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.