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 Trump173
Joe Biden196
Jo Jorgensen170
Howie Hawkins23
Tulsi Gabbard23
Dan Crenshaw9
Justin Amash44
Amy Klobuchar7
Bernie Sanders129
Andrew Yang37
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul26
Ted Cruz10
TOTAL:884

The winner is Joe Biden with 22.2% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump249
Joe Biden345
Jo Jorgensen355
Howie Hawkins142
Tulsi Gabbard269
Dan Crenshaw117
Justin Amash269
Amy Klobuchar149
Bernie Sanders375
Andrew Yang387
Elizabeth Warren290
John Kasich108
Jeb Bush78
Rand Paul297
Ted Cruz173
Ballots Cast:884

The winner is Andrew Yang with 43.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump148
Joe Biden64
Jo Jorgensen146
Howie Hawkins33
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash72
Amy Klobuchar11
Bernie Sanders175
Andrew Yang69
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul38
Ted Cruz21

Jeb Bush eliminated in this round.

Round 2:

Donald Trump148
Joe Biden64
Jo Jorgensen146
Howie Hawkins33
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash73
Amy Klobuchar11
Bernie Sanders176
Andrew Yang69
Elizabeth Warren54
John Kasich14
Rand Paul38
Ted Cruz24

Eliminated in this round:

Round 3:

Donald Trump149
Joe Biden69
Jo Jorgensen151
Howie Hawkins35
Tulsi Gabbard24
Justin Amash73
Bernie Sanders177
Andrew Yang71
Elizabeth Warren55
John Kasich14
Rand Paul39
Ted Cruz27

John Kasich eliminated in this round.

Round 4:

Donald Trump149
Joe Biden71
Jo Jorgensen151
Howie Hawkins35
Tulsi Gabbard26
Justin Amash74
Bernie Sanders178
Andrew Yang73
Elizabeth Warren57
Rand Paul42
Ted Cruz28

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump149
Joe Biden73
Jo Jorgensen159
Howie Hawkins35
Justin Amash79
Bernie Sanders181
Andrew Yang77
Elizabeth Warren58
Rand Paul45
Ted Cruz28

Ted Cruz eliminated in this round.

Round 6:

Donald Trump159
Joe Biden75
Jo Jorgensen162
Howie Hawkins36
Justin Amash79
Bernie Sanders182
Andrew Yang77
Elizabeth Warren58
Rand Paul56

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump159
Joe Biden79
Jo Jorgensen163
Justin Amash79
Bernie Sanders208
Andrew Yang80
Elizabeth Warren60
Rand Paul56

Rand Paul eliminated in this round.

Round 8:

Donald Trump178
Joe Biden79
Jo Jorgensen177
Justin Amash98
Bernie Sanders209
Andrew Yang82
Elizabeth Warren61

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump178
Joe Biden93
Jo Jorgensen179
Justin Amash99
Bernie Sanders242
Andrew Yang93

Eliminated in this round:

Round 10:

Donald Trump184
Jo Jorgensen217
Justin Amash120
Bernie Sanders363

Justin Amash eliminated in this round.

Round 11:

Donald Trump190
Jo Jorgensen314
Bernie Sanders380

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen461
Bernie Sanders423

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 Trump0/14/0 372 to
512		212 to
672		345 to
539		271 to
613		306 to
578		234 to
650		341 to
543		359 to
525		292 to
592		366 to
518		330 to
554		329 to
555		217 to
667		296 to
588
Joe Biden7/7/0512 to
372		 379 to
505		445 to
439		368 to
516		470 to
414		415 to
469		462 to
422		357 to
527		251 to
633		384 to
500		464 to
420		475 to
409		434 to
450		478 to
406
Jo Jorgensen13/1/0672 to
212		505 to
379		 579 to
305		504 to
380		631 to
253		534 to
350		531 to
353		461 to
423		440 to
444		494 to
390		606 to
278		637 to
247		603 to
281		649 to
235
Howie Hawkins6/8/0539 to
345		439 to
445		305 to
579		 342 to
542		483 to
401		400 to
484		441 to
443		368 to
516		294 to
590		449 to
435		457 to
427		484 to
400		434 to
450		504 to
380
Tulsi Gabbard12/2/0613 to
271		516 to
368		380 to
504		542 to
342		 616 to
268		503 to
381		597 to
287		460 to
424		429 to
455		522 to
362		635 to
249		642 to
242		516 to
368		602 to
282
Dan Crenshaw4/10/0578 to
306		414 to
470		253 to
631		401 to
483		268 to
616		 345 to
539		426 to
458		372 to
512		323 to
561		422 to
462		465 to
419		496 to
388		383 to
501		526 to
358
Justin Amash10/4/0650 to
234		469 to
415		350 to
534		484 to
400		381 to
503		539 to
345		 492 to
392		438 to
446		405 to
479		469 to
415		589 to
295		625 to
259		575 to
309		642 to
242
Amy Klobuchar8/6/0543 to
341		422 to
462		353 to
531		443 to
441		287 to
597		458 to
426		392 to
492		 384 to
500		262 to
622		444 to
440		541 to
343		543 to
341		460 to
424		529 to
355
Bernie Sanders11/3/0525 to
359		527 to
357		423 to
461		516 to
368		424 to
460		512 to
372		446 to
438		500 to
384		 390 to
494		516 to
368		528 to
356		532 to
352		478 to
406		522 to
362
Andrew Yang14/0/0592 to
292		633 to
251		444 to
440		590 to
294		455 to
429		561 to
323		479 to
405		622 to
262		494 to
390		 610 to
274		655 to
229		645 to
239		529 to
355		595 to
289
Elizabeth Warren7/7/0518 to
366		500 to
384		390 to
494		435 to
449		362 to
522		462 to
422		415 to
469		440 to
444		368 to
516		274 to
610		 499 to
385		518 to
366		456 to
428		508 to
376
John Kasich3/11/0554 to
330		420 to
464		278 to
606		427 to
457		249 to
635		419 to
465		295 to
589		343 to
541		356 to
528		229 to
655		385 to
499		 555 to
329		435 to
449		553 to
331
Jeb Bush2/12/0555 to
329		409 to
475		247 to
637		400 to
484		242 to
642		388 to
496		259 to
625		341 to
543		352 to
532		239 to
645		366 to
518		329 to
555		 381 to
503		526 to
358
Rand Paul7/7/0667 to
217		450 to
434		281 to
603		450 to
434		368 to
516		501 to
383		309 to
575		424 to
460		406 to
478		355 to
529		428 to
456		449 to
435		503 to
381		 671 to
213
Ted Cruz1/13/0588 to
296		406 to
478		235 to
649		380 to
504		282 to
602		358 to
526		242 to
642		355 to
529		362 to
522		289 to
595		376 to
508		331 to
553		358 to
526		213 to
671

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 Trump2523 2.9
Joe Biden3050 3.5
Jo Jorgensen3883 4.4
Howie Hawkins2227 2.5
Tulsi Gabbard3249 3.7
Dan Crenshaw2093 2.4
Justin Amash3325 3.8
Amy Klobuchar2306 2.6
Bernie Sanders3979 4.5
Andrew Yang4202 4.8
Elizabeth Warren3287 3.7
John Kasich1952 2.2
Jeb Bush1790 2.0
Rand Paul3251 3.7
Ted Cruz2298 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 Trump2523
Joe Biden3050
Jo Jorgensen3883
Howie Hawkins2227
Tulsi Gabbard3249
Dan Crenshaw2093
Justin Amash3325
Amy Klobuchar2306
Bernie Sanders3979
Andrew Yang4202
Elizabeth Warren3287
John Kasich1952
Jeb Bush1790
Rand Paul3251
Ted Cruz2298

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 Yang588
Bernie Sanders542

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 Trump0/14/0 317 to
446		197 to
546		319 to
367		247 to
469		254 to
270		218 to
471		321 to
393		322 to
478		262 to
543		331 to
436		315 to
334		311 to
318		186 to
416		233 to
242
Joe Biden9/5/0446 to
317		 362 to
405		396 to
261		328 to
426		450 to
277		387 to
347		366 to
178		200 to
384		183 to
489		233 to
310		418 to
208		439 to
215		408 to
397		445 to
308
Jo Jorgensen12/2/0546 to
197		405 to
362		 448 to
180		385 to
300		495 to
149		331 to
225		427 to
266		367 to
409		317 to
426		395 to
364		468 to
195		493 to
176		427 to
218		528 to
166
Howie Hawkins4/10/0367 to
319		261 to
396		180 to
448		 173 to
442		292 to
274		210 to
377		248 to
296		169 to
421		137 to
510		223 to
344		272 to
277		302 to
283		258 to
400		328 to
317
Tulsi Gabbard11/3/0469 to
247		426 to
328		300 to
385		442 to
173		 439 to
179		325 to
310		425 to
213		350 to
394		279 to
417		376 to
333		449 to
164		470 to
172		344 to
306		453 to
227
Dan Crenshaw2/12/0270 to
254		277 to
450		149 to
495		274 to
292		179 to
439		 153 to
389		249 to
338		267 to
468		209 to
516		275 to
413		254 to
271		265 to
268		157 to
375		243 to
230
Justin Amash8/6/0471 to
218		347 to
387		225 to
331		377 to
210		310 to
325		389 to
153		 337 to
286		328 to
420		272 to
441		337 to
383		370 to
193		410 to
181		342 to
228		438 to
181
Amy Klobuchar6/8/0393 to
321		178 to
366		266 to
427		296 to
248		213 to
425		338 to
249		286 to
337		 175 to
433		117 to
526		173 to
363		306 to
198		343 to
218		311 to
399		368 to
305
Bernie Sanders13/1/0478 to
322		384 to
200		409 to
367		421 to
169		394 to
350		468 to
267		420 to
328		433 to
175		 296 to
342		345 to
157		450 to
209		470 to
222		426 to
373		476 to
302
Andrew Yang14/0/0543 to
262		489 to
183		426 to
317		510 to
137		417 to
279		516 to
209		441 to
272		526 to
117		342 to
296		 420 to
196		538 to
138		556 to
152		444 to
317		520 to
251
Elizabeth Warren10/4/0436 to
331		310 to
233		364 to
395		344 to
223		333 to
376		413 to
275		383 to
337		363 to
173		157 to
345		196 to
420		 386 to
196		409 to
226		390 to
386		424 to
317
John Kasich5/9/0334 to
315		208 to
418		195 to
468		277 to
272		164 to
449		271 to
254		193 to
370		198 to
306		209 to
450		138 to
538		196 to
386		 245 to
170		234 to
379		297 to
278
Jeb Bush2/12/0318 to
311		215 to
439		176 to
493		283 to
302		172 to
470		268 to
265		181 to
410		218 to
343		222 to
470		152 to
556		226 to
409		170 to
245		 184 to
389		264 to
271
Rand Paul7/7/0416 to
186		397 to
408		218 to
427		400 to
258		306 to
344		375 to
157		228 to
342		399 to
311		373 to
426		317 to
444		386 to
390		379 to
234		389 to
184		 389 to
114
Ted Cruz2/12/0242 to
233		308 to
445		166 to
528		317 to
328		227 to
453		230 to
243		181 to
438		305 to
368		302 to
476		251 to
520		317 to
424		278 to
297		271 to
264		114 to
389

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
0499737.68%
110187.68%
28576.46%
38896.70%
48286.24%
59777.37%
67235.45%
77535.68%
87035.30%
95644.25%
109517.17%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump477362941314033352923110
Joe Biden30266495766726282562349
Jo Jorgensen222716269516839534960140
Howie Hawkins39083666356693829282141
Tulsi Gabbard229566584841018178463030
Dan Crenshaw40484676153613843331822
Justin Amash299735659466237395056107
Amy Klobuchar35865658667785747361411
Bernie Sanders300414634333934526277166
Andrew Yang18852475556837185866794
Elizabeth Warren33561473248415049717278
John Kasich3957172757586482917511
Jeb Bush38010580957268322214610
Rand Paul29874554743526467725557
Ted Cruz42080513147573943543725

Number of bullet votes: 20 (2.26%).
Number of "approval" votes: 12 (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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