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 Trump197
Joe Biden215
Jo Jorgensen175
Howie Hawkins24
Tulsi Gabbard25
Dan Crenshaw10
Justin Amash48
Amy Klobuchar10
Bernie Sanders147
Andrew Yang39
Elizabeth Warren28
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz14
TOTAL:974

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump283
Joe Biden382
Jo Jorgensen376
Howie Hawkins160
Tulsi Gabbard295
Dan Crenshaw130
Justin Amash284
Amy Klobuchar170
Bernie Sanders418
Andrew Yang411
Elizabeth Warren321
John Kasich122
Jeb Bush91
Rand Paul318
Ted Cruz193
Ballots Cast:974

The winner is Bernie Sanders with 42.9% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump173
Joe Biden78
Jo Jorgensen150
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash76
Amy Klobuchar14
Bernie Sanders192
Andrew Yang73
Elizabeth Warren61
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz25

Jeb Bush eliminated in this round.

Round 2:

Donald Trump173
Joe Biden78
Jo Jorgensen150
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash77
Amy Klobuchar14
Bernie Sanders193
Andrew Yang73
Elizabeth Warren61
John Kasich16
Rand Paul39
Ted Cruz28

Eliminated in this round:

Round 3:

Donald Trump174
Joe Biden86
Jo Jorgensen155
Howie Hawkins36
Tulsi Gabbard27
Justin Amash77
Bernie Sanders194
Andrew Yang75
Elizabeth Warren62
John Kasich17
Rand Paul40
Ted Cruz31

John Kasich eliminated in this round.

Round 4:

Donald Trump174
Joe Biden89
Jo Jorgensen155
Howie Hawkins36
Tulsi Gabbard30
Justin Amash78
Bernie Sanders196
Andrew Yang77
Elizabeth Warren64
Rand Paul43
Ted Cruz32

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump175
Joe Biden93
Jo Jorgensen163
Howie Hawkins37
Justin Amash83
Bernie Sanders199
Andrew Yang81
Elizabeth Warren65
Rand Paul46
Ted Cruz32

Ted Cruz eliminated in this round.

Round 6:

Donald Trump188
Joe Biden95
Jo Jorgensen166
Howie Hawkins38
Justin Amash83
Bernie Sanders200
Andrew Yang81
Elizabeth Warren65
Rand Paul58

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump188
Joe Biden100
Jo Jorgensen167
Justin Amash83
Bernie Sanders227
Andrew Yang84
Elizabeth Warren67
Rand Paul58

Rand Paul eliminated in this round.

Round 8:

Donald Trump207
Joe Biden100
Jo Jorgensen181
Justin Amash103
Bernie Sanders228
Andrew Yang87
Elizabeth Warren68

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump207
Joe Biden116
Jo Jorgensen185
Justin Amash104
Bernie Sanders263
Andrew Yang99

Andrew Yang eliminated in this round.

Round 10:

Donald Trump210
Joe Biden134
Jo Jorgensen200
Justin Amash118
Bernie Sanders312

Justin Amash eliminated in this round.

Round 11:

Donald Trump217
Joe Biden142
Jo Jorgensen296
Bernie Sanders319

Joe Biden eliminated in this round.

Round 12:

Donald Trump223
Jo Jorgensen330
Bernie Sanders421

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen503
Bernie Sanders471

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 Trump0/14/0 416 to
558
253 to
721
389 to
585
308 to
666
348 to
626
274 to
700
385 to
589
400 to
574
334 to
640
411 to
563
377 to
597
373 to
601
258 to
716
339 to
635
Joe Biden7/7/0558 to
416
423 to
551
491 to
483
413 to
561
519 to
455
467 to
507
510 to
464
396 to
578
296 to
678
424 to
550
514 to
460
524 to
450
484 to
490
531 to
443
Jo Jorgensen13/1/0721 to
253
551 to
423
633 to
341
554 to
420
686 to
288
592 to
382
585 to
389
503 to
471
485 to
489
540 to
434
666 to
308
699 to
275
660 to
314
709 to
265
Howie Hawkins8/6/0585 to
389
483 to
491
341 to
633
385 to
589
539 to
435
460 to
514
498 to
476
409 to
565
341 to
633
498 to
476
518 to
456
545 to
429
491 to
483
564 to
410
Tulsi Gabbard12/2/0666 to
308
561 to
413
420 to
554
589 to
385
677 to
297
568 to
406
659 to
315
505 to
469
482 to
492
573 to
401
702 to
272
709 to
265
578 to
396
664 to
310
Dan Crenshaw4/10/0626 to
348
455 to
519
288 to
686
435 to
539
297 to
677
398 to
576
479 to
495
411 to
563
366 to
608
466 to
508
521 to
453
551 to
423
434 to
540
582 to
392
Justin Amash10/4/0700 to
274
507 to
467
382 to
592
514 to
460
406 to
568
576 to
398
541 to
433
475 to
499
444 to
530
507 to
467
650 to
324
687 to
287
632 to
342
703 to
271
Amy Klobuchar6/8/0589 to
385
464 to
510
389 to
585
476 to
498
315 to
659
495 to
479
433 to
541
427 to
547
306 to
668
486 to
488
597 to
377
599 to
375
514 to
460
587 to
387
Bernie Sanders11/3/0574 to
400
578 to
396
471 to
503
565 to
409
469 to
505
563 to
411
499 to
475
547 to
427
446 to
528
576 to
398
591 to
383
593 to
381
540 to
434
583 to
391
Andrew Yang14/0/0640 to
334
678 to
296
489 to
485
633 to
341
492 to
482
608 to
366
530 to
444
668 to
306
528 to
446
661 to
313
720 to
254
710 to
264
594 to
380
659 to
315
Elizabeth Warren8/6/0563 to
411
550 to
424
434 to
540
476 to
498
401 to
573
508 to
466
467 to
507
488 to
486
398 to
576
313 to
661
559 to
415
579 to
395
511 to
463
566 to
408
John Kasich3/11/0597 to
377
460 to
514
308 to
666
456 to
518
272 to
702
453 to
521
324 to
650
377 to
597
383 to
591
254 to
720
415 to
559
616 to
358
483 to
491
609 to
365
Jeb Bush2/12/0601 to
373
450 to
524
275 to
699
429 to
545
265 to
709
423 to
551
287 to
687
375 to
599
381 to
593
264 to
710
395 to
579
358 to
616
425 to
549
581 to
393
Rand Paul6/8/0716 to
258
490 to
484
314 to
660
483 to
491
396 to
578
540 to
434
342 to
632
460 to
514
434 to
540
380 to
594
463 to
511
491 to
483
549 to
425
732 to
242
Ted Cruz1/13/0635 to
339
443 to
531
265 to
709
410 to
564
310 to
664
392 to
582
271 to
703
387 to
587
391 to
583
315 to
659
408 to
566
365 to
609
393 to
581
242 to
732

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 Trump2848 2.9
Joe Biden3375 3.5
Jo Jorgensen4160 4.3
Howie Hawkins2476 2.5
Tulsi Gabbard3556 3.7
Dan Crenshaw2326 2.4
Justin Amash3566 3.7
Amy Klobuchar2577 2.6
Bernie Sanders4376 4.5
Andrew Yang4508 4.6
Elizabeth Warren3567 3.7
John Kasich2168 2.2
Jeb Bush1998 2.1
Rand Paul3518 3.6
Ted Cruz2523 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 Trump2848
Joe Biden3375
Jo Jorgensen4160
Howie Hawkins2476
Tulsi Gabbard3556
Dan Crenshaw2326
Justin Amash3566
Amy Klobuchar2577
Bernie Sanders4376
Andrew Yang4508
Elizabeth Warren3567
John Kasich2168
Jeb Bush1998
Rand Paul3518
Ted Cruz2523

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 Yang640
Bernie Sanders614

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 Trump1/12/1 353 to
492
234 to
581
361 to
400
279 to
507
290 to
298
256 to
506
360 to
431
357 to
521
298 to
585
372 to
472
354 to
362
349 to
349
219 to
446
268 to
261
Joe Biden9/5/0492 to
353
406 to
437
434 to
288
362 to
462
492 to
305
430 to
371
403 to
205
226 to
425
217 to
521
268 to
340
457 to
236
480 to
237
451 to
427
492 to
336
Jo Jorgensen12/2/0581 to
234
437 to
406
477 to
200
410 to
332
527 to
170
354 to
252
455 to
301
391 to
459
339 to
466
428 to
397
504 to
215
532 to
199
456 to
246
568 to
185
Howie Hawkins5/9/0400 to
361
288 to
434
200 to
477
193 to
478
321 to
295
235 to
400
277 to
328
183 to
474
155 to
548
246 to
374
307 to
296
336 to
307
290 to
427
366 to
342
Tulsi Gabbard11/3/0507 to
279
462 to
362
332 to
410
478 to
193
471 to
194
354 to
331
460 to
238
377 to
437
309 to
446
410 to
360
486 to
179
510 to
188
381 to
327
494 to
247
Dan Crenshaw2/12/0298 to
290
305 to
492
170 to
527
295 to
321
194 to
471
171 to
415
275 to
370
290 to
518
232 to
554
304 to
446
278 to
293
290 to
296
176 to
401
269 to
248
Justin Amash8/6/0506 to
256
371 to
430
252 to
354
400 to
235
331 to
354
415 to
171
358 to
321
349 to
469
293 to
479
359 to
416
397 to
209
438 to
202
369 to
253
472 to
203
Amy Klobuchar6/8/0431 to
360
205 to
403
301 to
455
328 to
277
238 to
460
370 to
275
321 to
358
196 to
479
142 to
558
203 to
386
338 to
217
378 to
243
343 to
427
407 to
331
Bernie Sanders13/1/0521 to
357
425 to
226
459 to
391
474 to
183
437 to
377
518 to
290
469 to
349
479 to
196
334 to
360
390 to
171
500 to
227
519 to
244
473 to
399
524 to
326
Andrew Yang14/0/0585 to
298
521 to
217
466 to
339
548 to
155
446 to
309
554 to
232
479 to
293
558 to
142
360 to
334
451 to
222
580 to
158
596 to
172
480 to
342
560 to
271
Elizabeth Warren10/4/0472 to
372
340 to
268
397 to
428
374 to
246
360 to
410
446 to
304
416 to
359
386 to
203
171 to
390
222 to
451
419 to
218
444 to
254
423 to
419
461 to
348
John Kasich4/10/0362 to
354
236 to
457
215 to
504
296 to
307
179 to
486
293 to
278
209 to
397
217 to
338
227 to
500
158 to
580
218 to
419
272 to
190
256 to
408
328 to
301
Jeb Bush2/11/1349 to
349
237 to
480
199 to
532
307 to
336
188 to
510
296 to
290
202 to
438
243 to
378
244 to
519
172 to
596
254 to
444
190 to
272
205 to
413
297 to
295
Rand Paul7/7/0446 to
219
427 to
451
246 to
456
427 to
290
327 to
381
401 to
176
253 to
369
427 to
343
399 to
473
342 to
480
419 to
423
408 to
256
413 to
205
420 to
130
Ted Cruz0/14/0261 to
268
336 to
492
185 to
568
342 to
366
247 to
494
248 to
269
203 to
472
331 to
407
326 to
524
271 to
560
348 to
461
301 to
328
295 to
297
130 to
420

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
0546737.42%
111377.78%
29566.54%
310216.99%
49296.36%
511087.58%
67995.47%
78095.54%
87635.22%
95974.09%
1010247.01%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump515393548334636373228125
Joe Biden33070546776777187602854
Jo Jorgensen248817276598241565263144
Howie Hawkins42493707162784533342143
Tulsi Gabbard256646994911059586493134
Dan Crenshaw44294726957704047382025
Justin Amash335806268537639395257113
Amy Klobuchar38772709677906255371414
Bernie Sanders319495147404437567080181
Andrew Yang21457556366938187917097
Elizabeth Warren36670563954455554777781
John Kasich4317780868497513019613
Jeb Bush411115921058080352315711
Rand Paul32984625546627072785759
Ted Cruz46092563751634147593830

Number of bullet votes: 25 (2.57%).
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.