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 Trump184
Joe Biden203
Jo Jorgensen170
Howie Hawkins23
Tulsi Gabbard23
Dan Crenshaw10
Justin Amash45
Amy Klobuchar10
Bernie Sanders133
Andrew Yang38
Elizabeth Warren25
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz12
TOTAL:918

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump263
Joe Biden359
Jo Jorgensen359
Howie Hawkins145
Tulsi Gabbard277
Dan Crenshaw121
Justin Amash271
Amy Klobuchar156
Bernie Sanders387
Andrew Yang391
Elizabeth Warren296
John Kasich112
Jeb Bush82
Rand Paul301
Ted Cruz182
Ballots Cast:918

The winner is Andrew Yang with 42.6% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump159
Joe Biden72
Jo Jorgensen146
Howie Hawkins33
Tulsi Gabbard23
Dan Crenshaw12
Justin Amash73
Amy Klobuchar14
Bernie Sanders177
Andrew Yang70
Elizabeth Warren56
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz23

Jeb Bush eliminated in this round.

Round 2:

Donald Trump159
Joe Biden72
Jo Jorgensen146
Howie Hawkins33
Tulsi Gabbard23
Dan Crenshaw12
Justin Amash74
Amy Klobuchar14
Bernie Sanders178
Andrew Yang70
Elizabeth Warren56
John Kasich16
Rand Paul39
Ted Cruz26

Dan Crenshaw eliminated in this round.

Round 3:

Donald Trump160
Joe Biden72
Jo Jorgensen150
Howie Hawkins33
Tulsi Gabbard25
Justin Amash74
Amy Klobuchar14
Bernie Sanders178
Andrew Yang71
Elizabeth Warren56
John Kasich16
Rand Paul40
Ted Cruz29

Amy Klobuchar eliminated in this round.

Round 4:

Donald Trump160
Joe Biden79
Jo Jorgensen151
Howie Hawkins35
Tulsi Gabbard25
Justin Amash74
Bernie Sanders179
Andrew Yang72
Elizabeth Warren57
John Kasich17
Rand Paul40
Ted Cruz29

John Kasich eliminated in this round.

Round 5:

Donald Trump160
Joe Biden82
Jo Jorgensen151
Howie Hawkins35
Tulsi Gabbard28
Justin Amash75
Bernie Sanders181
Andrew Yang74
Elizabeth Warren59
Rand Paul43
Ted Cruz30

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump161
Joe Biden85
Jo Jorgensen159
Howie Hawkins35
Justin Amash80
Bernie Sanders184
Andrew Yang78
Elizabeth Warren60
Rand Paul46
Ted Cruz30

Ted Cruz eliminated in this round.

Round 7:

Donald Trump173
Joe Biden87
Jo Jorgensen162
Howie Hawkins36
Justin Amash80
Bernie Sanders185
Andrew Yang78
Elizabeth Warren60
Rand Paul57

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump173
Joe Biden91
Jo Jorgensen163
Justin Amash80
Bernie Sanders211
Andrew Yang81
Elizabeth Warren62
Rand Paul57

Rand Paul eliminated in this round.

Round 9:

Donald Trump192
Joe Biden91
Jo Jorgensen177
Justin Amash99
Bernie Sanders212
Andrew Yang84
Elizabeth Warren63

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump192
Joe Biden105
Jo Jorgensen180
Justin Amash100
Bernie Sanders246
Andrew Yang95

Andrew Yang eliminated in this round.

Round 11:

Donald Trump195
Joe Biden123
Jo Jorgensen195
Justin Amash112
Bernie Sanders293

Justin Amash eliminated in this round.

Round 12:

Donald Trump201
Joe Biden131
Jo Jorgensen287
Bernie Sanders299

Joe Biden eliminated in this round.

Round 13:

Donald Trump207
Jo Jorgensen319
Bernie Sanders392

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen479
Bernie Sanders439

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 Trump0/14/0 390 to
528		232 to
686		365 to
553		289 to
629		324 to
594		253 to
665		358 to
560		377 to
541		311 to
607		386 to
532		349 to
569		349 to
569		236 to
682		316 to
602
Joe Biden7/7/0528 to
390		 397 to
521		463 to
455		384 to
534		488 to
430		433 to
485		477 to
441		373 to
545		268 to
650		401 to
517		480 to
438		491 to
427		452 to
466		496 to
422
Jo Jorgensen13/1/0686 to
232		521 to
397		 599 to
319		519 to
399		649 to
269		555 to
363		549 to
369		479 to
439		457 to
461		512 to
406		627 to
291		661 to
257		624 to
294		670 to
248
Howie Hawkins7/7/0553 to
365		455 to
463		319 to
599		 358 to
560		503 to
415		423 to
495		460 to
458		385 to
533		314 to
604		470 to
448		479 to
439		510 to
408		456 to
462		525 to
393
Tulsi Gabbard12/2/0629 to
289		534 to
384		399 to
519		560 to
358		 638 to
280		529 to
389		617 to
301		481 to
437		454 to
464		544 to
374		659 to
259		668 to
250		541 to
377		623 to
295
Dan Crenshaw4/10/0594 to
324		430 to
488		269 to
649		415 to
503		280 to
638		 370 to
548		445 to
473		392 to
526		346 to
572		443 to
475		489 to
429		519 to
399		403 to
515		545 to
373
Justin Amash10/4/0665 to
253		485 to
433		363 to
555		495 to
423		389 to
529		548 to
370		 510 to
408		456 to
462		423 to
495		488 to
430		610 to
308		649 to
269		597 to
321		661 to
257
Amy Klobuchar7/7/0560 to
358		441 to
477		369 to
549		458 to
460		301 to
617		473 to
445		408 to
510		 406 to
512		282 to
636		465 to
453		561 to
357		565 to
353		482 to
436		548 to
370
Bernie Sanders11/3/0541 to
377		545 to
373		439 to
479		533 to
385		437 to
481		526 to
392		462 to
456		512 to
406		 413 to
505		539 to
379		550 to
368		554 to
364		500 to
418		542 to
376
Andrew Yang14/0/0607 to
311		650 to
268		461 to
457		604 to
314		464 to
454		572 to
346		495 to
423		636 to
282		505 to
413		 629 to
289		676 to
242		668 to
250		552 to
366		615 to
303
Elizabeth Warren7/7/0532 to
386		517 to
401		406 to
512		448 to
470		374 to
544		475 to
443		430 to
488		453 to
465		379 to
539		289 to
629		 521 to
397		540 to
378		477 to
441		526 to
392
John Kasich3/11/0569 to
349		438 to
480		291 to
627		439 to
479		259 to
659		429 to
489		308 to
610		357 to
561		368 to
550		242 to
676		397 to
521		 579 to
339		455 to
463		573 to
345
Jeb Bush2/12/0569 to
349		427 to
491		257 to
661		408 to
510		250 to
668		399 to
519		269 to
649		353 to
565		364 to
554		250 to
668		378 to
540		339 to
579		 398 to
520		542 to
376
Rand Paul7/7/0682 to
236		466 to
452		294 to
624		462 to
456		377 to
541		515 to
403		321 to
597		436 to
482		418 to
500		366 to
552		441 to
477		463 to
455		520 to
398		 692 to
226
Ted Cruz1/13/0602 to
316		422 to
496		248 to
670		393 to
525		295 to
623		373 to
545		257 to
661		370 to
548		376 to
542		303 to
615		392 to
526		345 to
573		376 to
542		226 to
692

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 Trump2655 2.9
Joe Biden3183 3.5
Jo Jorgensen3957 4.3
Howie Hawkins2305 2.5
Tulsi Gabbard3358 3.7
Dan Crenshaw2180 2.4
Justin Amash3403 3.7
Amy Klobuchar2416 2.6
Bernie Sanders4112 4.5
Andrew Yang4290 4.7
Elizabeth Warren3362 3.7
John Kasich2038 2.2
Jeb Bush1880 2.0
Rand Paul3356 3.7
Ted Cruz2405 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 Trump2655
Joe Biden3183
Jo Jorgensen3957
Howie Hawkins2305
Tulsi Gabbard3358
Dan Crenshaw2180
Justin Amash3403
Amy Klobuchar2416
Bernie Sanders4112
Andrew Yang4290
Elizabeth Warren3362
John Kasich2038
Jeb Bush1880
Rand Paul3356
Ted Cruz2405

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 Yang607
Bernie Sanders570

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 Trump0/14/0 331 to
462		215 to
557		337 to
379		263 to
482		271 to
281		235 to
482		337 to
407		337 to
494		280 to
554		348 to
448		332 to
345		327 to
330		200 to
427		249 to
252
Joe Biden9/5/0462 to
331		 381 to
414		414 to
269		343 to
440		467 to
287		404 to
356		379 to
190		213 to
397		200 to
500		251 to
318		433 to
218		455 to
225		425 to
410		462 to
322
Jo Jorgensen12/2/0557 to
215		414 to
381		 456 to
188		393 to
314		506 to
158		338 to
237		434 to
280		373 to
429		323 to
440		406 to
375		480 to
205		503 to
189		435 to
231		539 to
178
Howie Hawkins4/10/0379 to
337		269 to
414		188 to
456		 180 to
455		301 to
281		216 to
387		257 to
310		172 to
444		143 to
525		230 to
354		283 to
285		312 to
294		268 to
412		339 to
331
Tulsi Gabbard11/3/0482 to
263		440 to
343		314 to
393		455 to
180		 450 to
186		336 to
318		435 to
224		358 to
410		292 to
424		390 to
340		460 to
171		483 to
180		357 to
315		466 to
239
Dan Crenshaw2/12/0281 to
271		287 to
467		158 to
506		281 to
301		186 to
450		 159 to
399		257 to
350		275 to
487		218 to
527		285 to
422		262 to
279		271 to
279		163 to
387		251 to
240
Justin Amash8/6/0482 to
235		356 to
404		237 to
338		387 to
216		318 to
336		399 to
159		 344 to
298		334 to
438		282 to
452		345 to
391		378 to
201		418 to
192		351 to
239		447 to
193
Amy Klobuchar6/8/0407 to
337		190 to
379		280 to
434		310 to
257		224 to
435		350 to
257		298 to
344		 185 to
447		131 to
534		187 to
366		319 to
203		357 to
227		324 to
409		381 to
318
Bernie Sanders13/1/0494 to
337		397 to
213		429 to
373		444 to
172		410 to
358		487 to
275		438 to
334		447 to
185		 311 to
348		363 to
160		468 to
215		489 to
230		443 to
383		492 to
314
Andrew Yang14/0/0554 to
280		500 to
200		440 to
323		525 to
143		424 to
292		527 to
218		452 to
282		534 to
131		348 to
311		 433 to
203		550 to
147		568 to
161		454 to
328		531 to
262
Elizabeth Warren9/4/1448 to
348		318 to
251		375 to
406		354 to
230		340 to
390		422 to
285		391 to
345		366 to
187		160 to
363		203 to
433		 395 to
204		418 to
238		399 to
399		435 to
331
John Kasich5/9/0345 to
332		218 to
433		205 to
480		285 to
283		171 to
460		279 to
262		201 to
378		203 to
319		215 to
468		147 to
550		204 to
395		 254 to
179		245 to
389		308 to
290
Jeb Bush2/12/0330 to
327		225 to
455		189 to
503		294 to
312		180 to
483		279 to
271		192 to
418		227 to
357		230 to
489		161 to
568		238 to
418		179 to
254		 194 to
398		277 to
282
Rand Paul7/6/1427 to
200		410 to
425		231 to
435		412 to
268		315 to
357		387 to
163		239 to
351		409 to
324		383 to
443		328 to
454		399 to
399		389 to
245		398 to
194		 401 to
123
Ted Cruz2/12/0252 to
249		322 to
462		178 to
539		331 to
339		239 to
466		240 to
251		193 to
447		318 to
381		314 to
492		262 to
531		331 to
435		290 to
308		282 to
277		123 to
401

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
0516837.53%
110797.84%
28956.50%
39516.91%
48616.25%
510167.38%
67485.43%
77755.63%
87275.28%
95754.18%
109757.08%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump491373044314334373124116
Joe Biden31567496068736685562851
Jo Jorgensen232776773557139545060140
Howie Hawkins40388696758713930312141
Tulsi Gabbard239616688851028980463131
Dan Crenshaw41790696356633844362022
Justin Amash314765863476739395156108
Amy Klobuchar36967679170825850361414
Bernie Sanders306464841354035546777169
Andrew Yang19856515863847485886794
Elizabeth Warren34866503849425150747278
John Kasich4097375807790483018513
Jeb Bush390109851007373332314711
Rand Paul30679595244576569735559
Ted Cruz43187523350584045563828

Number of bullet votes: 22 (2.40%).
Number of "approval" votes: 13 (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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