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 Trump260
Joe Biden246
Jo Jorgensen191
Howie Hawkins30
Tulsi Gabbard32
Dan Crenshaw14
Justin Amash51
Amy Klobuchar13
Bernie Sanders188
Andrew Yang51
Elizabeth Warren33
John Kasich14
Jeb Bush7
Rand Paul33
Ted Cruz20
TOTAL:1183

The winner is Donald Trump with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump365
Joe Biden448
Jo Jorgensen416
Howie Hawkins200
Tulsi Gabbard338
Dan Crenshaw158
Justin Amash314
Amy Klobuchar197
Bernie Sanders505
Andrew Yang464
Elizabeth Warren368
John Kasich151
Jeb Bush118
Rand Paul360
Ted Cruz246
Ballots Cast:1183

The winner is Bernie Sanders with 42.7% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump230
Joe Biden102
Jo Jorgensen168
Howie Hawkins43
Tulsi Gabbard29
Dan Crenshaw20
Justin Amash81
Amy Klobuchar15
Bernie Sanders230
Andrew Yang90
Elizabeth Warren68
John Kasich18
Jeb Bush8
Rand Paul49
Ted Cruz32

Jeb Bush eliminated in this round.

Round 2:

Donald Trump231
Joe Biden102
Jo Jorgensen168
Howie Hawkins43
Tulsi Gabbard29
Dan Crenshaw20
Justin Amash82
Amy Klobuchar15
Bernie Sanders231
Andrew Yang90
Elizabeth Warren68
John Kasich20
Rand Paul49
Ted Cruz35

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump231
Joe Biden109
Jo Jorgensen169
Howie Hawkins45
Tulsi Gabbard29
Dan Crenshaw20
Justin Amash82
Bernie Sanders233
Andrew Yang91
Elizabeth Warren69
John Kasich21
Rand Paul49
Ted Cruz35

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump232
Joe Biden110
Jo Jorgensen173
Howie Hawkins45
Tulsi Gabbard32
Justin Amash83
Bernie Sanders233
Andrew Yang92
Elizabeth Warren69
John Kasich23
Rand Paul51
Ted Cruz40

John Kasich eliminated in this round.

Round 5:

Donald Trump233
Joe Biden114
Jo Jorgensen173
Howie Hawkins45
Tulsi Gabbard36
Justin Amash85
Bernie Sanders235
Andrew Yang94
Elizabeth Warren71
Rand Paul55
Ted Cruz42

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump236
Joe Biden118
Jo Jorgensen181
Howie Hawkins46
Justin Amash93
Bernie Sanders239
Andrew Yang98
Elizabeth Warren72
Rand Paul58
Ted Cruz42

Ted Cruz eliminated in this round.

Round 7:

Donald Trump255
Joe Biden120
Jo Jorgensen184
Howie Hawkins47
Justin Amash94
Bernie Sanders241
Andrew Yang98
Elizabeth Warren72
Rand Paul72

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump256
Joe Biden126
Jo Jorgensen186
Justin Amash94
Bernie Sanders274
Andrew Yang101
Elizabeth Warren74
Rand Paul72

Rand Paul eliminated in this round.

Round 9:

Donald Trump281
Joe Biden127
Jo Jorgensen201
Justin Amash118
Bernie Sanders275
Andrew Yang105
Elizabeth Warren76

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump281
Joe Biden144
Jo Jorgensen206
Justin Amash119
Bernie Sanders314
Andrew Yang119

Eliminated in this round:

Round 11:

Donald Trump296
Joe Biden174
Jo Jorgensen330
Bernie Sanders383

Joe Biden eliminated in this round.

Round 12:

Donald Trump307
Jo Jorgensen375
Bernie Sanders501

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen607
Bernie Sanders576

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 Trump0/14/0 527 to
656		349 to
834		498 to
685		405 to
778		451 to
732		373 to
810		496 to
687		504 to
679		434 to
749		528 to
655		484 to
699		479 to
704		357 to
826		448 to
735
Joe Biden6/8/0656 to
527		 515 to
668		578 to
605		504 to
679		623 to
560		566 to
617		606 to
577		468 to
715		366 to
817		518 to
665		613 to
570		625 to
558		584 to
599		639 to
544
Jo Jorgensen14/0/0834 to
349		668 to
515		 757 to
426		666 to
517		820 to
363		723 to
460		711 to
472		607 to
576		594 to
589		668 to
515		810 to
373		836 to
347		801 to
382		837 to
346
Howie Hawkins9/5/0685 to
498		605 to
578		426 to
757		 492 to
691		662 to
521		584 to
599		628 to
555		507 to
676		445 to
738		622 to
561		648 to
535		668 to
515		613 to
570		672 to
511
Tulsi Gabbard13/1/0778 to
405		679 to
504		517 to
666		691 to
492		 814 to
369		709 to
474		801 to
382		608 to
575		605 to
578		704 to
479		849 to
334		854 to
329		721 to
462		792 to
391
Dan Crenshaw5/9/0732 to
451		560 to
623		363 to
820		521 to
662		369 to
814		 503 to
680		598 to
585		510 to
673		472 to
711		590 to
593		650 to
533		676 to
507		563 to
620		708 to
475
Justin Amash10/4/0810 to
373		617 to
566		460 to
723		599 to
584		474 to
709		680 to
503		 653 to
530		571 to
612		548 to
635		631 to
552		785 to
398		819 to
364		772 to
411		829 to
354
Amy Klobuchar6/8/0687 to
496		577 to
606		472 to
711		555 to
628		382 to
801		585 to
598		530 to
653		 521 to
662		407 to
776		609 to
574		725 to
458		729 to
454		644 to
539		705 to
478
Bernie Sanders11/3/0679 to
504		715 to
468		576 to
607		676 to
507		575 to
608		673 to
510		612 to
571		662 to
521		 551 to
632		709 to
474		721 to
462		721 to
462		667 to
516		699 to
484
Andrew Yang12/2/0749 to
434		817 to
366		589 to
594		738 to
445		578 to
605		711 to
472		635 to
548		776 to
407		632 to
551		 793 to
390		861 to
322		850 to
333		734 to
449		780 to
403
Elizabeth Warren7/7/0655 to
528		665 to
518		515 to
668		561 to
622		479 to
704		593 to
590		552 to
631		574 to
609		474 to
709		390 to
793		 665 to
518		688 to
495		632 to
551		675 to
508
John Kasich4/10/0699 to
484		570 to
613		373 to
810		535 to
648		334 to
849		533 to
650		398 to
785		458 to
725		462 to
721		322 to
861		518 to
665		 745 to
438		608 to
575		730 to
453
Jeb Bush2/12/0704 to
479		558 to
625		347 to
836		515 to
668		329 to
854		507 to
676		364 to
819		454 to
729		462 to
721		333 to
850		495 to
688		438 to
745		 543 to
640		703 to
480
Rand Paul5/9/0826 to
357		599 to
584		382 to
801		570 to
613		462 to
721		620 to
563		411 to
772		539 to
644		516 to
667		449 to
734		551 to
632		575 to
608		640 to
543		 858 to
325
Ted Cruz1/13/0735 to
448		544 to
639		346 to
837		511 to
672		391 to
792		475 to
708		354 to
829		478 to
705		484 to
699		403 to
780		508 to
675		453 to
730		480 to
703		325 to
858

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 Trump3672 3.1
Joe Biden4004 3.4
Jo Jorgensen4836 4.1
Howie Hawkins3114 2.6
Tulsi Gabbard4260 3.6
Dan Crenshaw2884 2.4
Justin Amash4186 3.5
Amy Klobuchar3158 2.7
Bernie Sanders5281 4.5
Andrew Yang5224 4.4
Elizabeth Warren4167 3.5
John Kasich2703 2.3
Jeb Bush2563 2.2
Rand Paul4171 3.5
Ted Cruz3186 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 Trump3672
Joe Biden4004
Jo Jorgensen4836
Howie Hawkins3114
Tulsi Gabbard4260
Dan Crenshaw2884
Justin Amash4186
Amy Klobuchar3158
Bernie Sanders5281
Andrew Yang5224
Elizabeth Warren4167
John Kasich2703
Jeb Bush2563
Rand Paul4171
Ted Cruz3186

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 Sanders753
Andrew Yang758

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 Trump4/10/0 456 to
583		321 to
670		470 to
476		369 to
591		388 to
365		346 to
589		460 to
512		453 to
618		392 to
679		483 to
547		452 to
434		440 to
422		302 to
521		355 to
314
Joe Biden9/5/0583 to
456		 496 to
520		509 to
370		439 to
557		585 to
377		513 to
445		469 to
271		271 to
530		275 to
620		339 to
410		549 to
305		572 to
313		548 to
511		590 to
424
Jo Jorgensen12/2/0670 to
321		520 to
496		 546 to
254		467 to
400		604 to
219		419 to
307		526 to
361		461 to
563		397 to
548		507 to
467		591 to
269		614 to
263		532 to
303		658 to
255
Howie Hawkins5/9/0476 to
470		370 to
509		254 to
546		 243 to
553		388 to
361		299 to
464		337 to
387		222 to
581		211 to
631		314 to
425		380 to
360		405 to
379		359 to
507		440 to
433
Tulsi Gabbard11/3/0591 to
369		557 to
439		400 to
467		553 to
243		 560 to
236		431 to
379		538 to
292		446 to
539		373 to
516		493 to
416		577 to
224		597 to
243		455 to
385		579 to
319
Dan Crenshaw1/13/0365 to
388		377 to
585		219 to
604		361 to
388		236 to
560		 221 to
481		335 to
439		352 to
630		285 to
646		378 to
513		342 to
345		352 to
360		232 to
470		332 to
319
Justin Amash8/6/0589 to
346		445 to
513		307 to
419		464 to
299		379 to
431		481 to
221		 416 to
386		411 to
571		350 to
556		427 to
484		468 to
259		511 to
267		437 to
311		556 to
274
Amy Klobuchar6/8/0512 to
460		271 to
469		361 to
526		387 to
337		292 to
538		439 to
335		386 to
416		 241 to
584		184 to
645		261 to
439		412 to
263		453 to
307		414 to
498		488 to
415
Bernie Sanders13/1/0618 to
453		530 to
271		563 to
461		581 to
222		539 to
446		630 to
352		571 to
411		584 to
241		 425 to
430		498 to
204		611 to
287		624 to
304		576 to
473		627 to
410
Andrew Yang14/0/0679 to
392		620 to
275		548 to
397		631 to
211		516 to
373		646 to
285		556 to
350		645 to
184		430 to
425		 536 to
276		675 to
201		686 to
226		569 to
402		654 to
351
Elizabeth Warren9/5/0547 to
483		410 to
339		467 to
507		425 to
314		416 to
493		513 to
378		484 to
427		439 to
261		204 to
498		276 to
536		 487 to
279		511 to
331		494 to
501		537 to
446
John Kasich3/11/0434 to
452		305 to
549		269 to
591		360 to
380		224 to
577		345 to
342		259 to
468		263 to
412		287 to
611		201 to
675		279 to
487		 321 to
243		307 to
474		399 to
379
Jeb Bush1/13/0422 to
440		313 to
572		263 to
614		379 to
405		243 to
597		360 to
352		267 to
511		307 to
453		304 to
624		226 to
686		331 to
511		243 to
321		 262 to
472		362 to
366
Rand Paul8/6/0521 to
302		511 to
548		303 to
532		507 to
359		385 to
455		470 to
232		311 to
437		498 to
414		473 to
576		402 to
569		501 to
494		474 to
307		472 to
262		 491 to
186
Ted Cruz1/13/0314 to
355		424 to
590		255 to
658		433 to
440		319 to
579		319 to
332		274 to
556		415 to
488		410 to
627		351 to
654		446 to
537		379 to
399		366 to
362		186 to
491

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
0646036.40%
114127.96%
212096.81%
313227.45%
412226.89%
514508.17%
69635.43%
79565.39%
89035.09%
96993.94%
1011496.48%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump585505065436042494638155
Joe Biden39892708599928696693957
Jo Jorgensen30599871068310950635867156
Howie Hawkins493117868879975446452652
Tulsi Gabbard314768411111814011198583538
Dan Crenshaw517111909570975354432726
Justin Amash4009482947410747456160119
Amy Klobuchar4598979126931197965431714
Bernie Sanders374656856555849698595209
Andrew Yang26970778293118949610378103
Elizabeth Warren44488735176627162868288
John Kasich50210198112102120613727914
Jeb Bush477137113128110964234221014
Rand Paul394107807264887583866767
Ted Cruz529116725163874959714937

Number of bullet votes: 30 (2.54%).
Number of "approval" votes: 16 (1%).

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