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 Sanders134
Andrew Yang38
Elizabeth Warren25
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz12
TOTAL:919

The winner is Joe Biden with 22.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump263
Joe Biden360
Jo Jorgensen359
Howie Hawkins146
Tulsi Gabbard277
Dan Crenshaw121
Justin Amash271
Amy Klobuchar157
Bernie Sanders388
Andrew Yang392
Elizabeth Warren297
John Kasich112
Jeb Bush82
Rand Paul301
Ted Cruz182
Ballots Cast:919

The winner is Andrew Yang with 42.7% 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 Sanders178
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 Sanders179
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 Sanders179
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 Sanders180
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 Sanders182
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 Sanders185
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 Sanders186
Andrew Yang78
Elizabeth Warren60
Rand Paul57

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump173
Joe Biden91
Jo Jorgensen163
Justin Amash80
Bernie Sanders212
Andrew Yang81
Elizabeth Warren62
Rand Paul57

Rand Paul eliminated in this round.

Round 9:

Donald Trump192
Joe Biden91
Jo Jorgensen177
Justin Amash99
Bernie Sanders213
Andrew Yang84
Elizabeth Warren63

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump192
Joe Biden105
Jo Jorgensen180
Justin Amash100
Bernie Sanders247
Andrew Yang95

Andrew Yang eliminated in this round.

Round 11:

Donald Trump195
Joe Biden123
Jo Jorgensen195
Justin Amash112
Bernie Sanders294

Justin Amash eliminated in this round.

Round 12:

Donald Trump201
Joe Biden131
Jo Jorgensen287
Bernie Sanders300

Joe Biden eliminated in this round.

Round 13:

Donald Trump207
Jo Jorgensen319
Bernie Sanders393

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen479
Bernie Sanders440

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
529
232 to
687
365 to
554
289 to
630
324 to
595
253 to
666
358 to
561
377 to
542
311 to
608
386 to
533
349 to
570
349 to
570
236 to
683
316 to
603
Joe Biden7/7/0529 to
390
398 to
521
464 to
455
385 to
534
489 to
430
434 to
485
477 to
442
373 to
546
269 to
650
401 to
518
481 to
438
492 to
427
453 to
466
497 to
422
Jo Jorgensen13/1/0687 to
232
521 to
398
599 to
320
519 to
400
650 to
269
556 to
363
549 to
370
479 to
440
457 to
462
512 to
407
628 to
291
662 to
257
625 to
294
671 to
248
Howie Hawkins7/7/0554 to
365
455 to
464
320 to
599
359 to
560
504 to
415
424 to
495
460 to
459
385 to
534
315 to
604
470 to
449
480 to
439
511 to
408
457 to
462
526 to
393
Tulsi Gabbard12/2/0630 to
289
534 to
385
400 to
519
560 to
359
639 to
280
530 to
389
617 to
302
481 to
438
454 to
465
544 to
375
660 to
259
669 to
250
542 to
377
624 to
295
Dan Crenshaw4/10/0595 to
324
430 to
489
269 to
650
415 to
504
280 to
639
370 to
549
445 to
474
392 to
527
346 to
573
443 to
476
489 to
430
519 to
400
403 to
516
545 to
374
Justin Amash10/4/0666 to
253
485 to
434
363 to
556
495 to
424
389 to
530
549 to
370
510 to
409
456 to
463
423 to
496
488 to
431
611 to
308
650 to
269
598 to
321
662 to
257
Amy Klobuchar7/7/0561 to
358
442 to
477
370 to
549
459 to
460
302 to
617
474 to
445
409 to
510
406 to
513
283 to
636
465 to
454
562 to
357
566 to
353
483 to
436
549 to
370
Bernie Sanders11/3/0542 to
377
546 to
373
440 to
479
534 to
385
438 to
481
527 to
392
463 to
456
513 to
406
414 to
505
540 to
379
551 to
368
555 to
364
501 to
418
543 to
376
Andrew Yang14/0/0608 to
311
650 to
269
462 to
457
604 to
315
465 to
454
573 to
346
496 to
423
636 to
283
505 to
414
629 to
290
677 to
242
669 to
250
553 to
366
616 to
303
Elizabeth Warren7/7/0533 to
386
518 to
401
407 to
512
449 to
470
375 to
544
476 to
443
431 to
488
454 to
465
379 to
540
290 to
629
522 to
397
541 to
378
478 to
441
527 to
392
John Kasich3/11/0570 to
349
438 to
481
291 to
628
439 to
480
259 to
660
430 to
489
308 to
611
357 to
562
368 to
551
242 to
677
397 to
522
580 to
339
456 to
463
574 to
345
Jeb Bush2/12/0570 to
349
427 to
492
257 to
662
408 to
511
250 to
669
400 to
519
269 to
650
353 to
566
364 to
555
250 to
669
378 to
541
339 to
580
398 to
521
543 to
376
Rand Paul7/7/0683 to
236
466 to
453
294 to
625
462 to
457
377 to
542
516 to
403
321 to
598
436 to
483
418 to
501
366 to
553
441 to
478
463 to
456
521 to
398
693 to
226
Ted Cruz1/13/0603 to
316
422 to
497
248 to
671
393 to
526
295 to
624
374 to
545
257 to
662
370 to
549
376 to
543
303 to
616
392 to
527
345 to
574
376 to
543
226 to
693

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 Biden3189 3.5
Jo Jorgensen3961 4.3
Howie Hawkins2312 2.5
Tulsi Gabbard3360 3.7
Dan Crenshaw2180 2.4
Justin Amash3407 3.7
Amy Klobuchar2422 2.6
Bernie Sanders4122 4.5
Andrew Yang4296 4.7
Elizabeth Warren3371 3.7
John Kasich2042 2.2
Jeb Bush1881 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 Biden3189
Jo Jorgensen3961
Howie Hawkins2312
Tulsi Gabbard3360
Dan Crenshaw2180
Justin Amash3407
Amy Klobuchar2422
Bernie Sanders4122
Andrew Yang4296
Elizabeth Warren3371
John Kasich2042
Jeb Bush1881
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 Sanders571

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
463
215 to
558
337 to
380
263 to
483
271 to
281
235 to
483
337 to
408
337 to
495
280 to
555
348 to
449
332 to
346
327 to
331
200 to
427
249 to
252
Joe Biden9/5/0463 to
331
382 to
414
414 to
270
344 to
440
468 to
287
405 to
356
379 to
190
213 to
398
200 to
500
251 to
319
434 to
218
456 to
225
426 to
410
463 to
322
Jo Jorgensen12/2/0558 to
215
414 to
382
456 to
189
394 to
314
507 to
158
338 to
237
434 to
281
373 to
430
323 to
441
406 to
376
480 to
205
504 to
189
436 to
231
540 to
178
Howie Hawkins4/10/0380 to
337
270 to
414
189 to
456
181 to
455
302 to
281
217 to
387
258 to
310
172 to
445
144 to
525
230 to
355
284 to
285
313 to
294
269 to
412
340 to
331
Tulsi Gabbard11/3/0483 to
263
440 to
344
314 to
394
455 to
181
451 to
186
336 to
319
435 to
225
358 to
411
292 to
425
390 to
341
460 to
172
484 to
180
358 to
315
467 to
239
Dan Crenshaw2/12/0281 to
271
287 to
468
158 to
507
281 to
302
186 to
451
159 to
400
257 to
351
275 to
488
218 to
528
285 to
423
262 to
280
271 to
280
163 to
387
251 to
240
Justin Amash8/6/0483 to
235
356 to
405
237 to
338
387 to
217
319 to
336
400 to
159
344 to
299
334 to
439
282 to
453
345 to
392
378 to
201
419 to
192
352 to
239
448 to
193
Amy Klobuchar6/8/0408 to
337
190 to
379
281 to
434
310 to
258
225 to
435
351 to
257
299 to
344
185 to
448
131 to
534
187 to
367
320 to
203
358 to
227
325 to
409
382 to
318
Bernie Sanders13/1/0495 to
337
398 to
213
430 to
373
445 to
172
411 to
358
488 to
275
439 to
334
448 to
185
312 to
348
364 to
160
469 to
215
490 to
230
444 to
383
493 to
314
Andrew Yang14/0/0555 to
280
500 to
200
441 to
323
525 to
144
425 to
292
528 to
218
453 to
282
534 to
131
348 to
312
433 to
204
551 to
147
569 to
161
455 to
328
532 to
262
Elizabeth Warren10/4/0449 to
348
319 to
251
376 to
406
355 to
230
341 to
390
423 to
285
392 to
345
367 to
187
160 to
364
204 to
433
396 to
204
419 to
238
400 to
399
436 to
331
John Kasich5/9/0346 to
332
218 to
434
205 to
480
285 to
284
172 to
460
280 to
262
201 to
378
203 to
320
215 to
469
147 to
551
204 to
396
255 to
179
246 to
389
309 to
290
Jeb Bush2/12/0331 to
327
225 to
456
189 to
504
294 to
313
180 to
484
280 to
271
192 to
419
227 to
358
230 to
490
161 to
569
238 to
419
179 to
255
195 to
398
278 to
282
Rand Paul7/7/0427 to
200
410 to
426
231 to
436
412 to
269
315 to
358
387 to
163
239 to
352
409 to
325
383 to
444
328 to
455
399 to
400
389 to
246
398 to
195
401 to
123
Ted Cruz2/12/0252 to
249
322 to
463
178 to
540
331 to
340
239 to
467
240 to
251
193 to
448
318 to
382
314 to
493
262 to
532
331 to
436
290 to
309
282 to
278
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
0517237.52%
110807.83%
28966.50%
39516.90%
48646.27%
510167.37%
67515.45%
77765.63%
87275.27%
95764.18%
109767.08%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump492373044314334373124116
Joe Biden31567496068736785562851
Jo Jorgensen232776773567139545060140
Howie Hawkins40388696758713931312141
Tulsi Gabbard239616788851028980463131
Dan Crenshaw41890696356633844362022
Justin Amash314765863486739395156108
Amy Klobuchar36967679170825950361414
Bernie Sanders306464841354035546777170
Andrew Yang19856515863847585886794
Elizabeth Warren34866503849425150747378
John Kasich4097375807890483018513
Jeb Bush390110851007373332314711
Rand Paul30779595244576569735559
Ted Cruz43287523350584045563828

Number of bullet votes: 22 (2.39%).
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.