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 Sanders134
Andrew Yang38
Elizabeth Warren25
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz12
TOTAL:919

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump263
Joe Biden360
Jo Jorgensen359
Howie Hawkins146
Tulsi Gabbard277
Dan Crenshaw121
Justin Amash271
Amy Klobuchar157
Bernie Sanders388
Andrew Yang392
Elizabeth Warren297
John Kasich112
Jeb Bush82
Rand Paul301
Ted Cruz182
Ballots Cast:919

The winner is Andrew Yang with 42.7% 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 Sanders178
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 Sanders179
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 Sanders179
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 Sanders180
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 Sanders182
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 Sanders185
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 Sanders186
Andrew Yang78
Elizabeth Warren60
Rand Paul57

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump173
Joe Biden91
Jo Jorgensen163
Justin Amash80
Bernie Sanders212
Andrew Yang81
Elizabeth Warren62
Rand Paul57

Rand Paul eliminated in this round.

Round 9:

Donald Trump192
Joe Biden91
Jo Jorgensen177
Justin Amash99
Bernie Sanders213
Andrew Yang84
Elizabeth Warren63

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump192
Joe Biden105
Jo Jorgensen180
Justin Amash100
Bernie Sanders247
Andrew Yang95

Andrew Yang eliminated in this round.

Round 11:

Donald Trump195
Joe Biden123
Jo Jorgensen195
Justin Amash112
Bernie Sanders294

Justin Amash eliminated in this round.

Round 12:

Donald Trump201
Joe Biden131
Jo Jorgensen287
Bernie Sanders300

Joe Biden eliminated in this round.

Round 13:

Donald Trump207
Jo Jorgensen319
Bernie Sanders393

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen479
Bernie Sanders440

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
529		232 to
687		365 to
554		289 to
630		324 to
595		253 to
666		358 to
561		377 to
542		311 to
608		386 to
533		349 to
570		349 to
570		236 to
683		316 to
603
Joe Biden7/7/0529 to
390		 398 to
521		464 to
455		385 to
534		489 to
430		434 to
485		477 to
442		373 to
546		269 to
650		401 to
518		481 to
438		492 to
427		453 to
466		497 to
422
Jo Jorgensen13/1/0687 to
232		521 to
398		 599 to
320		519 to
400		650 to
269		556 to
363		549 to
370		479 to
440		457 to
462		512 to
407		628 to
291		662 to
257		625 to
294		671 to
248
Howie Hawkins7/7/0554 to
365		455 to
464		320 to
599		 359 to
560		504 to
415		424 to
495		460 to
459		385 to
534		315 to
604		470 to
449		480 to
439		511 to
408		457 to
462		526 to
393
Tulsi Gabbard12/2/0630 to
289		534 to
385		400 to
519		560 to
359		 639 to
280		530 to
389		617 to
302		481 to
438		454 to
465		544 to
375		660 to
259		669 to
250		542 to
377		624 to
295
Dan Crenshaw4/10/0595 to
324		430 to
489		269 to
650		415 to
504		280 to
639		 370 to
549		445 to
474		392 to
527		346 to
573		443 to
476		489 to
430		519 to
400		403 to
516		545 to
374
Justin Amash10/4/0666 to
253		485 to
434		363 to
556		495 to
424		389 to
530		549 to
370		 510 to
409		456 to
463		423 to
496		488 to
431		611 to
308		650 to
269		598 to
321		662 to
257
Amy Klobuchar7/7/0561 to
358		442 to
477		370 to
549		459 to
460		302 to
617		474 to
445		409 to
510		 406 to
513		283 to
636		465 to
454		562 to
357		566 to
353		483 to
436		549 to
370
Bernie Sanders11/3/0542 to
377		546 to
373		440 to
479		534 to
385		438 to
481		527 to
392		463 to
456		513 to
406		 414 to
505		540 to
379		551 to
368		555 to
364		501 to
418		543 to
376
Andrew Yang14/0/0608 to
311		650 to
269		462 to
457		604 to
315		465 to
454		573 to
346		496 to
423		636 to
283		505 to
414		 629 to
290		677 to
242		669 to
250		553 to
366		616 to
303
Elizabeth Warren7/7/0533 to
386		518 to
401		407 to
512		449 to
470		375 to
544		476 to
443		431 to
488		454 to
465		379 to
540		290 to
629		 522 to
397		541 to
378		478 to
441		527 to
392
John Kasich3/11/0570 to
349		438 to
481		291 to
628		439 to
480		259 to
660		430 to
489		308 to
611		357 to
562		368 to
551		242 to
677		397 to
522		 580 to
339		456 to
463		574 to
345
Jeb Bush2/12/0570 to
349		427 to
492		257 to
662		408 to
511		250 to
669		400 to
519		269 to
650		353 to
566		364 to
555		250 to
669		378 to
541		339 to
580		 398 to
521		543 to
376
Rand Paul7/7/0683 to
236		466 to
453		294 to
625		462 to
457		377 to
542		516 to
403		321 to
598		436 to
483		418 to
501		366 to
553		441 to
478		463 to
456		521 to
398		 693 to
226
Ted Cruz1/13/0603 to
316		422 to
497		248 to
671		393 to
526		295 to
624		374 to
545		257 to
662		370 to
549		376 to
543		303 to
616		392 to
527		345 to
574		376 to
543		226 to
693

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 Biden3189 3.5
Jo Jorgensen3961 4.3
Howie Hawkins2312 2.5
Tulsi Gabbard3360 3.7
Dan Crenshaw2180 2.4
Justin Amash3407 3.7
Amy Klobuchar2422 2.6
Bernie Sanders4122 4.5
Andrew Yang4296 4.7
Elizabeth Warren3371 3.7
John Kasich2042 2.2
Jeb Bush1881 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 Biden3189
Jo Jorgensen3961
Howie Hawkins2312
Tulsi Gabbard3360
Dan Crenshaw2180
Justin Amash3407
Amy Klobuchar2422
Bernie Sanders4122
Andrew Yang4296
Elizabeth Warren3371
John Kasich2042
Jeb Bush1881
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 Sanders571

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
463		215 to
558		337 to
380		263 to
483		271 to
281		235 to
483		337 to
408		337 to
495		280 to
555		348 to
449		332 to
346		327 to
331		200 to
427		249 to
252
Joe Biden9/5/0463 to
331		 382 to
414		414 to
270		344 to
440		468 to
287		405 to
356		379 to
190		213 to
398		200 to
500		251 to
319		434 to
218		456 to
225		426 to
410		463 to
322
Jo Jorgensen12/2/0558 to
215		414 to
382		 456 to
189		394 to
314		507 to
158		338 to
237		434 to
281		373 to
430		323 to
441		406 to
376		480 to
205		504 to
189		436 to
231		540 to
178
Howie Hawkins4/10/0380 to
337		270 to
414		189 to
456		 181 to
455		302 to
281		217 to
387		258 to
310		172 to
445		144 to
525		230 to
355		284 to
285		313 to
294		269 to
412		340 to
331
Tulsi Gabbard11/3/0483 to
263		440 to
344		314 to
394		455 to
181		 451 to
186		336 to
319		435 to
225		358 to
411		292 to
425		390 to
341		460 to
172		484 to
180		358 to
315		467 to
239
Dan Crenshaw2/12/0281 to
271		287 to
468		158 to
507		281 to
302		186 to
451		 159 to
400		257 to
351		275 to
488		218 to
528		285 to
423		262 to
280		271 to
280		163 to
387		251 to
240
Justin Amash8/6/0483 to
235		356 to
405		237 to
338		387 to
217		319 to
336		400 to
159		 344 to
299		334 to
439		282 to
453		345 to
392		378 to
201		419 to
192		352 to
239		448 to
193
Amy Klobuchar6/8/0408 to
337		190 to
379		281 to
434		310 to
258		225 to
435		351 to
257		299 to
344		 185 to
448		131 to
534		187 to
367		320 to
203		358 to
227		325 to
409		382 to
318
Bernie Sanders13/1/0495 to
337		398 to
213		430 to
373		445 to
172		411 to
358		488 to
275		439 to
334		448 to
185		 312 to
348		364 to
160		469 to
215		490 to
230		444 to
383		493 to
314
Andrew Yang14/0/0555 to
280		500 to
200		441 to
323		525 to
144		425 to
292		528 to
218		453 to
282		534 to
131		348 to
312		 433 to
204		551 to
147		569 to
161		455 to
328		532 to
262
Elizabeth Warren10/4/0449 to
348		319 to
251		376 to
406		355 to
230		341 to
390		423 to
285		392 to
345		367 to
187		160 to
364		204 to
433		 396 to
204		419 to
238		400 to
399		436 to
331
John Kasich5/9/0346 to
332		218 to
434		205 to
480		285 to
284		172 to
460		280 to
262		201 to
378		203 to
320		215 to
469		147 to
551		204 to
396		 255 to
179		246 to
389		309 to
290
Jeb Bush2/12/0331 to
327		225 to
456		189 to
504		294 to
313		180 to
484		280 to
271		192 to
419		227 to
358		230 to
490		161 to
569		238 to
419		179 to
255		 195 to
398		278 to
282
Rand Paul7/7/0427 to
200		410 to
426		231 to
436		412 to
269		315 to
358		387 to
163		239 to
352		409 to
325		383 to
444		328 to
455		399 to
400		389 to
246		398 to
195		 401 to
123
Ted Cruz2/12/0252 to
249		322 to
463		178 to
540		331 to
340		239 to
467		240 to
251		193 to
448		318 to
382		314 to
493		262 to
532		331 to
436		290 to
309		282 to
278		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
0517237.52%
110807.83%
28966.50%
39516.90%
48646.27%
510167.37%
67515.45%
77765.63%
87275.27%
95764.18%
109767.08%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump492373044314334373124116
Joe Biden31567496068736785562851
Jo Jorgensen232776773567139545060140
Howie Hawkins40388696758713931312141
Tulsi Gabbard239616788851028980463131
Dan Crenshaw41890696356633844362022
Justin Amash314765863486739395156108
Amy Klobuchar36967679170825950361414
Bernie Sanders306464841354035546777170
Andrew Yang19856515863847585886794
Elizabeth Warren34866503849425150747378
John Kasich4097375807890483018513
Jeb Bush390110851007373332314711
Rand Paul30779595244576569735559
Ted Cruz43287523350584045563828

Number of bullet votes: 22 (2.39%).
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.

Quiz2D Home | Presidential Poll | Blog | Third Party Strategy | Silly Radio Ads | Privacy | About/Contact