 to
344		471 to
512		429 to
320		418 to
501		517 to
385		488 to
431		445 to
265		207 to
504		277 to
542		 491 to
285		515 to
338		501 to
505		542 to
450
John Kasich3/11/0438 to
458		311 to
553		275 to
594		365 to
384		226 to
584		350 to
345		265 to
469		270 to
413		294 to
615		204 to
682		285 to
491		 324 to
247		312 to
476		403 to
382
Jeb Bush1/12/1426 to
445		317 to
577		267 to
619		384 to
410		246 to
603		365 to
356		273 to
512		314 to
455		311 to
628		231 to
691		338 to
515		247 to
324		 267 to
476		368 to
368
Rand Paul8/6/0524 to
307		516 to
554		307 to
536		510 to
364		387 to
461		473 to
237		315 to
441		502 to
417		478 to
581		405 to
577		505 to
501		476 to
312		476 to
267		 496 to
189
Ted Cruz0/13/1315 to
362		429 to
596		259 to
662		437 to
446		320 to
585		323 to
336		279 to
559		420 to
492		416 to
631		355 to
661		450 to
542		382 to
403		368 to
368		189 to
496

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
0649436.26%
114307.98%
212266.85%
313377.47%
412376.91%
514628.16%
69785.46%
79695.41%
89135.10%
97113.97%
1011536.44%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump589505166436042504740156
Joe Biden399957086101938797693958
Jo Jorgensen307101881078510952635967156
Howie Hawkins494119888980975547462653
Tulsi Gabbard3167685111118140111101603838
Dan Crenshaw521112909571995354442827
Justin Amash4039584957610748456260119
Amy Klobuchar4619181127931218165431714
Bernie Sanders377666957556049698598209
Andrew Yang27071788296119949810578103
Elizabeth Warren44689745279627264868288
John Kasich50410299113102122643827914
Jeb Bush478138115130110984334231114
Rand Paul397107817565887683866967
Ted Cruz532118735263875161714937

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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