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 Trump187
Joe Biden207
Jo Jorgensen170
Howie Hawkins24
Tulsi Gabbard23
Dan Crenshaw10
Justin Amash47
Amy Klobuchar10
Bernie Sanders135
Andrew Yang38
Elizabeth Warren25
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz12
TOTAL:930

The winner is Joe Biden with 22.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump267
Joe Biden363
Jo Jorgensen362
Howie Hawkins149
Tulsi Gabbard279
Dan Crenshaw122
Justin Amash274
Amy Klobuchar157
Bernie Sanders395
Andrew Yang393
Elizabeth Warren302
John Kasich113
Jeb Bush82
Rand Paul305
Ted Cruz184
Ballots Cast:930

The winner is Bernie Sanders with 42.5% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump162
Joe Biden73
Jo Jorgensen146
Howie Hawkins34
Tulsi Gabbard23
Dan Crenshaw12
Justin Amash75
Amy Klobuchar14
Bernie Sanders180
Andrew Yang70
Elizabeth Warren58
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz23

Jeb Bush eliminated in this round.

Round 2:

Donald Trump162
Joe Biden73
Jo Jorgensen146
Howie Hawkins34
Tulsi Gabbard23
Dan Crenshaw12
Justin Amash76
Amy Klobuchar14
Bernie Sanders181
Andrew Yang70
Elizabeth Warren58
John Kasich16
Rand Paul39
Ted Cruz26

Dan Crenshaw eliminated in this round.

Round 3:

Donald Trump163
Joe Biden73
Jo Jorgensen150
Howie Hawkins34
Tulsi Gabbard25
Justin Amash76
Amy Klobuchar14
Bernie Sanders181
Andrew Yang71
Elizabeth Warren58
John Kasich16
Rand Paul40
Ted Cruz29

Amy Klobuchar eliminated in this round.

Round 4:

Donald Trump163
Joe Biden80
Jo Jorgensen151
Howie Hawkins36
Tulsi Gabbard25
Justin Amash76
Bernie Sanders182
Andrew Yang72
Elizabeth Warren59
John Kasich17
Rand Paul40
Ted Cruz29

John Kasich eliminated in this round.

Round 5:

Donald Trump163
Joe Biden83
Jo Jorgensen151
Howie Hawkins36
Tulsi Gabbard28
Justin Amash77
Bernie Sanders184
Andrew Yang74
Elizabeth Warren61
Rand Paul43
Ted Cruz30

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump164
Joe Biden86
Jo Jorgensen159
Howie Hawkins36
Justin Amash82
Bernie Sanders187
Andrew Yang78
Elizabeth Warren62
Rand Paul46
Ted Cruz30

Ted Cruz eliminated in this round.

Round 7:

Donald Trump176
Joe Biden88
Jo Jorgensen162
Howie Hawkins37
Justin Amash82
Bernie Sanders188
Andrew Yang78
Elizabeth Warren62
Rand Paul57

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump176
Joe Biden92
Jo Jorgensen163
Justin Amash82
Bernie Sanders215
Andrew Yang81
Elizabeth Warren64
Rand Paul57

Rand Paul eliminated in this round.

Round 9:

Donald Trump195
Joe Biden92
Jo Jorgensen177
Justin Amash101
Bernie Sanders216
Andrew Yang84
Elizabeth Warren65

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump195
Joe Biden107
Jo Jorgensen181
Justin Amash102
Bernie Sanders250
Andrew Yang95

Andrew Yang eliminated in this round.

Round 11:

Donald Trump198
Joe Biden125
Jo Jorgensen196
Justin Amash114
Bernie Sanders297

Justin Amash eliminated in this round.

Round 12:

Donald Trump205
Joe Biden133
Jo Jorgensen289
Bernie Sanders303

Joe Biden eliminated in this round.

Round 13:

Donald Trump211
Jo Jorgensen321
Bernie Sanders398

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen485
Bernie Sanders445

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 Trump0/14/0 396 to
534
237 to
693
371 to
559
293 to
637
330 to
600
257 to
673
365 to
565
382 to
548
317 to
613
391 to
539
355 to
575
355 to
575
242 to
688
321 to
609
Joe Biden7/7/0534 to
396
402 to
528
469 to
461
391 to
539
496 to
434
441 to
489
485 to
445
378 to
552
275 to
655
406 to
524
488 to
442
498 to
432
459 to
471
503 to
427
Jo Jorgensen13/1/0693 to
237
528 to
402
604 to
326
526 to
404
659 to
271
562 to
368
557 to
373
485 to
445
463 to
467
517 to
413
636 to
294
672 to
258
631 to
299
679 to
251
Howie Hawkins7/7/0559 to
371
461 to
469
326 to
604
365 to
565
512 to
418
433 to
497
469 to
461
392 to
538
322 to
608
476 to
454
489 to
441
518 to
412
464 to
466
533 to
397
Tulsi Gabbard12/2/0637 to
293
539 to
391
404 to
526
565 to
365
648 to
282
538 to
392
627 to
303
486 to
444
460 to
470
549 to
381
670 to
260
679 to
251
549 to
381
632 to
298
Dan Crenshaw4/10/0600 to
330
434 to
496
271 to
659
418 to
512
282 to
648
375 to
555
453 to
477
396 to
534
350 to
580
448 to
482
496 to
434
527 to
403
410 to
520
551 to
379
Justin Amash10/4/0673 to
257
489 to
441
368 to
562
497 to
433
392 to
538
555 to
375
518 to
412
460 to
470
427 to
503
492 to
438
621 to
309
659 to
271
606 to
324
671 to
259
Amy Klobuchar7/7/0565 to
365
445 to
485
373 to
557
461 to
469
303 to
627
477 to
453
412 to
518
410 to
520
288 to
642
469 to
461
570 to
360
574 to
356
490 to
440
556 to
374
Bernie Sanders11/3/0548 to
382
552 to
378
445 to
485
538 to
392
444 to
486
534 to
396
470 to
460
520 to
410
421 to
509
546 to
384
559 to
371
561 to
369
507 to
423
549 to
381
Andrew Yang14/0/0613 to
317
655 to
275
467 to
463
608 to
322
470 to
460
580 to
350
503 to
427
642 to
288
509 to
421
634 to
296
686 to
244
676 to
254
560 to
370
623 to
307
Elizabeth Warren7/7/0539 to
391
524 to
406
413 to
517
454 to
476
381 to
549
482 to
448
438 to
492
461 to
469
384 to
546
296 to
634
530 to
400
548 to
382
485 to
445
534 to
396
John Kasich3/11/0575 to
355
442 to
488
294 to
636
441 to
489
260 to
670
434 to
496
309 to
621
360 to
570
371 to
559
244 to
686
400 to
530
586 to
344
461 to
469
579 to
351
Jeb Bush2/12/0575 to
355
432 to
498
258 to
672
412 to
518
251 to
679
403 to
527
271 to
659
356 to
574
369 to
561
254 to
676
382 to
548
344 to
586
404 to
526
549 to
381
Rand Paul7/7/0688 to
242
471 to
459
299 to
631
466 to
464
381 to
549
520 to
410
324 to
606
440 to
490
423 to
507
370 to
560
445 to
485
469 to
461
526 to
404
699 to
231
Ted Cruz1/13/0609 to
321
427 to
503
251 to
679
397 to
533
298 to
632
379 to
551
259 to
671
374 to
556
381 to
549
307 to
623
396 to
534
351 to
579
381 to
549
231 to
699

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 Trump2696 2.9
Joe Biden3219 3.5
Jo Jorgensen4005 4.3
Howie Hawkins2340 2.5
Tulsi Gabbard3395 3.7
Dan Crenshaw2200 2.4
Justin Amash3444 3.7
Amy Klobuchar2445 2.6
Bernie Sanders4171 4.5
Andrew Yang4331 4.7
Elizabeth Warren3413 3.7
John Kasich2062 2.2
Jeb Bush1898 2.0
Rand Paul3392 3.6
Ted Cruz2430 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 Trump2696
Joe Biden3219
Jo Jorgensen4005
Howie Hawkins2340
Tulsi Gabbard3395
Dan Crenshaw2200
Justin Amash3444
Amy Klobuchar2445
Bernie Sanders4171
Andrew Yang4331
Elizabeth Warren3413
John Kasich2062
Jeb Bush1898
Rand Paul3392
Ted Cruz2430

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 Yang612
Bernie Sanders581

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 Trump1/13/0 335 to
469
220 to
563
342 to
385
266 to
489
276 to
283
239 to
489
343 to
411
341 to
501
284 to
561
352 to
455
336 to
349
331 to
334
204 to
429
253 to
252
Joe Biden9/5/0469 to
335
386 to
420
417 to
273
347 to
443
473 to
289
409 to
359
384 to
192
215 to
404
202 to
505
253 to
324
438 to
220
461 to
227
432 to
414
469 to
325
Jo Jorgensen12/2/0563 to
220
420 to
386
461 to
192
398 to
317
513 to
160
342 to
242
439 to
284
377 to
436
327 to
447
410 to
381
486 to
207
511 to
191
441 to
235
546 to
179
Howie Hawkins5/9/0385 to
342
273 to
417
192 to
461
185 to
460
307 to
284
221 to
391
262 to
313
173 to
451
145 to
530
231 to
360
289 to
287
318 to
297
274 to
417
345 to
334
Tulsi Gabbard11/3/0489 to
266
443 to
347
317 to
398
460 to
185
457 to
187
339 to
323
441 to
227
361 to
418
296 to
430
393 to
347
465 to
174
490 to
182
363 to
319
474 to
241
Dan Crenshaw2/12/0283 to
276
289 to
473
160 to
513
284 to
307
187 to
457
160 to
405
260 to
354
277 to
495
220 to
534
287 to
429
264 to
283
275 to
284
165 to
391
254 to
242
Justin Amash8/6/0489 to
239
359 to
409
242 to
342
391 to
221
323 to
339
405 to
160
347 to
301
336 to
446
284 to
460
347 to
398
382 to
202
425 to
194
358 to
241
455 to
195
Amy Klobuchar6/8/0411 to
343
192 to
384
284 to
439
313 to
262
227 to
441
354 to
260
301 to
347
186 to
455
133 to
540
188 to
372
322 to
206
362 to
230
328 to
414
386 to
322
Bernie Sanders13/1/0501 to
341
404 to
215
436 to
377
451 to
173
418 to
361
495 to
277
446 to
336
455 to
186
318 to
349
368 to
163
476 to
216
496 to
232
450 to
387
499 to
317
Andrew Yang14/0/0561 to
284
505 to
202
447 to
327
530 to
145
430 to
296
534 to
220
460 to
284
540 to
133
349 to
318
435 to
209
558 to
148
576 to
163
461 to
332
538 to
265
Elizabeth Warren10/4/0455 to
352
324 to
253
381 to
410
360 to
231
347 to
393
429 to
287
398 to
347
372 to
188
163 to
368
209 to
435
402 to
205
425 to
240
406 to
403
442 to
334
John Kasich4/10/0349 to
336
220 to
438
207 to
486
287 to
289
174 to
465
283 to
264
202 to
382
206 to
322
216 to
476
148 to
558
205 to
402
258 to
181
249 to
393
312 to
292
Jeb Bush2/12/0334 to
331
227 to
461
191 to
511
297 to
318
182 to
490
284 to
275
194 to
425
230 to
362
232 to
496
163 to
576
240 to
425
181 to
258
198 to
402
281 to
285
Rand Paul7/7/0429 to
204
414 to
432
235 to
441
417 to
274
319 to
363
391 to
165
241 to
358
414 to
328
387 to
450
332 to
461
403 to
406
393 to
249
402 to
198
405 to
124
Ted Cruz1/13/0252 to
253
325 to
469
179 to
546
334 to
345
241 to
474
242 to
254
195 to
455
322 to
386
317 to
499
265 to
538
334 to
442
292 to
312
285 to
281
124 to
405

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
0524137.57%
110867.78%
29106.52%
39606.88%
48786.29%
510337.41%
67615.46%
77845.62%
87335.25%
95804.16%
109847.05%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump497373145314335373124119
Joe Biden31968506170736885562852
Jo Jorgensen234786775567539545161140
Howie Hawkins40889706759724031312142
Tulsi Gabbard242616791871039081463131
Dan Crenshaw42490716357643845362022
Justin Amash318765963516839395256109
Amy Klobuchar37468689171846050361414
Bernie Sanders310464941354036566878171
Andrew Yang20256525863877885886794
Elizabeth Warren35366503849435252757478
John Kasich4157376808092483018513
Jeb Bush395111861027573332314711
Rand Paul31279615244576570755659
Ted Cruz43888533350594046563829

Number of bullet votes: 23 (2.47%).
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.