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 Trump219
Joe Biden228
Jo Jorgensen184
Howie Hawkins28
Tulsi Gabbard27
Dan Crenshaw12
Justin Amash50
Amy Klobuchar11
Bernie Sanders165
Andrew Yang47
Elizabeth Warren31
John Kasich13
Jeb Bush6
Rand Paul30
Ted Cruz17
TOTAL:1068

The winner is Joe Biden with 21.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump315
Joe Biden412
Jo Jorgensen398
Howie Hawkins183
Tulsi Gabbard317
Dan Crenshaw139
Justin Amash302
Amy Klobuchar186
Bernie Sanders459
Andrew Yang445
Elizabeth Warren346
John Kasich138
Jeb Bush103
Rand Paul342
Ted Cruz214
Ballots Cast:1068

The winner is Bernie Sanders with 43.0% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump194
Joe Biden85
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Amy Klobuchar14
Bernie Sanders210
Andrew Yang84
Elizabeth Warren65
John Kasich18
Jeb Bush6
Rand Paul42
Ted Cruz28

Jeb Bush eliminated in this round.

Round 2:

Donald Trump194
Joe Biden85
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash81
Amy Klobuchar14
Bernie Sanders211
Andrew Yang84
Elizabeth Warren65
John Kasich19
Rand Paul42
Ted Cruz31

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump194
Joe Biden92
Jo Jorgensen160
Howie Hawkins43
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash81
Bernie Sanders212
Andrew Yang85
Elizabeth Warren66
John Kasich20
Rand Paul42
Ted Cruz31

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump195
Joe Biden93
Jo Jorgensen164
Howie Hawkins43
Tulsi Gabbard29
Justin Amash81
Bernie Sanders212
Andrew Yang86
Elizabeth Warren66
John Kasich20
Rand Paul44
Ted Cruz35

John Kasich eliminated in this round.

Round 5:

Donald Trump196
Joe Biden97
Jo Jorgensen164
Howie Hawkins43
Tulsi Gabbard33
Justin Amash82
Bernie Sanders214
Andrew Yang88
Elizabeth Warren68
Rand Paul47
Ted Cruz36

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump198
Joe Biden101
Jo Jorgensen172
Howie Hawkins44
Justin Amash89
Bernie Sanders217
Andrew Yang92
Elizabeth Warren69
Rand Paul50
Ted Cruz36

Ted Cruz eliminated in this round.

Round 7:

Donald Trump213
Joe Biden103
Jo Jorgensen175
Howie Hawkins45
Justin Amash89
Bernie Sanders218
Andrew Yang92
Elizabeth Warren69
Rand Paul64

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump213
Joe Biden109
Jo Jorgensen177
Justin Amash89
Bernie Sanders250
Andrew Yang95
Elizabeth Warren71
Rand Paul64

Rand Paul eliminated in this round.

Round 9:

Donald Trump234
Joe Biden109
Jo Jorgensen192
Justin Amash111
Bernie Sanders251
Andrew Yang99
Elizabeth Warren72

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump234
Joe Biden126
Jo Jorgensen196
Justin Amash112
Bernie Sanders288
Andrew Yang112

Eliminated in this round:

Round 11:

Donald Trump247
Joe Biden156
Jo Jorgensen315
Bernie Sanders350

Joe Biden eliminated in this round.

Round 12:

Donald Trump254
Jo Jorgensen354
Bernie Sanders460

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen554
Bernie Sanders514

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 Trump0/14/0 465 to
603		285 to
783		431 to
637		344 to
724		388 to
680		310 to
758		429 to
639		444 to
624		371 to
697		460 to
608		417 to
651		414 to
654		295 to
773		384 to
684
Joe Biden6/8/0603 to
465		 464 to
604		523 to
545		454 to
614		567 to
501		511 to
557		552 to
516		427 to
641		323 to
745		465 to
603		558 to
510		571 to
497		529 to
539		582 to
486
Jo Jorgensen13/1/0783 to
285		604 to
464		 691 to
377		605 to
463		749 to
319		652 to
416		638 to
430		554 to
514		529 to
539		596 to
472		729 to
339		764 to
304		724 to
344		772 to
296
Howie Hawkins9/5/0637 to
431		545 to
523		377 to
691		 429 to
639		597 to
471		514 to
554		556 to
512		458 to
610		384 to
684		553 to
515		574 to
494		602 to
466		543 to
525		616 to
452
Tulsi Gabbard13/1/0724 to
344		614 to
454		463 to
605		639 to
429		 743 to
325		633 to
435		721 to
347		551 to
517		535 to
533		630 to
438		766 to
302		775 to
293		639 to
429		726 to
342
Dan Crenshaw4/10/0680 to
388		501 to
567		319 to
749		471 to
597		325 to
743		 434 to
634		529 to
539		451 to
617		401 to
667		517 to
551		567 to
501		599 to
469		483 to
585		640 to
428
Justin Amash10/4/0758 to
310		557 to
511		416 to
652		554 to
514		435 to
633		634 to
434		 590 to
478		516 to
552		486 to
582		559 to
509		706 to
362		748 to
320		691 to
377		765 to
303
Amy Klobuchar7/7/0639 to
429		516 to
552		430 to
638		512 to
556		347 to
721		539 to
529		478 to
590		 469 to
599		347 to
721		539 to
529		652 to
416		659 to
409		569 to
499		644 to
424
Bernie Sanders11/3/0624 to
444		641 to
427		514 to
554		610 to
458		517 to
551		617 to
451		552 to
516		599 to
469		 487 to
581		636 to
432		648 to
420		651 to
417		593 to
475		637 to
431
Andrew Yang13/1/0697 to
371		745 to
323		539 to
529		684 to
384		533 to
535		667 to
401		582 to
486		721 to
347		581 to
487		 719 to
349		778 to
290		774 to
294		654 to
414		720 to
348
Elizabeth Warren7/7/0608 to
460		603 to
465		472 to
596		515 to
553		438 to
630		551 to
517		509 to
559		529 to
539		432 to
636		349 to
719		 605 to
463		626 to
442		562 to
506		618 to
450
John Kasich4/10/0651 to
417		510 to
558		339 to
729		494 to
574		302 to
766		501 to
567		362 to
706		416 to
652		420 to
648		290 to
778		463 to
605		 678 to
390		539 to
529		670 to
398
Jeb Bush2/12/0654 to
414		497 to
571		304 to
764		466 to
602		293 to
775		469 to
599		320 to
748		409 to
659		417 to
651		294 to
774		442 to
626		390 to
678		 477 to
591		641 to
427
Rand Paul5/9/0773 to
295		539 to
529		344 to
724		525 to
543		429 to
639		585 to
483		377 to
691		499 to
569		475 to
593		414 to
654		506 to
562		529 to
539		591 to
477		 795 to
273
Ted Cruz1/13/0684 to
384		486 to
582		296 to
772		452 to
616		342 to
726		428 to
640		303 to
765		424 to
644		431 to
637		348 to
720		450 to
618		398 to
670		427 to
641		273 to
795

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 Trump3168 3.0
Joe Biden3652 3.4
Jo Jorgensen4503 4.2
Howie Hawkins2793 2.6
Tulsi Gabbard3892 3.6
Dan Crenshaw2561 2.4
Justin Amash3862 3.6
Amy Klobuchar2846 2.7
Bernie Sanders4799 4.5
Andrew Yang4857 4.5
Elizabeth Warren3845 3.6
John Kasich2419 2.3
Jeb Bush2226 2.1
Rand Paul3818 3.6
Ted Cruz2792 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 Trump3168
Joe Biden3652
Jo Jorgensen4503
Howie Hawkins2793
Tulsi Gabbard3892
Dan Crenshaw2561
Justin Amash3862
Amy Klobuchar2846
Bernie Sanders4799
Andrew Yang4857
Elizabeth Warren3845
John Kasich2419
Jeb Bush2226
Rand Paul3818
Ted Cruz2792

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 Yang694
Bernie Sanders671

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 Trump1/13/0 397 to
537		265 to
632		406 to
441		313 to
552		330 to
331		289 to
551		400 to
473		400 to
568		334 to
636		418 to
510		391 to
400		385 to
389		248 to
487		304 to
284
Joe Biden9/5/0537 to
397		 450 to
477		467 to
330		398 to
506		539 to
335		471 to
405		432 to
234		246 to
472		239 to
571		298 to
371		500 to
269		525 to
268		500 to
466		542 to
372
Jo Jorgensen12/2/0632 to
265		477 to
450		 512 to
228		438 to
363		571 to
188		389 to
278		492 to
332		429 to
504		369 to
505		469 to
432		546 to
240		576 to
222		495 to
268		616 to
211
Howie Hawkins5/9/0441 to
406		330 to
467		228 to
512		 220 to
514		358 to
323		269 to
431		309 to
355		205 to
521		185 to
585		282 to
398		340 to
329		371 to
336		326 to
464		403 to
379
Tulsi Gabbard11/3/0552 to
313		506 to
398		363 to
438		514 to
220		 518 to
208		391 to
354		496 to
264		410 to
485		342 to
479		451 to
390		530 to
203		557 to
209		417 to
354		540 to
275
Dan Crenshaw2/12/0331 to
330		335 to
539		188 to
571		323 to
358		208 to
518		 190 to
448		303 to
405		319 to
571		252 to
603		335 to
482		303 to
323		318 to
327		199 to
435		300 to
275
Justin Amash8/6/0551 to
289		405 to
471		278 to
389		431 to
269		354 to
391		448 to
190		 387 to
353		380 to
518		322 to
518		391 to
452		429 to
234		476 to
232		404 to
280		514 to
230
Amy Klobuchar6/8/0473 to
400		234 to
432		332 to
492		355 to
309		264 to
496		405 to
303		353 to
387		 219 to
527		161 to
601		229 to
414		372 to
241		418 to
269		380 to
464		447 to
365
Bernie Sanders13/1/0568 to
400		472 to
246		504 to
429		521 to
205		485 to
410		571 to
319		518 to
380		527 to
219		 374 to
397		444 to
185		554 to
257		576 to
268		525 to
437		577 to
362
Andrew Yang14/0/0636 to
334		571 to
239		505 to
369		585 to
185		479 to
342		603 to
252		518 to
322		601 to
161		397 to
374		 492 to
250		627 to
179		644 to
194		525 to
374		612 to
302
Elizabeth Warren10/4/0510 to
418		371 to
298		432 to
469		398 to
282		390 to
451		482 to
335		452 to
391		414 to
229		185 to
444		250 to
492		 455 to
246		483 to
285		462 to
459		499 to
388
John Kasich4/10/0400 to
391		269 to
500		240 to
546		329 to
340		203 to
530		323 to
303		234 to
429		241 to
372		257 to
554		179 to
627		246 to
455		 301 to
211		284 to
439		364 to
332
Jeb Bush3/11/0389 to
385		268 to
525		222 to
576		336 to
371		209 to
557		327 to
318		232 to
476		269 to
418		268 to
576		194 to
644		285 to
483		211 to
301		 233 to
444		331 to
327
Rand Paul7/7/0487 to
248		466 to
500		268 to
495		464 to
326		354 to
417		435 to
199		280 to
404		464 to
380		437 to
525		374 to
525		459 to
462		439 to
284		444 to
233		 457 to
150
Ted Cruz0/14/0284 to
304		372 to
542		211 to
616		379 to
403		275 to
540		275 to
300		230 to
514		365 to
447		362 to
577		302 to
612		388 to
499		332 to
364		327 to
331		150 to
457

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
0591836.94%
112607.87%
210506.55%
311707.30%
410616.62%
512537.82%
68735.45%
78835.51%
88205.12%
96454.03%
1010876.79%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump548484555374840423733135
Joe Biden36084607187847894643155
Jo Jorgensen270877694729344605565152
Howie Hawkins457101738072854739392451
Tulsi Gabbard281687510310212210292533337
Dan Crenshaw48098828060854749392325
Justin Amash366846981619043425559118
Amy Klobuchar4198073109851027159401614
Bernie Sanders340586051494642618087194
Andrew Yang2376464717710287949674102
Elizabeth Warren40574644361526559827984
John Kasich463848510194111553321813
Jeb Bush440129981199685382815911
Rand Paul35797646754747278806263
Ted Cruz495104624554744253644233

Number of bullet votes: 25 (2.34%).
Number of "approval" votes: 15 (1%).

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