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 Trump198
Joe Biden217
Jo Jorgensen175
Howie Hawkins24
Tulsi Gabbard25
Dan Crenshaw10
Justin Amash48
Amy Klobuchar10
Bernie Sanders147
Andrew Yang41
Elizabeth Warren28
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz15
TOTAL:980

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump285
Joe Biden383
Jo Jorgensen376
Howie Hawkins160
Tulsi Gabbard296
Dan Crenshaw130
Justin Amash284
Amy Klobuchar170
Bernie Sanders422
Andrew Yang413
Elizabeth Warren322
John Kasich122
Jeb Bush91
Rand Paul318
Ted Cruz196
Ballots Cast:980

The winner is Bernie Sanders with 43.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump174
Joe Biden78
Jo Jorgensen150
Howie Hawkins35
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash76
Amy Klobuchar14
Bernie Sanders193
Andrew Yang75
Elizabeth Warren61
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz26

Jeb Bush eliminated in this round.

Round 2:

Donald Trump174
Joe Biden78
Jo Jorgensen150
Howie Hawkins35
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash77
Amy Klobuchar14
Bernie Sanders194
Andrew Yang75
Elizabeth Warren61
John Kasich16
Rand Paul39
Ted Cruz29

Eliminated in this round:

Round 3:

Donald Trump175
Joe Biden86
Jo Jorgensen155
Howie Hawkins37
Tulsi Gabbard27
Justin Amash77
Bernie Sanders195
Andrew Yang77
Elizabeth Warren62
John Kasich17
Rand Paul40
Ted Cruz32

John Kasich eliminated in this round.

Round 4:

Donald Trump175
Joe Biden89
Jo Jorgensen155
Howie Hawkins37
Tulsi Gabbard30
Justin Amash78
Bernie Sanders197
Andrew Yang79
Elizabeth Warren64
Rand Paul43
Ted Cruz33

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump176
Joe Biden93
Jo Jorgensen163
Howie Hawkins38
Justin Amash83
Bernie Sanders200
Andrew Yang83
Elizabeth Warren65
Rand Paul46
Ted Cruz33

Ted Cruz eliminated in this round.

Round 6:

Donald Trump190
Joe Biden95
Jo Jorgensen166
Howie Hawkins39
Justin Amash83
Bernie Sanders201
Andrew Yang83
Elizabeth Warren65
Rand Paul58

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump190
Joe Biden101
Jo Jorgensen167
Justin Amash83
Bernie Sanders228
Andrew Yang86
Elizabeth Warren67
Rand Paul58

Rand Paul eliminated in this round.

Round 8:

Donald Trump209
Joe Biden101
Jo Jorgensen181
Justin Amash103
Bernie Sanders229
Andrew Yang89
Elizabeth Warren68

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump209
Joe Biden117
Jo Jorgensen185
Justin Amash104
Bernie Sanders264
Andrew Yang101

Andrew Yang eliminated in this round.

Round 10:

Donald Trump212
Joe Biden135
Jo Jorgensen200
Justin Amash118
Bernie Sanders315

Justin Amash eliminated in this round.

Round 11:

Donald Trump219
Joe Biden143
Jo Jorgensen296
Bernie Sanders322

Joe Biden eliminated in this round.

Round 12:

Donald Trump225
Jo Jorgensen330
Bernie Sanders425

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen505
Bernie Sanders475

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 Trump0/14/0 419 to
561		256 to
724		392 to
588		310 to
670		350 to
630		276 to
704		387 to
593		402 to
578		336 to
644		414 to
566		379 to
601		375 to
605		260 to
720		340 to
640
Joe Biden7/7/0561 to
419		 426 to
554		492 to
488		415 to
565		522 to
458		469 to
511		513 to
467		397 to
583		298 to
682		427 to
553		517 to
463		527 to
453		487 to
493		534 to
446
Jo Jorgensen13/1/0724 to
256		554 to
426		 636 to
344		556 to
424		687 to
293		595 to
385		587 to
393		505 to
475		487 to
493		543 to
437		669 to
311		704 to
276		664 to
316		712 to
268
Howie Hawkins8/6/0588 to
392		488 to
492		344 to
636		 388 to
592		542 to
438		465 to
515		502 to
478		413 to
567		344 to
636		502 to
478		522 to
458		549 to
431		495 to
485		567 to
413
Tulsi Gabbard12/2/0670 to
310		565 to
415		424 to
556		592 to
388		 680 to
300		572 to
408		663 to
317		508 to
472		486 to
494		578 to
402		708 to
272		715 to
265		583 to
397		668 to
312
Dan Crenshaw4/10/0630 to
350		458 to
522		293 to
687		438 to
542		300 to
680		 401 to
579		482 to
498		414 to
566		370 to
610		471 to
509		526 to
454		556 to
424		440 to
540		586 to
394
Justin Amash10/4/0704 to
276		511 to
469		385 to
595		515 to
465		408 to
572		579 to
401		 542 to
438		476 to
504		448 to
532		512 to
468		655 to
325		692 to
288		637 to
343		707 to
273
Amy Klobuchar7/7/0593 to
387		467 to
513		393 to
587		478 to
502		317 to
663		498 to
482		438 to
542		 428 to
552		310 to
670		491 to
489		603 to
377		605 to
375		519 to
461		591 to
389
Bernie Sanders11/3/0578 to
402		583 to
397		475 to
505		567 to
413		472 to
508		566 to
414		504 to
476		552 to
428		 449 to
531		581 to
399		596 to
384		598 to
382		545 to
435		587 to
393
Andrew Yang14/0/0644 to
336		682 to
298		493 to
487		636 to
344		494 to
486		610 to
370		532 to
448		670 to
310		531 to
449		 665 to
315		725 to
255		715 to
265		599 to
381		663 to
317
Elizabeth Warren7/7/0566 to
414		553 to
427		437 to
543		478 to
502		402 to
578		509 to
471		468 to
512		489 to
491		399 to
581		315 to
665		 563 to
417		583 to
397		515 to
465		569 to
411
John Kasich3/11/0601 to
379		463 to
517		311 to
669		458 to
522		272 to
708		454 to
526		325 to
655		377 to
603		384 to
596		255 to
725		417 to
563		 621 to
359		487 to
493		613 to
367
Jeb Bush2/12/0605 to
375		453 to
527		276 to
704		431 to
549		265 to
715		424 to
556		288 to
692		375 to
605		382 to
598		265 to
715		397 to
583		359 to
621		 430 to
550		585 to
395
Rand Paul6/8/0720 to
260		493 to
487		316 to
664		485 to
495		397 to
583		540 to
440		343 to
637		461 to
519		435 to
545		381 to
599		465 to
515		493 to
487		550 to
430		 735 to
245
Ted Cruz1/13/0640 to
340		446 to
534		268 to
712		413 to
567		312 to
668		394 to
586		273 to
707		389 to
591		393 to
587		317 to
663		411 to
569		367 to
613		395 to
585		245 to
735

And the Condorcet winner is: Andrew Yang.

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 Trump2871 2.9
Joe Biden3392 3.5
Jo Jorgensen4173 4.3
Howie Hawkins2495 2.5
Tulsi Gabbard3578 3.7
Dan Crenshaw2331 2.4
Justin Amash3573 3.6
Amy Klobuchar2591 2.6
Bernie Sanders4403 4.5
Andrew Yang4530 4.6
Elizabeth Warren3578 3.7
John Kasich2174 2.2
Jeb Bush2006 2.0
Rand Paul3528 3.6
Ted Cruz2544 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 Trump2871
Joe Biden3392
Jo Jorgensen4173
Howie Hawkins2495
Tulsi Gabbard3578
Dan Crenshaw2331
Justin Amash3573
Amy Klobuchar2591
Bernie Sanders4403
Andrew Yang4530
Elizabeth Warren3578
John Kasich2174
Jeb Bush2006
Rand Paul3528
Ted Cruz2544

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 Yang644
Bernie Sanders618

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 Trump2/12/0 356 to
495		237 to
582		365 to
402		282 to
510		294 to
299		260 to
507		362 to
433		360 to
524		301 to
588		375 to
473		357 to
362		352 to
349		223 to
446		270 to
263
Joe Biden9/5/0495 to
356		 409 to
440		436 to
291		364 to
465		496 to
306		434 to
372		406 to
207		227 to
429		219 to
524		271 to
342		460 to
238		483 to
240		455 to
429		495 to
339
Jo Jorgensen12/2/0582 to
237		440 to
409		 480 to
202		412 to
335		530 to
170		357 to
253		456 to
303		393 to
463		342 to
468		430 to
399		506 to
215		534 to
199		458 to
247		570 to
188
Howie Hawkins5/9/0402 to
365		291 to
436		202 to
480		 195 to
480		325 to
296		239 to
401		280 to
331		185 to
478		157 to
550		249 to
376		310 to
298		338 to
310		293 to
429		369 to
345
Tulsi Gabbard11/3/0510 to
282		465 to
364		335 to
412		480 to
195		 475 to
194		357 to
332		463 to
240		379 to
440		311 to
447		412 to
361		490 to
179		514 to
189		385 to
328		497 to
250
Dan Crenshaw2/12/0299 to
294		306 to
496		170 to
530		296 to
325		194 to
475		 171 to
416		275 to
373		291 to
522		233 to
556		305 to
448		279 to
294		292 to
298		177 to
403		270 to
251
Justin Amash8/6/0507 to
260		372 to
434		253 to
357		401 to
239		332 to
357		416 to
171		 359 to
324		350 to
473		294 to
481		361 to
417		399 to
210		440 to
204		371 to
255		473 to
206
Amy Klobuchar6/8/0433 to
362		207 to
406		303 to
456		331 to
280		240 to
463		373 to
275		324 to
359		 198 to
482		145 to
560		205 to
388		341 to
217		382 to
244		346 to
428		409 to
334
Bernie Sanders13/1/0524 to
360		429 to
227		463 to
393		478 to
185		440 to
379		522 to
291		473 to
350		482 to
198		 336 to
362		393 to
172		504 to
228		523 to
245		477 to
401		527 to
329
Andrew Yang14/0/0588 to
301		524 to
219		468 to
342		550 to
157		447 to
311		556 to
233		481 to
294		560 to
145		362 to
336		 454 to
223		583 to
159		599 to
173		483 to
344		563 to
274
Elizabeth Warren10/4/0473 to
375		342 to
271		399 to
430		376 to
249		361 to
412		448 to
305		417 to
361		388 to
205		172 to
393		223 to
454		 421 to
218		446 to
255		425 to
420		462 to
351
John Kasich4/10/0362 to
357		238 to
460		215 to
506		298 to
310		179 to
490		294 to
279		210 to
399		217 to
341		228 to
504		159 to
583		218 to
421		 273 to
191		257 to
409		329 to
304
Jeb Bush1/12/1349 to
352		240 to
483		199 to
534		310 to
338		189 to
514		298 to
292		204 to
440		244 to
382		245 to
523		173 to
599		255 to
446		191 to
273		 206 to
415		298 to
298
Rand Paul7/7/0446 to
223		429 to
455		247 to
458		429 to
293		328 to
385		403 to
177		255 to
371		428 to
346		401 to
477		344 to
483		420 to
425		409 to
257		415 to
206		 421 to
133
Ted Cruz0/13/1263 to
270		339 to
495		188 to
570		345 to
369		250 to
497		251 to
270		206 to
473		334 to
409		329 to
527		274 to
563		351 to
462		304 to
329		298 to
298		133 to
421

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
0550637.46%
111407.76%
29656.56%
310357.04%
49366.37%
511127.56%
68015.45%
78135.53%
87665.21%
95974.06%
1010297.00%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump517393550334636383228126
Joe Biden33270556778777188602854
Jo Jorgensen250817279608241565263144
Howie Hawkins42595717162794533342144
Tulsi Gabbard258646995921069586493135
Dan Crenshaw44694737057704047382025
Justin Amash339806368537739395257113
Amy Klobuchar38972709879906255371414
Bernie Sanders320495347404438577080182
Andrew Yang21657576366938187927098
Elizabeth Warren37070563955455555777781
John Kasich4357780888497513019613
Jeb Bush414115931078080352315711
Rand Paul33285625646627172785759
Ted Cruz46392563751644147613830

Number of bullet votes: 25 (2.55%).
Number of "approval" votes: 14 (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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