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 Trump198
Joe Biden217
Jo Jorgensen175
Howie Hawkins24
Tulsi Gabbard25
Dan Crenshaw10
Justin Amash48
Amy Klobuchar10
Bernie Sanders147
Andrew Yang41
Elizabeth Warren28
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz15
TOTAL:980

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump285
Joe Biden383
Jo Jorgensen376
Howie Hawkins160
Tulsi Gabbard296
Dan Crenshaw130
Justin Amash284
Amy Klobuchar170
Bernie Sanders422
Andrew Yang413
Elizabeth Warren322
John Kasich122
Jeb Bush91
Rand Paul318
Ted Cruz196
Ballots Cast:980

The winner is Bernie Sanders with 43.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump174
Joe Biden78
Jo Jorgensen150
Howie Hawkins35
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash76
Amy Klobuchar14
Bernie Sanders193
Andrew Yang75
Elizabeth Warren61
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz26

Jeb Bush eliminated in this round.

Round 2:

Donald Trump174
Joe Biden78
Jo Jorgensen150
Howie Hawkins35
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash77
Amy Klobuchar14
Bernie Sanders194
Andrew Yang75
Elizabeth Warren61
John Kasich16
Rand Paul39
Ted Cruz29

Eliminated in this round:

Round 3:

Donald Trump175
Joe Biden86
Jo Jorgensen155
Howie Hawkins37
Tulsi Gabbard27
Justin Amash77
Bernie Sanders195
Andrew Yang77
Elizabeth Warren62
John Kasich17
Rand Paul40
Ted Cruz32

John Kasich eliminated in this round.

Round 4:

Donald Trump175
Joe Biden89
Jo Jorgensen155
Howie Hawkins37
Tulsi Gabbard30
Justin Amash78
Bernie Sanders197
Andrew Yang79
Elizabeth Warren64
Rand Paul43
Ted Cruz33

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump176
Joe Biden93
Jo Jorgensen163
Howie Hawkins38
Justin Amash83
Bernie Sanders200
Andrew Yang83
Elizabeth Warren65
Rand Paul46
Ted Cruz33

Ted Cruz eliminated in this round.

Round 6:

Donald Trump190
Joe Biden95
Jo Jorgensen166
Howie Hawkins39
Justin Amash83
Bernie Sanders201
Andrew Yang83
Elizabeth Warren65
Rand Paul58

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump190
Joe Biden101
Jo Jorgensen167
Justin Amash83
Bernie Sanders228
Andrew Yang86
Elizabeth Warren67
Rand Paul58

Rand Paul eliminated in this round.

Round 8:

Donald Trump209
Joe Biden101
Jo Jorgensen181
Justin Amash103
Bernie Sanders229
Andrew Yang89
Elizabeth Warren68

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump209
Joe Biden117
Jo Jorgensen185
Justin Amash104
Bernie Sanders264
Andrew Yang101

Andrew Yang eliminated in this round.

Round 10:

Donald Trump212
Joe Biden135
Jo Jorgensen200
Justin Amash118
Bernie Sanders315

Justin Amash eliminated in this round.

Round 11:

Donald Trump219
Joe Biden143
Jo Jorgensen296
Bernie Sanders322

Joe Biden eliminated in this round.

Round 12:

Donald Trump225
Jo Jorgensen330
Bernie Sanders425

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen505
Bernie Sanders475

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 Trump0/14/0 419 to
561
256 to
724
392 to
588
310 to
670
350 to
630
276 to
704
387 to
593
402 to
578
336 to
644
414 to
566
379 to
601
375 to
605
260 to
720
340 to
640
Joe Biden7/7/0561 to
419
426 to
554
492 to
488
415 to
565
522 to
458
469 to
511
513 to
467
397 to
583
298 to
682
427 to
553
517 to
463
527 to
453
487 to
493
534 to
446
Jo Jorgensen13/1/0724 to
256
554 to
426
636 to
344
556 to
424
687 to
293
595 to
385
587 to
393
505 to
475
487 to
493
543 to
437
669 to
311
704 to
276
664 to
316
712 to
268
Howie Hawkins8/6/0588 to
392
488 to
492
344 to
636
388 to
592
542 to
438
465 to
515
502 to
478
413 to
567
344 to
636
502 to
478
522 to
458
549 to
431
495 to
485
567 to
413
Tulsi Gabbard12/2/0670 to
310
565 to
415
424 to
556
592 to
388
680 to
300
572 to
408
663 to
317
508 to
472
486 to
494
578 to
402
708 to
272
715 to
265
583 to
397
668 to
312
Dan Crenshaw4/10/0630 to
350
458 to
522
293 to
687
438 to
542
300 to
680
401 to
579
482 to
498
414 to
566
370 to
610
471 to
509
526 to
454
556 to
424
440 to
540
586 to
394
Justin Amash10/4/0704 to
276
511 to
469
385 to
595
515 to
465
408 to
572
579 to
401
542 to
438
476 to
504
448 to
532
512 to
468
655 to
325
692 to
288
637 to
343
707 to
273
Amy Klobuchar7/7/0593 to
387
467 to
513
393 to
587
478 to
502
317 to
663
498 to
482
438 to
542
428 to
552
310 to
670
491 to
489
603 to
377
605 to
375
519 to
461
591 to
389
Bernie Sanders11/3/0578 to
402
583 to
397
475 to
505
567 to
413
472 to
508
566 to
414
504 to
476
552 to
428
449 to
531
581 to
399
596 to
384
598 to
382
545 to
435
587 to
393
Andrew Yang14/0/0644 to
336
682 to
298
493 to
487
636 to
344
494 to
486
610 to
370
532 to
448
670 to
310
531 to
449
665 to
315
725 to
255
715 to
265
599 to
381
663 to
317
Elizabeth Warren7/7/0566 to
414
553 to
427
437 to
543
478 to
502
402 to
578
509 to
471
468 to
512
489 to
491
399 to
581
315 to
665
563 to
417
583 to
397
515 to
465
569 to
411
John Kasich3/11/0601 to
379
463 to
517
311 to
669
458 to
522
272 to
708
454 to
526
325 to
655
377 to
603
384 to
596
255 to
725
417 to
563
621 to
359
487 to
493
613 to
367
Jeb Bush2/12/0605 to
375
453 to
527
276 to
704
431 to
549
265 to
715
424 to
556
288 to
692
375 to
605
382 to
598
265 to
715
397 to
583
359 to
621
430 to
550
585 to
395
Rand Paul6/8/0720 to
260
493 to
487
316 to
664
485 to
495
397 to
583
540 to
440
343 to
637
461 to
519
435 to
545
381 to
599
465 to
515
493 to
487
550 to
430
735 to
245
Ted Cruz1/13/0640 to
340
446 to
534
268 to
712
413 to
567
312 to
668
394 to
586
273 to
707
389 to
591
393 to
587
317 to
663
411 to
569
367 to
613
395 to
585
245 to
735

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 Trump2871 2.9
Joe Biden3392 3.5
Jo Jorgensen4173 4.3
Howie Hawkins2495 2.5
Tulsi Gabbard3578 3.7
Dan Crenshaw2331 2.4
Justin Amash3573 3.6
Amy Klobuchar2591 2.6
Bernie Sanders4403 4.5
Andrew Yang4530 4.6
Elizabeth Warren3578 3.7
John Kasich2174 2.2
Jeb Bush2006 2.0
Rand Paul3528 3.6
Ted Cruz2544 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 Trump2871
Joe Biden3392
Jo Jorgensen4173
Howie Hawkins2495
Tulsi Gabbard3578
Dan Crenshaw2331
Justin Amash3573
Amy Klobuchar2591
Bernie Sanders4403
Andrew Yang4530
Elizabeth Warren3578
John Kasich2174
Jeb Bush2006
Rand Paul3528
Ted Cruz2544

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 Yang644
Bernie Sanders618

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 Trump2/12/0 356 to
495
237 to
582
365 to
402
282 to
510
294 to
299
260 to
507
362 to
433
360 to
524
301 to
588
375 to
473
357 to
362
352 to
349
223 to
446
270 to
263
Joe Biden9/5/0495 to
356
409 to
440
436 to
291
364 to
465
496 to
306
434 to
372
406 to
207
227 to
429
219 to
524
271 to
342
460 to
238
483 to
240
455 to
429
495 to
339
Jo Jorgensen12/2/0582 to
237
440 to
409
480 to
202
412 to
335
530 to
170
357 to
253
456 to
303
393 to
463
342 to
468
430 to
399
506 to
215
534 to
199
458 to
247
570 to
188
Howie Hawkins5/9/0402 to
365
291 to
436
202 to
480
195 to
480
325 to
296
239 to
401
280 to
331
185 to
478
157 to
550
249 to
376
310 to
298
338 to
310
293 to
429
369 to
345
Tulsi Gabbard11/3/0510 to
282
465 to
364
335 to
412
480 to
195
475 to
194
357 to
332
463 to
240
379 to
440
311 to
447
412 to
361
490 to
179
514 to
189
385 to
328
497 to
250
Dan Crenshaw2/12/0299 to
294
306 to
496
170 to
530
296 to
325
194 to
475
171 to
416
275 to
373
291 to
522
233 to
556
305 to
448
279 to
294
292 to
298
177 to
403
270 to
251
Justin Amash8/6/0507 to
260
372 to
434
253 to
357
401 to
239
332 to
357
416 to
171
359 to
324
350 to
473
294 to
481
361 to
417
399 to
210
440 to
204
371 to
255
473 to
206
Amy Klobuchar6/8/0433 to
362
207 to
406
303 to
456
331 to
280
240 to
463
373 to
275
324 to
359
198 to
482
145 to
560
205 to
388
341 to
217
382 to
244
346 to
428
409 to
334
Bernie Sanders13/1/0524 to
360
429 to
227
463 to
393
478 to
185
440 to
379
522 to
291
473 to
350
482 to
198
336 to
362
393 to
172
504 to
228
523 to
245
477 to
401
527 to
329
Andrew Yang14/0/0588 to
301
524 to
219
468 to
342
550 to
157
447 to
311
556 to
233
481 to
294
560 to
145
362 to
336
454 to
223
583 to
159
599 to
173
483 to
344
563 to
274
Elizabeth Warren10/4/0473 to
375
342 to
271
399 to
430
376 to
249
361 to
412
448 to
305
417 to
361
388 to
205
172 to
393
223 to
454
421 to
218
446 to
255
425 to
420
462 to
351
John Kasich4/10/0362 to
357
238 to
460
215 to
506
298 to
310
179 to
490
294 to
279
210 to
399
217 to
341
228 to
504
159 to
583
218 to
421
273 to
191
257 to
409
329 to
304
Jeb Bush1/12/1349 to
352
240 to
483
199 to
534
310 to
338
189 to
514
298 to
292
204 to
440
244 to
382
245 to
523
173 to
599
255 to
446
191 to
273
206 to
415
298 to
298
Rand Paul7/7/0446 to
223
429 to
455
247 to
458
429 to
293
328 to
385
403 to
177
255 to
371
428 to
346
401 to
477
344 to
483
420 to
425
409 to
257
415 to
206
421 to
133
Ted Cruz0/13/1263 to
270
339 to
495
188 to
570
345 to
369
250 to
497
251 to
270
206 to
473
334 to
409
329 to
527
274 to
563
351 to
462
304 to
329
298 to
298
133 to
421

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
0550637.46%
111407.76%
29656.56%
310357.04%
49366.37%
511127.56%
68015.45%
78135.53%
87665.21%
95974.06%
1010297.00%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump517393550334636383228126
Joe Biden33270556778777188602854
Jo Jorgensen250817279608241565263144
Howie Hawkins42595717162794533342144
Tulsi Gabbard258646995921069586493135
Dan Crenshaw44694737057704047382025
Justin Amash339806368537739395257113
Amy Klobuchar38972709879906255371414
Bernie Sanders320495347404438577080182
Andrew Yang21657576366938187927098
Elizabeth Warren37070563955455555777781
John Kasich4357780888497513019613
Jeb Bush414115931078080352315711
Rand Paul33285625646627172785759
Ted Cruz46392563751644147613830

Number of bullet votes: 25 (2.55%).
Number of "approval" votes: 14 (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.