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 Trump207
Joe Biden227
Jo Jorgensen183
Howie Hawkins26
Tulsi Gabbard27
Dan Crenshaw12
Justin Amash49
Amy Klobuchar11
Bernie Sanders161
Andrew Yang45
Elizabeth Warren31
John Kasich13
Jeb Bush6
Rand Paul30
Ted Cruz16
TOTAL:1044

The winner is Joe Biden with 21.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump301
Joe Biden409
Jo Jorgensen393
Howie Hawkins176
Tulsi Gabbard314
Dan Crenshaw136
Justin Amash298
Amy Klobuchar183
Bernie Sanders451
Andrew Yang439
Elizabeth Warren344
John Kasich135
Jeb Bush100
Rand Paul336
Ted Cruz205
Ballots Cast:1044

The winner is Bernie Sanders with 43.2% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump182
Joe Biden85
Jo Jorgensen158
Howie Hawkins39
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash79
Amy Klobuchar14
Bernie Sanders206
Andrew Yang81
Elizabeth Warren65
John Kasich18
Jeb Bush6
Rand Paul42
Ted Cruz27

Jeb Bush eliminated in this round.

Round 2:

Donald Trump182
Joe Biden85
Jo Jorgensen158
Howie Hawkins39
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Amy Klobuchar14
Bernie Sanders207
Andrew Yang81
Elizabeth Warren65
John Kasich19
Rand Paul42
Ted Cruz30

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump182
Joe Biden92
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Bernie Sanders208
Andrew Yang82
Elizabeth Warren66
John Kasich20
Rand Paul42
Ted Cruz30

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump183
Joe Biden93
Jo Jorgensen163
Howie Hawkins41
Tulsi Gabbard29
Justin Amash80
Bernie Sanders208
Andrew Yang83
Elizabeth Warren66
John Kasich20
Rand Paul44
Ted Cruz34

John Kasich eliminated in this round.

Round 5:

Donald Trump184
Joe Biden97
Jo Jorgensen163
Howie Hawkins41
Tulsi Gabbard33
Justin Amash81
Bernie Sanders210
Andrew Yang85
Elizabeth Warren68
Rand Paul47
Ted Cruz35

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump186
Joe Biden101
Jo Jorgensen171
Howie Hawkins42
Justin Amash88
Bernie Sanders213
Andrew Yang89
Elizabeth Warren69
Rand Paul50
Ted Cruz35

Ted Cruz eliminated in this round.

Round 7:

Donald Trump200
Joe Biden103
Jo Jorgensen174
Howie Hawkins43
Justin Amash88
Bernie Sanders214
Andrew Yang89
Elizabeth Warren69
Rand Paul64

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump200
Joe Biden109
Jo Jorgensen176
Justin Amash88
Bernie Sanders244
Andrew Yang92
Elizabeth Warren71
Rand Paul64

Rand Paul eliminated in this round.

Round 9:

Donald Trump221
Joe Biden109
Jo Jorgensen191
Justin Amash110
Bernie Sanders245
Andrew Yang96
Elizabeth Warren72

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump221
Joe Biden126
Jo Jorgensen195
Justin Amash111
Bernie Sanders282
Andrew Yang109

Andrew Yang eliminated in this round.

Round 11:

Donald Trump225
Joe Biden147
Jo Jorgensen211
Justin Amash125
Bernie Sanders336

Justin Amash eliminated in this round.

Round 12:

Donald Trump234
Joe Biden155
Jo Jorgensen312
Bernie Sanders343

Joe Biden eliminated in this round.

Round 13:

Donald Trump241
Jo Jorgensen350
Bernie Sanders453

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen540
Bernie Sanders504

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 Trump0/14/0 448 to
596		272 to
772		416 to
628		328 to
716		372 to
672		295 to
749		414 to
630		428 to
616		356 to
688		443 to
601		402 to
642		399 to
645		278 to
766		369 to
675
Joe Biden6/8/0596 to
448		 457 to
587		518 to
526		447 to
597		558 to
486		504 to
540		545 to
499		423 to
621		321 to
723		458 to
586		550 to
494		562 to
482		521 to
523		573 to
471
Jo Jorgensen13/1/0772 to
272		587 to
457		 677 to
367		590 to
454		734 to
310		636 to
408		623 to
421		540 to
504		519 to
525		580 to
464		713 to
331		749 to
295		710 to
334		759 to
285
Howie Hawkins9/5/0628 to
416		526 to
518		367 to
677		 416 to
628		583 to
461		501 to
543		538 to
506		446 to
598		373 to
671		535 to
509		558 to
486		587 to
457		532 to
512		606 to
438
Tulsi Gabbard12/1/1716 to
328		597 to
447		454 to
590		628 to
416		 727 to
317		617 to
427		702 to
342		539 to
505		522 to
522		615 to
429		749 to
295		760 to
284		623 to
421		714 to
330
Dan Crenshaw4/10/0672 to
372		486 to
558		310 to
734		461 to
583		317 to
727		 422 to
622		511 to
533		441 to
603		391 to
653		503 to
541		553 to
491		585 to
459		472 to
572		628 to
416
Justin Amash10/4/0749 to
295		540 to
504		408 to
636		543 to
501		427 to
617		622 to
422		 573 to
471		505 to
539		478 to
566		544 to
500		691 to
353		734 to
310		678 to
366		753 to
291
Amy Klobuchar6/8/0630 to
414		499 to
545		421 to
623		506 to
538		342 to
702		533 to
511		471 to
573		 458 to
586		338 to
706		521 to
523		639 to
405		644 to
400		557 to
487		632 to
412
Bernie Sanders11/3/0616 to
428		621 to
423		504 to
540		598 to
446		505 to
539		603 to
441		539 to
505		586 to
458		 477 to
567		620 to
424		636 to
408		637 to
407		581 to
463		626 to
418
Andrew Yang13/0/1688 to
356		723 to
321		525 to
519		671 to
373		522 to
522		653 to
391		566 to
478		706 to
338		567 to
477		 702 to
342		764 to
280		759 to
285		641 to
403		708 to
336
Elizabeth Warren8/6/0601 to
443		586 to
458		464 to
580		509 to
535		429 to
615		541 to
503		500 to
544		523 to
521		424 to
620		342 to
702		 598 to
446		619 to
425		552 to
492		608 to
436
John Kasich4/10/0642 to
402		494 to
550		331 to
713		486 to
558		295 to
749		491 to
553		353 to
691		405 to
639		408 to
636		280 to
764		446 to
598		 665 to
379		528 to
516		658 to
386
Jeb Bush2/12/0645 to
399		482 to
562		295 to
749		457 to
587		284 to
760		459 to
585		310 to
734		400 to
644		407 to
637		285 to
759		425 to
619		379 to
665		 465 to
579		631 to
413
Rand Paul5/9/0766 to
278		523 to
521		334 to
710		512 to
532		421 to
623		572 to
472		366 to
678		487 to
557		463 to
581		403 to
641		492 to
552		516 to
528		579 to
465		 784 to
260
Ted Cruz1/13/0675 to
369		471 to
573		285 to
759		438 to
606		330 to
714		416 to
628		291 to
753		412 to
632		418 to
626		336 to
708		436 to
608		386 to
658		413 to
631		260 to
784

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 Trump3037 2.9
Joe Biden3622 3.5
Jo Jorgensen4432 4.2
Howie Hawkins2718 2.6
Tulsi Gabbard3833 3.7
Dan Crenshaw2493 2.4
Justin Amash3799 3.6
Amy Klobuchar2800 2.7
Bernie Sanders4713 4.5
Andrew Yang4793 4.6
Elizabeth Warren3807 3.6
John Kasich2368 2.3
Jeb Bush2170 2.1
Rand Paul3743 3.6
Ted Cruz2697 2.6

And the winner is: Andrew Yang

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 Trump3037
Joe Biden3622
Jo Jorgensen4432
Howie Hawkins2718
Tulsi Gabbard3833
Dan Crenshaw2493
Justin Amash3799
Amy Klobuchar2800
Bernie Sanders4713
Andrew Yang4793
Elizabeth Warren3807
John Kasich2368
Jeb Bush2170
Rand Paul3743
Ted Cruz2697

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
Andrew Yang680
Bernie Sanders655

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 Trump1/13/0 382 to
531		251 to
624		391 to
433		297 to
547		315 to
327		275 to
543		386 to
466		385 to
560		320 to
628		402 to
504		377 to
392		371 to
384		233 to
482		292 to
281
Joe Biden9/5/0531 to
382		 443 to
466		462 to
318		391 to
497		530 to
326		464 to
395		427 to
226		244 to
460		237 to
557		292 to
364		494 to
260		518 to
259		491 to
455		533 to
361
Jo Jorgensen12/2/0624 to
251		466 to
443		 503 to
222		432 to
359		563 to
179		381 to
275		482 to
327		420 to
495		363 to
497		458 to
427		534 to
235		566 to
215		487 to
261		608 to
200
Howie Hawkins5/9/0433 to
391		318 to
462		222 to
503		 214 to
508		351 to
313		260 to
424		302 to
351		197 to
512		177 to
578		271 to
395		332 to
323		364 to
329		319 to
455		396 to
367
Tulsi Gabbard11/3/0547 to
297		497 to
391		359 to
432		508 to
214		 510 to
201		385 to
350		489 to
259		402 to
475		337 to
471		443 to
384		521 to
197		549 to
201		411 to
347		535 to
263
Dan Crenshaw2/12/0327 to
315		326 to
530		179 to
563		313 to
351		201 to
510		 181 to
442		293 to
400		310 to
560		244 to
594		327 to
478		294 to
316		309 to
321		191 to
427		295 to
265
Justin Amash8/6/0543 to
275		395 to
464		275 to
381		424 to
260		350 to
385		442 to
181		 378 to
348		371 to
508		316 to
510		382 to
446		420 to
229		468 to
223		398 to
273		507 to
219
Amy Klobuchar6/8/0466 to
386		226 to
427		327 to
482		351 to
302		259 to
489		400 to
293		348 to
378		 213 to
515		159 to
593		223 to
407		366 to
235		414 to
260		374 to
452		441 to
354
Bernie Sanders13/1/0560 to
385		460 to
244		495 to
420		512 to
197		475 to
402		560 to
310		508 to
371		515 to
213		 364 to
389		429 to
182		541 to
250		562 to
261		514 to
428		566 to
352
Andrew Yang14/0/0628 to
320		557 to
237		497 to
363		578 to
177		471 to
337		594 to
244		510 to
316		593 to
159		389 to
364		 482 to
244		617 to
174		635 to
188		516 to
364		603 to
291
Elizabeth Warren10/4/0504 to
402		364 to
292		427 to
458		395 to
271		384 to
443		478 to
327		446 to
382		407 to
223		182 to
429		244 to
482		 449 to
239		477 to
275		456 to
448		494 to
376
John Kasich4/10/0392 to
377		260 to
494		235 to
534		323 to
332		197 to
521		316 to
294		229 to
420		235 to
366		250 to
541		174 to
617		239 to
449		 297 to
204		279 to
429		358 to
321
Jeb Bush3/11/0384 to
371		259 to
518		215 to
566		329 to
364		201 to
549		321 to
309		223 to
468		260 to
414		261 to
562		188 to
635		275 to
477		204 to
297		 226 to
437		325 to
316
Rand Paul7/7/0482 to
233		455 to
491		261 to
487		455 to
319		347 to
411		427 to
191		273 to
398		452 to
374		428 to
514		364 to
516		448 to
456		429 to
279		437 to
226		 451 to
140
Ted Cruz0/14/0281 to
292		361 to
533		200 to
608		367 to
396		263 to
535		265 to
295		219 to
507		354 to
441		352 to
566		291 to
603		376 to
494		321 to
358		316 to
325		140 to
451

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
0578036.91%
112137.75%
210316.58%
311387.27%
410326.59%
512327.87%
68595.49%
78685.54%
88095.17%
96344.05%
1010646.79%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump542464355374839403630128
Joe Biden34878597084847893643155
Jo Jorgensen261847693689142595565150
Howie Hawkins44898737671834738392348
Tulsi Gabbard270657510110012110091523336
Dan Crenshaw47097817859824348392225
Justin Amash357816877598943415359117
Amy Klobuchar4087772104841027059381614
Bernie Sanders333555849474541607986191
Andrew Yang2286062707510087939574100
Elizabeth Warren39273604260506359827984
John Kasich45481829892109553220813
Jeb Bush432124971179284372715811
Rand Paul34994646451717278796062
Ted Cruz488100614453734250634030

Number of bullet votes: 25 (2.39%).
Number of "approval" votes: 14 (1%).

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Use the form below to look at the results for other parties or to toggle the inclusion of test runs.

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