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 Trump197
Joe Biden215
Jo Jorgensen175
Howie Hawkins24
Tulsi Gabbard25
Dan Crenshaw10
Justin Amash48
Amy Klobuchar10
Bernie Sanders147
Andrew Yang39
Elizabeth Warren28
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz14
TOTAL:974

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump283
Joe Biden382
Jo Jorgensen376
Howie Hawkins160
Tulsi Gabbard295
Dan Crenshaw130
Justin Amash284
Amy Klobuchar170
Bernie Sanders418
Andrew Yang411
Elizabeth Warren321
John Kasich122
Jeb Bush91
Rand Paul318
Ted Cruz193
Ballots Cast:974

The winner is Bernie Sanders with 42.9% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump173
Joe Biden78
Jo Jorgensen150
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash76
Amy Klobuchar14
Bernie Sanders192
Andrew Yang73
Elizabeth Warren61
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz25

Jeb Bush eliminated in this round.

Round 2:

Donald Trump173
Joe Biden78
Jo Jorgensen150
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash77
Amy Klobuchar14
Bernie Sanders193
Andrew Yang73
Elizabeth Warren61
John Kasich16
Rand Paul39
Ted Cruz28

Eliminated in this round:

Round 3:

Donald Trump174
Joe Biden86
Jo Jorgensen155
Howie Hawkins36
Tulsi Gabbard27
Justin Amash77
Bernie Sanders194
Andrew Yang75
Elizabeth Warren62
John Kasich17
Rand Paul40
Ted Cruz31

John Kasich eliminated in this round.

Round 4:

Donald Trump174
Joe Biden89
Jo Jorgensen155
Howie Hawkins36
Tulsi Gabbard30
Justin Amash78
Bernie Sanders196
Andrew Yang77
Elizabeth Warren64
Rand Paul43
Ted Cruz32

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump175
Joe Biden93
Jo Jorgensen163
Howie Hawkins37
Justin Amash83
Bernie Sanders199
Andrew Yang81
Elizabeth Warren65
Rand Paul46
Ted Cruz32

Ted Cruz eliminated in this round.

Round 6:

Donald Trump188
Joe Biden95
Jo Jorgensen166
Howie Hawkins38
Justin Amash83
Bernie Sanders200
Andrew Yang81
Elizabeth Warren65
Rand Paul58

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump188
Joe Biden100
Jo Jorgensen167
Justin Amash83
Bernie Sanders227
Andrew Yang84
Elizabeth Warren67
Rand Paul58

Rand Paul eliminated in this round.

Round 8:

Donald Trump207
Joe Biden100
Jo Jorgensen181
Justin Amash103
Bernie Sanders228
Andrew Yang87
Elizabeth Warren68

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump207
Joe Biden116
Jo Jorgensen185
Justin Amash104
Bernie Sanders263
Andrew Yang99

Andrew Yang eliminated in this round.

Round 10:

Donald Trump210
Joe Biden134
Jo Jorgensen200
Justin Amash118
Bernie Sanders312

Justin Amash eliminated in this round.

Round 11:

Donald Trump217
Joe Biden142
Jo Jorgensen296
Bernie Sanders319

Joe Biden eliminated in this round.

Round 12:

Donald Trump223
Jo Jorgensen330
Bernie Sanders421

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen503
Bernie Sanders471

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 Trump0/14/0 416 to
558		253 to
721		389 to
585		308 to
666		348 to
626		274 to
700		385 to
589		400 to
574		334 to
640		411 to
563		377 to
597		373 to
601		258 to
716		339 to
635
Joe Biden7/7/0558 to
416		 423 to
551		491 to
483		413 to
561		519 to
455		467 to
507		510 to
464		396 to
578		296 to
678		424 to
550		514 to
460		524 to
450		484 to
490		531 to
443
Jo Jorgensen13/1/0721 to
253		551 to
423		 633 to
341		554 to
420		686 to
288		592 to
382		585 to
389		503 to
471		485 to
489		540 to
434		666 to
308		699 to
275		660 to
314		709 to
265
Howie Hawkins8/6/0585 to
389		483 to
491		341 to
633		 385 to
589		539 to
435		460 to
514		498 to
476		409 to
565		341 to
633		498 to
476		518 to
456		545 to
429		491 to
483		564 to
410
Tulsi Gabbard12/2/0666 to
308		561 to
413		420 to
554		589 to
385		 677 to
297		568 to
406		659 to
315		505 to
469		482 to
492		573 to
401		702 to
272		709 to
265		578 to
396		664 to
310
Dan Crenshaw4/10/0626 to
348		455 to
519		288 to
686		435 to
539		297 to
677		 398 to
576		479 to
495		411 to
563		366 to
608		466 to
508		521 to
453		551 to
423		434 to
540		582 to
392
Justin Amash10/4/0700 to
274		507 to
467		382 to
592		514 to
460		406 to
568		576 to
398		 541 to
433		475 to
499		444 to
530		507 to
467		650 to
324		687 to
287		632 to
342		703 to
271
Amy Klobuchar6/8/0589 to
385		464 to
510		389 to
585		476 to
498		315 to
659		495 to
479		433 to
541		 427 to
547		306 to
668		486 to
488		597 to
377		599 to
375		514 to
460		587 to
387
Bernie Sanders11/3/0574 to
400		578 to
396		471 to
503		565 to
409		469 to
505		563 to
411		499 to
475		547 to
427		 446 to
528		576 to
398		591 to
383		593 to
381		540 to
434		583 to
391
Andrew Yang14/0/0640 to
334		678 to
296		489 to
485		633 to
341		492 to
482		608 to
366		530 to
444		668 to
306		528 to
446		 661 to
313		720 to
254		710 to
264		594 to
380		659 to
315
Elizabeth Warren8/6/0563 to
411		550 to
424		434 to
540		476 to
498		401 to
573		508 to
466		467 to
507		488 to
486		398 to
576		313 to
661		 559 to
415		579 to
395		511 to
463		566 to
408
John Kasich3/11/0597 to
377		460 to
514		308 to
666		456 to
518		272 to
702		453 to
521		324 to
650		377 to
597		383 to
591		254 to
720		415 to
559		 616 to
358		483 to
491		609 to
365
Jeb Bush2/12/0601 to
373		450 to
524		275 to
699		429 to
545		265 to
709		423 to
551		287 to
687		375 to
599		381 to
593		264 to
710		395 to
579		358 to
616		 425 to
549		581 to
393
Rand Paul6/8/0716 to
258		490 to
484		314 to
660		483 to
491		396 to
578		540 to
434		342 to
632		460 to
514		434 to
540		380 to
594		463 to
511		491 to
483		549 to
425		 732 to
242
Ted Cruz1/13/0635 to
339		443 to
531		265 to
709		410 to
564		310 to
664		392 to
582		271 to
703		387 to
587		391 to
583		315 to
659		408 to
566		365 to
609		393 to
581		242 to
732

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 Trump2848 2.9
Joe Biden3375 3.5
Jo Jorgensen4160 4.3
Howie Hawkins2476 2.5
Tulsi Gabbard3556 3.7
Dan Crenshaw2326 2.4
Justin Amash3566 3.7
Amy Klobuchar2577 2.6
Bernie Sanders4376 4.5
Andrew Yang4508 4.6
Elizabeth Warren3567 3.7
John Kasich2168 2.2
Jeb Bush1998 2.1
Rand Paul3518 3.6
Ted Cruz2523 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 Trump2848
Joe Biden3375
Jo Jorgensen4160
Howie Hawkins2476
Tulsi Gabbard3556
Dan Crenshaw2326
Justin Amash3566
Amy Klobuchar2577
Bernie Sanders4376
Andrew Yang4508
Elizabeth Warren3567
John Kasich2168
Jeb Bush1998
Rand Paul3518
Ted Cruz2523

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 Yang640
Bernie Sanders614

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 Trump1/12/1 353 to
492		234 to
581		361 to
400		279 to
507		290 to
298		256 to
506		360 to
431		357 to
521		298 to
585		372 to
472		354 to
362		349 to
349		219 to
446		268 to
261
Joe Biden9/5/0492 to
353		 406 to
437		434 to
288		362 to
462		492 to
305		430 to
371		403 to
205		226 to
425		217 to
521		268 to
340		457 to
236		480 to
237		451 to
427		492 to
336
Jo Jorgensen12/2/0581 to
234		437 to
406		 477 to
200		410 to
332		527 to
170		354 to
252		455 to
301		391 to
459		339 to
466		428 to
397		504 to
215		532 to
199		456 to
246		568 to
185
Howie Hawkins5/9/0400 to
361		288 to
434		200 to
477		 193 to
478		321 to
295		235 to
400		277 to
328		183 to
474		155 to
548		246 to
374		307 to
296		336 to
307		290 to
427		366 to
342
Tulsi Gabbard11/3/0507 to
279		462 to
362		332 to
410		478 to
193		 471 to
194		354 to
331		460 to
238		377 to
437		309 to
446		410 to
360		486 to
179		510 to
188		381 to
327		494 to
247
Dan Crenshaw2/12/0298 to
290		305 to
492		170 to
527		295 to
321		194 to
471		 171 to
415		275 to
370		290 to
518		232 to
554		304 to
446		278 to
293		290 to
296		176 to
401		269 to
248
Justin Amash8/6/0506 to
256		371 to
430		252 to
354		400 to
235		331 to
354		415 to
171		 358 to
321		349 to
469		293 to
479		359 to
416		397 to
209		438 to
202		369 to
253		472 to
203
Amy Klobuchar6/8/0431 to
360		205 to
403		301 to
455		328 to
277		238 to
460		370 to
275		321 to
358		 196 to
479		142 to
558		203 to
386		338 to
217		378 to
243		343 to
427		407 to
331
Bernie Sanders13/1/0521 to
357		425 to
226		459 to
391		474 to
183		437 to
377		518 to
290		469 to
349		479 to
196		 334 to
360		390 to
171		500 to
227		519 to
244		473 to
399		524 to
326
Andrew Yang14/0/0585 to
298		521 to
217		466 to
339		548 to
155		446 to
309		554 to
232		479 to
293		558 to
142		360 to
334		 451 to
222		580 to
158		596 to
172		480 to
342		560 to
271
Elizabeth Warren10/4/0472 to
372		340 to
268		397 to
428		374 to
246		360 to
410		446 to
304		416 to
359		386 to
203		171 to
390		222 to
451		 419 to
218		444 to
254		423 to
419		461 to
348
John Kasich4/10/0362 to
354		236 to
457		215 to
504		296 to
307		179 to
486		293 to
278		209 to
397		217 to
338		227 to
500		158 to
580		218 to
419		 272 to
190		256 to
408		328 to
301
Jeb Bush2/11/1349 to
349		237 to
480		199 to
532		307 to
336		188 to
510		296 to
290		202 to
438		243 to
378		244 to
519		172 to
596		254 to
444		190 to
272		 205 to
413		297 to
295
Rand Paul7/7/0446 to
219		427 to
451		246 to
456		427 to
290		327 to
381		401 to
176		253 to
369		427 to
343		399 to
473		342 to
480		419 to
423		408 to
256		413 to
205		 420 to
130
Ted Cruz0/14/0261 to
268		336 to
492		185 to
568		342 to
366		247 to
494		248 to
269		203 to
472		331 to
407		326 to
524		271 to
560		348 to
461		301 to
328		295 to
297		130 to
420

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
0546737.42%
111377.78%
29566.54%
310216.99%
49296.36%
511087.58%
67995.47%
78095.54%
87635.22%
95974.09%
1010247.01%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump515393548334636373228125
Joe Biden33070546776777187602854
Jo Jorgensen248817276598241565263144
Howie Hawkins42493707162784533342143
Tulsi Gabbard256646994911059586493134
Dan Crenshaw44294726957704047382025
Justin Amash335806268537639395257113
Amy Klobuchar38772709677906255371414
Bernie Sanders319495147404437567080181
Andrew Yang21457556366938187917097
Elizabeth Warren36670563954455554777781
John Kasich4317780868497513019613
Jeb Bush411115921058080352315711
Rand Paul32984625546627072785759
Ted Cruz46092563751634147593830

Number of bullet votes: 25 (2.57%).
Number of "approval" votes: 14 (1%).

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