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 Trump249
Joe Biden238
Jo Jorgensen187
Howie Hawkins28
Tulsi Gabbard29
Dan Crenshaw14
Justin Amash51
Amy Klobuchar11
Bernie Sanders183
Andrew Yang50
Elizabeth Warren32
John Kasich14
Jeb Bush7
Rand Paul32
Ted Cruz18
TOTAL:1143

The winner is Donald Trump with 21.8% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump349
Joe Biden436
Jo Jorgensen406
Howie Hawkins194
Tulsi Gabbard330
Dan Crenshaw152
Justin Amash309
Amy Klobuchar194
Bernie Sanders490
Andrew Yang456
Elizabeth Warren360
John Kasich149
Jeb Bush112
Rand Paul353
Ted Cruz236
Ballots Cast:1143

The winner is Bernie Sanders with 42.9% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump220
Joe Biden96
Jo Jorgensen162
Howie Hawkins41
Tulsi Gabbard27
Dan Crenshaw19
Justin Amash81
Amy Klobuchar14
Bernie Sanders225
Andrew Yang90
Elizabeth Warren66
John Kasich18
Jeb Bush7
Rand Paul46
Ted Cruz31

Jeb Bush eliminated in this round.

Round 2:

Donald Trump220
Joe Biden96
Jo Jorgensen162
Howie Hawkins41
Tulsi Gabbard27
Dan Crenshaw19
Justin Amash82
Amy Klobuchar14
Bernie Sanders226
Andrew Yang90
Elizabeth Warren66
John Kasich20
Rand Paul46
Ted Cruz34

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump220
Joe Biden103
Jo Jorgensen163
Howie Hawkins43
Tulsi Gabbard27
Dan Crenshaw19
Justin Amash82
Bernie Sanders227
Andrew Yang91
Elizabeth Warren67
John Kasich21
Rand Paul46
Ted Cruz34

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump221
Joe Biden104
Jo Jorgensen167
Howie Hawkins43
Tulsi Gabbard30
Justin Amash83
Bernie Sanders227
Andrew Yang92
Elizabeth Warren67
John Kasich22
Rand Paul48
Ted Cruz39

John Kasich eliminated in this round.

Round 5:

Donald Trump222
Joe Biden108
Jo Jorgensen167
Howie Hawkins43
Tulsi Gabbard34
Justin Amash85
Bernie Sanders229
Andrew Yang94
Elizabeth Warren69
Rand Paul51
Ted Cruz41

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump224
Joe Biden112
Jo Jorgensen175
Howie Hawkins44
Justin Amash92
Bernie Sanders233
Andrew Yang98
Elizabeth Warren70
Rand Paul54
Ted Cruz41

Ted Cruz eliminated in this round.

Round 7:

Donald Trump242
Joe Biden114
Jo Jorgensen178
Howie Hawkins45
Justin Amash93
Bernie Sanders235
Andrew Yang98
Elizabeth Warren70
Rand Paul68

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump242
Joe Biden120
Jo Jorgensen180
Justin Amash93
Bernie Sanders267
Andrew Yang101
Elizabeth Warren72
Rand Paul68

Rand Paul eliminated in this round.

Round 9:

Donald Trump265
Joe Biden120
Jo Jorgensen195
Justin Amash116
Bernie Sanders268
Andrew Yang105
Elizabeth Warren74

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump265
Joe Biden137
Jo Jorgensen199
Justin Amash117
Bernie Sanders306
Andrew Yang119

Justin Amash eliminated in this round.

Round 11:

Donald Trump273
Joe Biden141
Jo Jorgensen292
Bernie Sanders310
Andrew Yang127

Andrew Yang eliminated in this round.

Round 12:

Donald Trump280
Joe Biden167
Jo Jorgensen321
Bernie Sanders375

Joe Biden eliminated in this round.

Round 13:

Donald Trump290
Jo Jorgensen364
Bernie Sanders489

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen584
Bernie Sanders559

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 Trump0/14/0 507 to
636		329 to
814		479 to
664		386 to
757		429 to
714		352 to
791		472 to
671		483 to
660		411 to
732		505 to
638		461 to
682		458 to
685		338 to
805		428 to
715
Joe Biden6/8/0636 to
507		 497 to
646		559 to
584		488 to
655		605 to
538		546 to
597		587 to
556		453 to
690		349 to
794		501 to
642		594 to
549		607 to
536		567 to
576		622 to
521
Jo Jorgensen13/1/0814 to
329		646 to
497		 731 to
412		641 to
502		793 to
350		693 to
450		682 to
461		584 to
559		566 to
577		639 to
504		777 to
366		808 to
335		772 to
371		812 to
331
Howie Hawkins9/5/0664 to
479		584 to
559		412 to
731		 472 to
671		637 to
506		557 to
586		601 to
542		486 to
657		420 to
723		595 to
548		619 to
524		644 to
499		587 to
556		650 to
493
Tulsi Gabbard13/1/0757 to
386		655 to
488		502 to
641		671 to
472		 790 to
353		682 to
461		773 to
370		587 to
556		579 to
564		678 to
465		819 to
324		827 to
316		692 to
451		768 to
375
Dan Crenshaw5/9/0714 to
429		538 to
605		350 to
793		506 to
637		353 to
790		 479 to
664		573 to
570		490 to
653		445 to
698		565 to
578		617 to
526		648 to
495		533 to
610		685 to
458
Justin Amash10/4/0791 to
352		597 to
546		450 to
693		586 to
557		461 to
682		664 to
479		 628 to
515		550 to
593		527 to
616		604 to
539		758 to
385		796 to
347		744 to
399		805 to
338
Amy Klobuchar6/8/0671 to
472		556 to
587		461 to
682		542 to
601		370 to
773		570 to
573		515 to
628		 501 to
642		386 to
757		583 to
560		699 to
444		707 to
436		619 to
524		685 to
458
Bernie Sanders11/3/0660 to
483		690 to
453		559 to
584		657 to
486		556 to
587		653 to
490		593 to
550		642 to
501		 528 to
615		684 to
459		696 to
447		698 to
445		644 to
499		678 to
465
Andrew Yang13/1/0732 to
411		794 to
349		577 to
566		723 to
420		564 to
579		698 to
445		616 to
527		757 to
386		615 to
528		 766 to
377		831 to
312		825 to
318		705 to
438		760 to
383
Elizabeth Warren7/7/0638 to
505		642 to
501		504 to
639		548 to
595		465 to
678		578 to
565		539 to
604		560 to
583		459 to
684		377 to
766		 643 to
500		669 to
474		608 to
535		655 to
488
John Kasich4/10/0682 to
461		549 to
594		366 to
777		524 to
619		324 to
819		526 to
617		385 to
758		444 to
699		447 to
696		312 to
831		500 to
643		 725 to
418		586 to
557		709 to
434
Jeb Bush2/12/0685 to
458		536 to
607		335 to
808		499 to
644		316 to
827		495 to
648		347 to
796		436 to
707		445 to
698		318 to
825		474 to
669		418 to
725		 520 to
623		680 to
463
Rand Paul5/9/0805 to
338		576 to
567		371 to
772		556 to
587		451 to
692		610 to
533		399 to
744		524 to
619		499 to
644		438 to
705		535 to
608		557 to
586		623 to
520		 834 to
309
Ted Cruz1/13/0715 to
428		521 to
622		331 to
812		493 to
650		375 to
768		458 to
685		338 to
805		458 to
685		465 to
678		383 to
760		488 to
655		434 to
709		463 to
680		309 to
834

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 Trump3495 3.1
Joe Biden3889 3.4
Jo Jorgensen4709 4.1
Howie Hawkins2999 2.6
Tulsi Gabbard4131 3.6
Dan Crenshaw2776 2.4
Justin Amash4081 3.6
Amy Klobuchar3062 2.7
Bernie Sanders5147 4.5
Andrew Yang5113 4.5
Elizabeth Warren4068 3.6
John Kasich2619 2.3
Jeb Bush2459 2.2
Rand Paul4030 3.5
Ted Cruz3038 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 Trump3495
Joe Biden3889
Jo Jorgensen4709
Howie Hawkins2999
Tulsi Gabbard4131
Dan Crenshaw2776
Justin Amash4081
Amy Klobuchar3062
Bernie Sanders5147
Andrew Yang5113
Elizabeth Warren4068
John Kasich2619
Jeb Bush2459
Rand Paul4030
Ted Cruz3038

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 Sanders728
Andrew Yang736

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 Trump4/10/0 435 to
566		303 to
656		448 to
464		350 to
575		368 to
354		326 to
575		438 to
499		433 to
600		371 to
663		458 to
534		428 to
422		420 to
411		285 to
504		336 to
302
Joe Biden9/5/0566 to
435		 480 to
504		494 to
355		425 to
537		569 to
362		497 to
429		453 to
258		262 to
513		263 to
603		325 to
396		531 to
292		554 to
299		532 to
493		575 to
403
Jo Jorgensen12/2/0656 to
303		504 to
480		 531 to
246		455 to
385		592 to
208		405 to
298		512 to
353		445 to
545		386 to
532		490 to
457		573 to
260		598 to
248		520 to
287		644 to
238
Howie Hawkins5/9/0464 to
448		355 to
494		246 to
531		 233 to
535		378 to
348		286 to
450		324 to
378		211 to
563		200 to
613		297 to
415		364 to
347		391 to
363		347 to
487		429 to
412
Tulsi Gabbard11/3/0575 to
350		537 to
425		385 to
455		535 to
233		 542 to
224		411 to
369		520 to
281		428 to
522		360 to
501		475 to
406		557 to
217		579 to
229		442 to
370		564 to
300
Dan Crenshaw1/13/0354 to
368		362 to
569		208 to
592		348 to
378		224 to
542		 208 to
468		322 to
426		339 to
609		272 to
631		362 to
503		327 to
338		339 to
347		222 to
452		323 to
301
Justin Amash8/6/0575 to
326		429 to
497		298 to
405		450 to
286		369 to
411		468 to
208		 405 to
372		394 to
554		340 to
540		411 to
474		453 to
250		496 to
255		428 to
295		541 to
257
Amy Klobuchar6/8/0499 to
438		258 to
453		353 to
512		378 to
324		281 to
520		426 to
322		372 to
405		 232 to
566		178 to
629		249 to
431		398 to
257		441 to
294		404 to
482		477 to
394
Bernie Sanders13/1/0600 to
433		513 to
262		545 to
445		563 to
211		522 to
428		609 to
339		554 to
394		566 to
232		 407 to
415		481 to
194		592 to
274		608 to
289		563 to
455		614 to
389
Andrew Yang14/0/0663 to
371		603 to
263		532 to
386		613 to
200		501 to
360		631 to
272		540 to
340		629 to
178		415 to
407		 518 to
267		657 to
193		670 to
215		556 to
389		641 to
331
Elizabeth Warren10/4/0534 to
458		396 to
325		457 to
490		415 to
297		406 to
475		503 to
362		474 to
411		431 to
249		194 to
481		267 to
518		 476 to
269		503 to
312		486 to
481		526 to
422
John Kasich3/11/0422 to
428		292 to
531		260 to
573		347 to
364		217 to
557		338 to
327		250 to
453		257 to
398		274 to
592		193 to
657		269 to
476		 314 to
229		303 to
455		389 to
358
Jeb Bush2/12/0411 to
420		299 to
554		248 to
598		363 to
391		229 to
579		347 to
339		255 to
496		294 to
441		289 to
608		215 to
670		312 to
503		229 to
314		 253 to
455		351 to
348
Rand Paul7/7/0504 to
285		493 to
532		287 to
520		487 to
347		370 to
442		452 to
222		295 to
428		482 to
404		455 to
563		389 to
556		481 to
486		455 to
303		455 to
253		 475 to
173
Ted Cruz0/14/0302 to
336		403 to
575		238 to
644		412 to
429		300 to
564		301 to
323		257 to
541		394 to
477		389 to
614		331 to
641		422 to
526		358 to
389		348 to
351		173 to
475

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
0628236.64%
113527.89%
211356.62%
312617.35%
411746.85%
513858.08%
69335.44%
79345.45%
88785.12%
96803.97%
1011316.60%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump573494861405641494238146
Joe Biden38190678395898396673557
Jo Jorgensen29594841008010348625766154
Howie Hawkins483108838378945143442551
Tulsi Gabbard306738010810813310996573538
Dan Crenshaw503106859268955052412526
Justin Amash3909272877210147446059119
Amy Klobuchar4448576120921137763421714
Bernie Sanders361626454525346688492207
Andrew Yang25867717889111919510278103
Elizabeth Warren43181685070596962858286
John Kasich4909490106101118603625914
Jeb Bush465135103124107934033191014
Rand Paul384103746961857480846366
Ted Cruz518113704661824755694636

Number of bullet votes: 29 (2.54%).
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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