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 Trump196
Joe Biden211
Jo Jorgensen170
Howie Hawkins24
Tulsi Gabbard25
Dan Crenshaw10
Justin Amash48
Amy Klobuchar10
Bernie Sanders143
Andrew Yang39
Elizabeth Warren28
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz14
TOTAL:960

The winner is Joe Biden with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump280
Joe Biden376
Jo Jorgensen370
Howie Hawkins157
Tulsi Gabbard293
Dan Crenshaw130
Justin Amash280
Amy Klobuchar166
Bernie Sanders411
Andrew Yang407
Elizabeth Warren314
John Kasich120
Jeb Bush89
Rand Paul317
Ted Cruz193
Ballots Cast:960

The winner is Bernie Sanders with 42.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump171
Joe Biden75
Jo Jorgensen147
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash75
Amy Klobuchar14
Bernie Sanders188
Andrew Yang73
Elizabeth Warren60
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz25

Jeb Bush eliminated in this round.

Round 2:

Donald Trump171
Joe Biden75
Jo Jorgensen147
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash76
Amy Klobuchar14
Bernie Sanders189
Andrew Yang73
Elizabeth Warren60
John Kasich16
Rand Paul39
Ted Cruz28

Eliminated in this round:

Round 3:

Donald Trump172
Joe Biden83
Jo Jorgensen152
Howie Hawkins36
Tulsi Gabbard27
Justin Amash76
Bernie Sanders190
Andrew Yang75
Elizabeth Warren61
John Kasich17
Rand Paul40
Ted Cruz31

John Kasich eliminated in this round.

Round 4:

Donald Trump172
Joe Biden86
Jo Jorgensen152
Howie Hawkins36
Tulsi Gabbard30
Justin Amash77
Bernie Sanders192
Andrew Yang77
Elizabeth Warren63
Rand Paul43
Ted Cruz32

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump173
Joe Biden90
Jo Jorgensen160
Howie Hawkins37
Justin Amash82
Bernie Sanders195
Andrew Yang81
Elizabeth Warren64
Rand Paul46
Ted Cruz32

Ted Cruz eliminated in this round.

Round 6:

Donald Trump186
Joe Biden92
Jo Jorgensen163
Howie Hawkins38
Justin Amash82
Bernie Sanders196
Andrew Yang81
Elizabeth Warren64
Rand Paul58

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump186
Joe Biden97
Jo Jorgensen164
Justin Amash82
Bernie Sanders223
Andrew Yang84
Elizabeth Warren66
Rand Paul58

Rand Paul eliminated in this round.

Round 8:

Donald Trump205
Joe Biden97
Jo Jorgensen178
Justin Amash102
Bernie Sanders224
Andrew Yang87
Elizabeth Warren67

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump205
Joe Biden112
Jo Jorgensen182
Justin Amash103
Bernie Sanders259
Andrew Yang99

Andrew Yang eliminated in this round.

Round 10:

Donald Trump208
Joe Biden130
Jo Jorgensen197
Justin Amash117
Bernie Sanders308

Justin Amash eliminated in this round.

Round 11:

Donald Trump215
Joe Biden138
Jo Jorgensen292
Bernie Sanders315

Joe Biden eliminated in this round.

Round 12:

Donald Trump221
Jo Jorgensen326
Bernie Sanders413

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen497
Bernie Sanders463

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 Trump0/14/0 412 to
548
250 to
710
384 to
576
304 to
656
343 to
617
271 to
689
381 to
579
396 to
564
331 to
629
406 to
554
373 to
587
369 to
591
255 to
705
335 to
625
Joe Biden7/7/0548 to
412
416 to
544
483 to
477
403 to
557
509 to
451
457 to
503
501 to
459
388 to
572
287 to
673
416 to
544
505 to
455
514 to
446
474 to
486
521 to
439
Jo Jorgensen13/1/0710 to
250
544 to
416
624 to
336
545 to
415
674 to
286
584 to
376
578 to
382
497 to
463
478 to
482
533 to
427
656 to
304
688 to
272
648 to
312
697 to
263
Howie Hawkins8/6/0576 to
384
477 to
483
336 to
624
378 to
582
529 to
431
452 to
508
491 to
469
404 to
556
336 to
624
490 to
470
510 to
450
536 to
424
481 to
479
553 to
407
Tulsi Gabbard12/2/0656 to
304
557 to
403
415 to
545
582 to
378
665 to
295
559 to
401
652 to
308
501 to
459
477 to
483
567 to
393
692 to
268
698 to
262
567 to
393
652 to
308
Dan Crenshaw4/10/0617 to
343
451 to
509
286 to
674
431 to
529
295 to
665
395 to
565
476 to
484
409 to
551
366 to
594
463 to
497
518 to
442
545 to
415
428 to
532
571 to
389
Justin Amash10/4/0689 to
271
503 to
457
376 to
584
508 to
452
401 to
559
565 to
395
536 to
424
472 to
488
440 to
520
503 to
457
641 to
319
676 to
284
621 to
339
691 to
269
Amy Klobuchar6/7/1579 to
381
459 to
501
382 to
578
469 to
491
308 to
652
484 to
476
424 to
536
421 to
539
302 to
658
480 to
480
589 to
371
589 to
371
505 to
455
575 to
385
Bernie Sanders11/3/0564 to
396
572 to
388
463 to
497
556 to
404
459 to
501
551 to
409
488 to
472
539 to
421
438 to
522
566 to
394
581 to
379
583 to
377
529 to
431
571 to
389
Andrew Yang14/0/0629 to
331
673 to
287
482 to
478
624 to
336
483 to
477
594 to
366
520 to
440
658 to
302
522 to
438
655 to
305
710 to
250
699 to
261
583 to
377
646 to
314
Elizabeth Warren7/6/1554 to
406
544 to
416
427 to
533
470 to
490
393 to
567
497 to
463
457 to
503
480 to
480
394 to
566
305 to
655
549 to
411
568 to
392
501 to
459
554 to
406
John Kasich3/11/0587 to
373
455 to
505
304 to
656
450 to
510
268 to
692
442 to
518
319 to
641
371 to
589
379 to
581
250 to
710
411 to
549
607 to
353
475 to
485
597 to
363
Jeb Bush2/12/0591 to
369
446 to
514
272 to
688
424 to
536
262 to
698
415 to
545
284 to
676
371 to
589
377 to
583
261 to
699
392 to
568
353 to
607
419 to
541
569 to
391
Rand Paul6/8/0705 to
255
486 to
474
312 to
648
479 to
481
393 to
567
532 to
428
339 to
621
455 to
505
431 to
529
377 to
583
459 to
501
485 to
475
541 to
419
720 to
240
Ted Cruz1/13/0625 to
335
439 to
521
263 to
697
407 to
553
308 to
652
389 to
571
269 to
691
385 to
575
389 to
571
314 to
646
406 to
554
363 to
597
391 to
569
240 to
720

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 Trump2818 2.9
Joe Biden3311 3.4
Jo Jorgensen4095 4.3
Howie Hawkins2421 2.5
Tulsi Gabbard3514 3.7
Dan Crenshaw2304 2.4
Justin Amash3523 3.7
Amy Klobuchar2529 2.6
Bernie Sanders4307 4.5
Andrew Yang4457 4.6
Elizabeth Warren3509 3.7
John Kasich2136 2.2
Jeb Bush1964 2.0
Rand Paul3489 3.6
Ted Cruz2503 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 Trump2818
Joe Biden3311
Jo Jorgensen4095
Howie Hawkins2421
Tulsi Gabbard3514
Dan Crenshaw2304
Justin Amash3523
Amy Klobuchar2529
Bernie Sanders4307
Andrew Yang4457
Elizabeth Warren3509
John Kasich2136
Jeb Bush1964
Rand Paul3489
Ted Cruz2503

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 Yang634
Bernie Sanders604

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 Trump2/12/0 349 to
482
231 to
573
357 to
393
275 to
501
286 to
295
252 to
499
356 to
423
353 to
513
295 to
576
368 to
464
350 to
357
344 to
343
215 to
441
264 to
258
Joe Biden9/5/0482 to
349
398 to
431
429 to
282
354 to
457
483 to
302
422 to
368
396 to
201
222 to
418
209 to
518
262 to
335
449 to
231
473 to
233
442 to
424
483 to
334
Jo Jorgensen12/2/0573 to
231
431 to
398
471 to
195
404 to
329
519 to
170
349 to
248
449 to
294
385 to
452
333 to
459
422 to
389
497 to
211
524 to
196
446 to
245
558 to
185
Howie Hawkins5/9/0393 to
357
282 to
429
195 to
471
188 to
474
312 to
294
228 to
397
271 to
324
179 to
467
149 to
542
240 to
368
298 to
294
328 to
304
280 to
426
356 to
341
Tulsi Gabbard11/3/0501 to
275
457 to
354
329 to
404
474 to
188
465 to
193
349 to
328
455 to
232
373 to
430
306 to
439
405 to
353
478 to
178
503 to
186
373 to
326
487 to
245
Dan Crenshaw2/12/0295 to
286
302 to
483
170 to
519
294 to
312
193 to
465
169 to
410
273 to
361
288 to
510
231 to
545
300 to
438
276 to
287
286 to
291
173 to
397
265 to
246
Justin Amash8/6/0499 to
252
368 to
422
248 to
349
397 to
228
328 to
349
410 to
169
355 to
313
345 to
461
289 to
473
355 to
408
392 to
206
434 to
201
363 to
251
465 to
201
Amy Klobuchar6/8/0423 to
356
201 to
396
294 to
449
324 to
271
232 to
455
361 to
273
313 to
355
193 to
472
138 to
554
198 to
381
332 to
214
371 to
240
335 to
425
398 to
329
Bernie Sanders13/1/0513 to
353
418 to
222
452 to
385
467 to
179
430 to
373
510 to
288
461 to
345
472 to
193
326 to
356
383 to
169
492 to
225
512 to
240
465 to
396
515 to
324
Andrew Yang14/0/0576 to
295
518 to
209
459 to
333
542 to
149
439 to
306
545 to
231
473 to
289
554 to
138
356 to
326
446 to
215
572 to
155
589 to
169
473 to
340
551 to
270
Elizabeth Warren9/4/1464 to
368
335 to
262
389 to
422
368 to
240
353 to
405
438 to
300
408 to
355
381 to
198
169 to
383
215 to
446
412 to
214
437 to
249
415 to
415
453 to
344
John Kasich4/10/0357 to
350
231 to
449
211 to
497
294 to
298
178 to
478
287 to
276
206 to
392
214 to
332
225 to
492
155 to
572
214 to
412
267 to
186
251 to
404
322 to
298
Jeb Bush1/13/0343 to
344
233 to
473
196 to
524
304 to
328
186 to
503
291 to
286
201 to
434
240 to
371
240 to
512
169 to
589
249 to
437
186 to
267
201 to
411
291 to
292
Rand Paul7/6/1441 to
215
424 to
442
245 to
446
426 to
280
326 to
373
397 to
173
251 to
363
425 to
335
396 to
465
340 to
473
415 to
415
404 to
251
411 to
201
416 to
128
Ted Cruz1/13/0258 to
264
334 to
483
185 to
558
341 to
356
245 to
487
246 to
265
201 to
465
329 to
398
324 to
515
270 to
551
344 to
453
298 to
322
292 to
291
128 to
416

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
0539137.44%
111287.83%
29406.53%
39956.91%
49106.32%
510937.59%
67885.47%
77985.54%
87565.25%
95904.10%
1010117.02%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump506393546334536373227124
Joe Biden32770536575766986592852
Jo Jorgensen245797075598241565161141
Howie Hawkins42093706961774133322143
Tulsi Gabbard251646892891059384493134
Dan Crenshaw43593716557704046382025
Justin Amash330796166527439395257111
Amy Klobuchar38372699573906152371414
Bernie Sanders315495146384237566980177
Andrew Yang21157536164928085907097
Elizabeth Warren36269553953435453777580
John Kasich4257779828396513019513
Jeb Bush406114901047878352314711
Rand Paul32382615444617072785659
Ted Cruz45291543651624146593830

Number of bullet votes: 25 (2.60%).
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.