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 Trump173
Joe Biden196
Jo Jorgensen170
Howie Hawkins23
Tulsi Gabbard23
Dan Crenshaw9
Justin Amash44
Amy Klobuchar7
Bernie Sanders129
Andrew Yang37
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul26
Ted Cruz10
TOTAL:884

The winner is Joe Biden with 22.2% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump249
Joe Biden345
Jo Jorgensen355
Howie Hawkins142
Tulsi Gabbard269
Dan Crenshaw117
Justin Amash269
Amy Klobuchar149
Bernie Sanders375
Andrew Yang387
Elizabeth Warren290
John Kasich108
Jeb Bush78
Rand Paul297
Ted Cruz173
Ballots Cast:884

The winner is Andrew Yang with 43.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump148
Joe Biden64
Jo Jorgensen146
Howie Hawkins33
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash72
Amy Klobuchar11
Bernie Sanders175
Andrew Yang69
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul38
Ted Cruz21

Jeb Bush eliminated in this round.

Round 2:

Donald Trump148
Joe Biden64
Jo Jorgensen146
Howie Hawkins33
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash73
Amy Klobuchar11
Bernie Sanders176
Andrew Yang69
Elizabeth Warren54
John Kasich14
Rand Paul38
Ted Cruz24

Eliminated in this round:

Round 3:

Donald Trump149
Joe Biden69
Jo Jorgensen151
Howie Hawkins35
Tulsi Gabbard24
Justin Amash73
Bernie Sanders177
Andrew Yang71
Elizabeth Warren55
John Kasich14
Rand Paul39
Ted Cruz27

John Kasich eliminated in this round.

Round 4:

Donald Trump149
Joe Biden71
Jo Jorgensen151
Howie Hawkins35
Tulsi Gabbard26
Justin Amash74
Bernie Sanders178
Andrew Yang73
Elizabeth Warren57
Rand Paul42
Ted Cruz28

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump149
Joe Biden73
Jo Jorgensen159
Howie Hawkins35
Justin Amash79
Bernie Sanders181
Andrew Yang77
Elizabeth Warren58
Rand Paul45
Ted Cruz28

Ted Cruz eliminated in this round.

Round 6:

Donald Trump159
Joe Biden75
Jo Jorgensen162
Howie Hawkins36
Justin Amash79
Bernie Sanders182
Andrew Yang77
Elizabeth Warren58
Rand Paul56

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump159
Joe Biden79
Jo Jorgensen163
Justin Amash79
Bernie Sanders208
Andrew Yang80
Elizabeth Warren60
Rand Paul56

Rand Paul eliminated in this round.

Round 8:

Donald Trump178
Joe Biden79
Jo Jorgensen177
Justin Amash98
Bernie Sanders209
Andrew Yang82
Elizabeth Warren61

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump178
Joe Biden93
Jo Jorgensen179
Justin Amash99
Bernie Sanders242
Andrew Yang93

Eliminated in this round:

Round 10:

Donald Trump184
Jo Jorgensen217
Justin Amash120
Bernie Sanders363

Justin Amash eliminated in this round.

Round 11:

Donald Trump190
Jo Jorgensen314
Bernie Sanders380

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen461
Bernie Sanders423

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 Trump0/14/0 372 to
512
212 to
672
345 to
539
271 to
613
306 to
578
234 to
650
341 to
543
359 to
525
292 to
592
366 to
518
330 to
554
329 to
555
217 to
667
296 to
588
Joe Biden7/7/0512 to
372
379 to
505
445 to
439
368 to
516
470 to
414
415 to
469
462 to
422
357 to
527
251 to
633
384 to
500
464 to
420
475 to
409
434 to
450
478 to
406
Jo Jorgensen13/1/0672 to
212
505 to
379
579 to
305
504 to
380
631 to
253
534 to
350
531 to
353
461 to
423
440 to
444
494 to
390
606 to
278
637 to
247
603 to
281
649 to
235
Howie Hawkins6/8/0539 to
345
439 to
445
305 to
579
342 to
542
483 to
401
400 to
484
441 to
443
368 to
516
294 to
590
449 to
435
457 to
427
484 to
400
434 to
450
504 to
380
Tulsi Gabbard12/2/0613 to
271
516 to
368
380 to
504
542 to
342
616 to
268
503 to
381
597 to
287
460 to
424
429 to
455
522 to
362
635 to
249
642 to
242
516 to
368
602 to
282
Dan Crenshaw4/10/0578 to
306
414 to
470
253 to
631
401 to
483
268 to
616
345 to
539
426 to
458
372 to
512
323 to
561
422 to
462
465 to
419
496 to
388
383 to
501
526 to
358
Justin Amash10/4/0650 to
234
469 to
415
350 to
534
484 to
400
381 to
503
539 to
345
492 to
392
438 to
446
405 to
479
469 to
415
589 to
295
625 to
259
575 to
309
642 to
242
Amy Klobuchar8/6/0543 to
341
422 to
462
353 to
531
443 to
441
287 to
597
458 to
426
392 to
492
384 to
500
262 to
622
444 to
440
541 to
343
543 to
341
460 to
424
529 to
355
Bernie Sanders11/3/0525 to
359
527 to
357
423 to
461
516 to
368
424 to
460
512 to
372
446 to
438
500 to
384
390 to
494
516 to
368
528 to
356
532 to
352
478 to
406
522 to
362
Andrew Yang14/0/0592 to
292
633 to
251
444 to
440
590 to
294
455 to
429
561 to
323
479 to
405
622 to
262
494 to
390
610 to
274
655 to
229
645 to
239
529 to
355
595 to
289
Elizabeth Warren7/7/0518 to
366
500 to
384
390 to
494
435 to
449
362 to
522
462 to
422
415 to
469
440 to
444
368 to
516
274 to
610
499 to
385
518 to
366
456 to
428
508 to
376
John Kasich3/11/0554 to
330
420 to
464
278 to
606
427 to
457
249 to
635
419 to
465
295 to
589
343 to
541
356 to
528
229 to
655
385 to
499
555 to
329
435 to
449
553 to
331
Jeb Bush2/12/0555 to
329
409 to
475
247 to
637
400 to
484
242 to
642
388 to
496
259 to
625
341 to
543
352 to
532
239 to
645
366 to
518
329 to
555
381 to
503
526 to
358
Rand Paul7/7/0667 to
217
450 to
434
281 to
603
450 to
434
368 to
516
501 to
383
309 to
575
424 to
460
406 to
478
355 to
529
428 to
456
449 to
435
503 to
381
671 to
213
Ted Cruz1/13/0588 to
296
406 to
478
235 to
649
380 to
504
282 to
602
358 to
526
242 to
642
355 to
529
362 to
522
289 to
595
376 to
508
331 to
553
358 to
526
213 to
671

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 Trump2523 2.9
Joe Biden3050 3.5
Jo Jorgensen3883 4.4
Howie Hawkins2227 2.5
Tulsi Gabbard3249 3.7
Dan Crenshaw2093 2.4
Justin Amash3325 3.8
Amy Klobuchar2306 2.6
Bernie Sanders3979 4.5
Andrew Yang4202 4.8
Elizabeth Warren3287 3.7
John Kasich1952 2.2
Jeb Bush1790 2.0
Rand Paul3251 3.7
Ted Cruz2298 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 Trump2523
Joe Biden3050
Jo Jorgensen3883
Howie Hawkins2227
Tulsi Gabbard3249
Dan Crenshaw2093
Justin Amash3325
Amy Klobuchar2306
Bernie Sanders3979
Andrew Yang4202
Elizabeth Warren3287
John Kasich1952
Jeb Bush1790
Rand Paul3251
Ted Cruz2298

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 Yang588
Bernie Sanders542

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 Trump0/14/0 317 to
446
197 to
546
319 to
367
247 to
469
254 to
270
218 to
471
321 to
393
322 to
478
262 to
543
331 to
436
315 to
334
311 to
318
186 to
416
233 to
242
Joe Biden9/5/0446 to
317
362 to
405
396 to
261
328 to
426
450 to
277
387 to
347
366 to
178
200 to
384
183 to
489
233 to
310
418 to
208
439 to
215
408 to
397
445 to
308
Jo Jorgensen12/2/0546 to
197
405 to
362
448 to
180
385 to
300
495 to
149
331 to
225
427 to
266
367 to
409
317 to
426
395 to
364
468 to
195
493 to
176
427 to
218
528 to
166
Howie Hawkins4/10/0367 to
319
261 to
396
180 to
448
173 to
442
292 to
274
210 to
377
248 to
296
169 to
421
137 to
510
223 to
344
272 to
277
302 to
283
258 to
400
328 to
317
Tulsi Gabbard11/3/0469 to
247
426 to
328
300 to
385
442 to
173
439 to
179
325 to
310
425 to
213
350 to
394
279 to
417
376 to
333
449 to
164
470 to
172
344 to
306
453 to
227
Dan Crenshaw2/12/0270 to
254
277 to
450
149 to
495
274 to
292
179 to
439
153 to
389
249 to
338
267 to
468
209 to
516
275 to
413
254 to
271
265 to
268
157 to
375
243 to
230
Justin Amash8/6/0471 to
218
347 to
387
225 to
331
377 to
210
310 to
325
389 to
153
337 to
286
328 to
420
272 to
441
337 to
383
370 to
193
410 to
181
342 to
228
438 to
181
Amy Klobuchar6/8/0393 to
321
178 to
366
266 to
427
296 to
248
213 to
425
338 to
249
286 to
337
175 to
433
117 to
526
173 to
363
306 to
198
343 to
218
311 to
399
368 to
305
Bernie Sanders13/1/0478 to
322
384 to
200
409 to
367
421 to
169
394 to
350
468 to
267
420 to
328
433 to
175
296 to
342
345 to
157
450 to
209
470 to
222
426 to
373
476 to
302
Andrew Yang14/0/0543 to
262
489 to
183
426 to
317
510 to
137
417 to
279
516 to
209
441 to
272
526 to
117
342 to
296
420 to
196
538 to
138
556 to
152
444 to
317
520 to
251
Elizabeth Warren10/4/0436 to
331
310 to
233
364 to
395
344 to
223
333 to
376
413 to
275
383 to
337
363 to
173
157 to
345
196 to
420
386 to
196
409 to
226
390 to
386
424 to
317
John Kasich5/9/0334 to
315
208 to
418
195 to
468
277 to
272
164 to
449
271 to
254
193 to
370
198 to
306
209 to
450
138 to
538
196 to
386
245 to
170
234 to
379
297 to
278
Jeb Bush2/12/0318 to
311
215 to
439
176 to
493
283 to
302
172 to
470
268 to
265
181 to
410
218 to
343
222 to
470
152 to
556
226 to
409
170 to
245
184 to
389
264 to
271
Rand Paul7/7/0416 to
186
397 to
408
218 to
427
400 to
258
306 to
344
375 to
157
228 to
342
399 to
311
373 to
426
317 to
444
386 to
390
379 to
234
389 to
184
389 to
114
Ted Cruz2/12/0242 to
233
308 to
445
166 to
528
317 to
328
227 to
453
230 to
243
181 to
438
305 to
368
302 to
476
251 to
520
317 to
424
278 to
297
271 to
264
114 to
389

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
0499737.68%
110187.68%
28576.46%
38896.70%
48286.24%
59777.37%
67235.45%
77535.68%
87035.30%
95644.25%
109517.17%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump477362941314033352923110
Joe Biden30266495766726282562349
Jo Jorgensen222716269516839534960140
Howie Hawkins39083666356693829282141
Tulsi Gabbard229566584841018178463030
Dan Crenshaw40484676153613843331822
Justin Amash299735659466237395056107
Amy Klobuchar35865658667785747361411
Bernie Sanders300414634333934526277166
Andrew Yang18852475556837185866794
Elizabeth Warren33561473248415049717278
John Kasich3957172757586482917511
Jeb Bush38010580957268322214610
Rand Paul29874554743526467725557
Ted Cruz42080513147573943543725

Number of bullet votes: 20 (2.26%).
Number of "approval" votes: 12 (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.