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 Trump169
Joe Biden195
Jo Jorgensen168
Howie Hawkins23
Tulsi Gabbard23
Dan Crenshaw9
Justin Amash39
Amy Klobuchar7
Bernie Sanders123
Andrew Yang36
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul25
Ted Cruz9
TOTAL:863

The winner is Joe Biden with 22.6% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump241
Joe Biden340
Jo Jorgensen345
Howie Hawkins139
Tulsi Gabbard262
Dan Crenshaw112
Justin Amash259
Amy Klobuchar148
Bernie Sanders368
Andrew Yang378
Elizabeth Warren287
John Kasich106
Jeb Bush76
Rand Paul285
Ted Cruz166
Ballots Cast:863

The winner is Andrew Yang with 43.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump145
Joe Biden63
Jo Jorgensen144
Howie Hawkins32
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash67
Amy Klobuchar11
Bernie Sanders169
Andrew Yang69
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul37
Ted Cruz19

Jeb Bush eliminated in this round.

Round 2:

Donald Trump145
Joe Biden63
Jo Jorgensen144
Howie Hawkins32
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash68
Amy Klobuchar11
Bernie Sanders170
Andrew Yang69
Elizabeth Warren54
John Kasich14
Rand Paul37
Ted Cruz22

Eliminated in this round:

Round 3:

Donald Trump146
Joe Biden68
Jo Jorgensen149
Howie Hawkins34
Tulsi Gabbard24
Justin Amash68
Bernie Sanders171
Andrew Yang71
Elizabeth Warren55
John Kasich14
Rand Paul38
Ted Cruz25

John Kasich eliminated in this round.

Round 4:

Donald Trump146
Joe Biden70
Jo Jorgensen149
Howie Hawkins34
Tulsi Gabbard26
Justin Amash69
Bernie Sanders172
Andrew Yang73
Elizabeth Warren57
Rand Paul41
Ted Cruz26

Eliminated in this round:

Round 5:

Donald Trump155
Joe Biden74
Jo Jorgensen160
Howie Hawkins35
Justin Amash74
Bernie Sanders176
Andrew Yang77
Elizabeth Warren58
Rand Paul54

Howie Hawkins eliminated in this round.

Round 6:

Donald Trump155
Joe Biden78
Jo Jorgensen161
Justin Amash74
Bernie Sanders201
Andrew Yang80
Elizabeth Warren60
Rand Paul54

Rand Paul eliminated in this round.

Round 7:

Donald Trump174
Joe Biden78
Jo Jorgensen174
Justin Amash92
Bernie Sanders202
Andrew Yang82
Elizabeth Warren61

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump174
Joe Biden92
Jo Jorgensen176
Justin Amash93
Bernie Sanders235
Andrew Yang93

Joe Biden eliminated in this round.

Round 9:

Donald Trump177
Jo Jorgensen194
Justin Amash96
Bernie Sanders275
Andrew Yang121

Justin Amash eliminated in this round.

Round 10:

Donald Trump180
Jo Jorgensen275
Bernie Sanders278
Andrew Yang130

Andrew Yang eliminated in this round.

Round 11:

Donald Trump185
Jo Jorgensen306
Bernie Sanders372

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen449
Bernie Sanders414

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 Trump0/14/0 361 to
502
206 to
657
334 to
529
264 to
599
297 to
566
227 to
636
330 to
533
349 to
514
286 to
577
356 to
507
319 to
544
319 to
544
211 to
652
288 to
575
Joe Biden7/7/0502 to
361
373 to
490
436 to
427
363 to
500
462 to
401
408 to
455
451 to
412
351 to
512
245 to
618
375 to
488
457 to
406
468 to
395
427 to
436
469 to
394
Jo Jorgensen13/1/0657 to
206
490 to
373
562 to
301
487 to
376
615 to
248
521 to
342
514 to
349
449 to
414
425 to
438
478 to
385
590 to
273
621 to
242
590 to
273
636 to
227
Howie Hawkins6/8/0529 to
334
427 to
436
301 to
562
336 to
527
473 to
390
394 to
469
429 to
434
358 to
505
288 to
575
435 to
428
447 to
416
473 to
390
426 to
437
496 to
367
Tulsi Gabbard12/2/0599 to
264
500 to
363
376 to
487
527 to
336
600 to
263
495 to
368
581 to
282
448 to
415
418 to
445
506 to
357
618 to
245
625 to
238
506 to
357
591 to
272
Dan Crenshaw4/10/0566 to
297
401 to
462
248 to
615
390 to
473
263 to
600
336 to
527
413 to
450
362 to
501
315 to
548
408 to
455
452 to
411
483 to
380
376 to
487
516 to
347
Justin Amash10/4/0636 to
227
455 to
408
342 to
521
469 to
394
368 to
495
527 to
336
478 to
385
426 to
437
392 to
471
454 to
409
573 to
290
610 to
253
562 to
301
630 to
233
Amy Klobuchar7/7/0533 to
330
412 to
451
349 to
514
434 to
429
282 to
581
450 to
413
385 to
478
374 to
489
258 to
605
430 to
433
531 to
332
533 to
330
452 to
411
521 to
342
Bernie Sanders11/3/0514 to
349
512 to
351
414 to
449
505 to
358
415 to
448
501 to
362
437 to
426
489 to
374
380 to
483
501 to
362
517 to
346
519 to
344
468 to
395
512 to
351
Andrew Yang14/0/0577 to
286
618 to
245
438 to
425
575 to
288
445 to
418
548 to
315
471 to
392
605 to
258
483 to
380
592 to
271
642 to
221
630 to
233
520 to
343
582 to
281
Elizabeth Warren8/6/0507 to
356
488 to
375
385 to
478
428 to
435
357 to
506
455 to
408
409 to
454
433 to
430
362 to
501
271 to
592
491 to
372
507 to
356
448 to
415
500 to
363
John Kasich3/11/0544 to
319
406 to
457
273 to
590
416 to
447
245 to
618
411 to
452
290 to
573
332 to
531
346 to
517
221 to
642
372 to
491
542 to
321
428 to
435
546 to
317
Jeb Bush2/12/0544 to
319
395 to
468
242 to
621
390 to
473
238 to
625
380 to
483
253 to
610
330 to
533
344 to
519
233 to
630
356 to
507
321 to
542
375 to
488
519 to
344
Rand Paul7/7/0652 to
211
436 to
427
273 to
590
437 to
426
357 to
506
487 to
376
301 to
562
411 to
452
395 to
468
343 to
520
415 to
448
435 to
428
488 to
375
657 to
206
Ted Cruz1/13/0575 to
288
394 to
469
227 to
636
367 to
496
272 to
591
347 to
516
233 to
630
342 to
521
351 to
512
281 to
582
363 to
500
317 to
546
344 to
519
206 to
657

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 Trump2453 2.8
Joe Biden3001 3.5
Jo Jorgensen3771 4.4
Howie Hawkins2184 2.5
Tulsi Gabbard3177 3.7
Dan Crenshaw2041 2.4
Justin Amash3216 3.7
Amy Klobuchar2270 2.6
Bernie Sanders3902 4.5
Andrew Yang4114 4.8
Elizabeth Warren3248 3.8
John Kasich1901 2.2
Jeb Bush1749 2.0
Rand Paul3141 3.6
Ted Cruz2222 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 Trump2453
Joe Biden3001
Jo Jorgensen3771
Howie Hawkins2184
Tulsi Gabbard3177
Dan Crenshaw2041
Justin Amash3216
Amy Klobuchar2270
Bernie Sanders3902
Andrew Yang4114
Elizabeth Warren3248
John Kasich1901
Jeb Bush1749
Rand Paul3141
Ted Cruz2222

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 Yang572
Bernie Sanders528

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 Trump0/14/0 307 to
439
191 to
533
309 to
360
241 to
459
247 to
266
211 to
459
310 to
387
313 to
469
256 to
531
322 to
429
305 to
328
301 to
312
182 to
403
227 to
235
Joe Biden9/5/0439 to
307
356 to
392
389 to
257
323 to
413
443 to
269
381 to
333
358 to
173
197 to
374
178 to
478
227 to
306
412 to
200
433 to
209
402 to
383
436 to
298
Jo Jorgensen12/2/0533 to
191
392 to
356
433 to
176
373 to
295
484 to
144
325 to
218
413 to
261
355 to
402
303 to
420
382 to
359
455 to
192
479 to
173
422 to
212
518 to
162
Howie Hawkins5/9/0360 to
309
257 to
389
176 to
433
169 to
430
285 to
266
206 to
364
243 to
288
166 to
413
135 to
497
218 to
339
269 to
268
296 to
276
253 to
386
321 to
307
Tulsi Gabbard11/3/0459 to
241
413 to
323
295 to
373
430 to
169
429 to
175
322 to
297
413 to
207
341 to
386
271 to
405
364 to
329
439 to
161
459 to
169
338 to
296
444 to
220
Dan Crenshaw2/12/0266 to
247
269 to
443
144 to
484
266 to
285
175 to
429
147 to
378
240 to
331
260 to
459
204 to
503
266 to
405
245 to
265
257 to
263
154 to
363
237 to
223
Justin Amash8/6/0459 to
211
333 to
381
218 to
325
364 to
206
297 to
322
378 to
147
325 to
281
317 to
413
262 to
433
324 to
378
358 to
191
397 to
179
336 to
222
427 to
176
Amy Klobuchar6/8/0387 to
310
173 to
358
261 to
413
288 to
243
207 to
413
331 to
240
281 to
325
171 to
424
116 to
514
167 to
358
299 to
191
335 to
212
306 to
386
361 to
294
Bernie Sanders13/1/0469 to
313
374 to
197
402 to
355
413 to
166
386 to
341
459 to
260
413 to
317
424 to
171
291 to
335
336 to
156
442 to
202
460 to
218
418 to
362
467 to
292
Andrew Yang14/0/0531 to
256
478 to
178
420 to
303
497 to
135
405 to
271
503 to
204
433 to
262
514 to
116
335 to
291
408 to
193
525 to
133
541 to
149
436 to
306
507 to
244
Elizabeth Warren10/4/0429 to
322
306 to
227
359 to
382
339 to
218
329 to
364
405 to
266
378 to
324
358 to
167
156 to
336
193 to
408
381 to
189
403 to
220
385 to
374
416 to
306
John Kasich4/10/0328 to
305
200 to
412
192 to
455
268 to
269
161 to
439
265 to
245
191 to
358
191 to
299
202 to
442
133 to
525
189 to
381
239 to
165
231 to
367
291 to
269
Jeb Bush2/12/0312 to
301
209 to
433
173 to
479
276 to
296
169 to
459
263 to
257
179 to
397
212 to
335
218 to
460
149 to
541
220 to
403
165 to
239
181 to
376
257 to
262
Rand Paul7/7/0403 to
182
383 to
402
212 to
422
386 to
253
296 to
338
363 to
154
222 to
336
386 to
306
362 to
418
306 to
436
374 to
385
367 to
231
376 to
181
377 to
110
Ted Cruz2/12/0235 to
227
298 to
436
162 to
518
307 to
321
220 to
444
223 to
237
176 to
427
294 to
361
292 to
467
244 to
507
306 to
416
269 to
291
262 to
257
110 to
377

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
0487937.69%
19897.64%
28376.47%
38686.71%
48076.23%
59557.38%
67135.51%
77365.69%
86875.31%
95464.22%
109287.17%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump468362739303932342921108
Joe Biden29264495463726282552149
Jo Jorgensen219686267506639524658136
Howie Hawkins37982646255663729282140
Tulsi Gabbard22453638284997875463029
Dan Crenshaw39582655951613742331721
Justin Amash295705559465937384852104
Amy Klobuchar34862638366785746361311
Bernie Sanders291394534323934506076163
Andrew Yang18352445555797081836794
Elizabeth Warren32359473047404949697278
John Kasich3867069747383482916510
Jeb Bush37010280936967312214510
Rand Paul29471554642516365715253
Ted Cruz41279493144563942533622

Number of bullet votes: 19 (2.20%).
Number of "approval" votes: 11 (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.