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 Trump142
Joe Biden175
Jo Jorgensen153
Howie Hawkins16
Tulsi Gabbard18
Dan Crenshaw8
Justin Amash37
Amy Klobuchar5
Bernie Sanders98
Andrew Yang33
Elizabeth Warren21
John Kasich8
Jeb Bush4
Rand Paul22
Ted Cruz8
TOTAL:748

The winner is Joe Biden with 23.4% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump205
Joe Biden286
Jo Jorgensen319
Howie Hawkins120
Tulsi Gabbard230
Dan Crenshaw105
Justin Amash241
Amy Klobuchar128
Bernie Sanders311
Andrew Yang333
Elizabeth Warren254
John Kasich92
Jeb Bush59
Rand Paul263
Ted Cruz148
Ballots Cast:748

The winner is Andrew Yang with 44.5% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump121
Joe Biden52
Jo Jorgensen130
Howie Hawkins25
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash64
Amy Klobuchar8
Bernie Sanders141
Andrew Yang62
Elizabeth Warren50
John Kasich12
Jeb Bush4
Rand Paul34
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump121
Joe Biden52
Jo Jorgensen130
Howie Hawkins25
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Amy Klobuchar8
Bernie Sanders142
Andrew Yang62
Elizabeth Warren50
John Kasich12
Rand Paul34
Ted Cruz20

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump121
Joe Biden55
Jo Jorgensen131
Howie Hawkins26
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Bernie Sanders143
Andrew Yang63
Elizabeth Warren51
John Kasich12
Rand Paul34
Ted Cruz20

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump121
Joe Biden55
Jo Jorgensen135
Howie Hawkins26
Tulsi Gabbard18
Justin Amash65
Bernie Sanders143
Andrew Yang64
Elizabeth Warren51
John Kasich12
Rand Paul35
Ted Cruz23

John Kasich eliminated in this round.

Round 5:

Donald Trump121
Joe Biden56
Jo Jorgensen135
Howie Hawkins26
Tulsi Gabbard20
Justin Amash66
Bernie Sanders144
Andrew Yang66
Elizabeth Warren52
Rand Paul38
Ted Cruz24

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump121
Joe Biden56
Jo Jorgensen143
Howie Hawkins26
Justin Amash70
Bernie Sanders145
Andrew Yang70
Elizabeth Warren53
Rand Paul40
Ted Cruz24

Ted Cruz eliminated in this round.

Round 7:

Donald Trump129
Joe Biden58
Jo Jorgensen146
Howie Hawkins27
Justin Amash70
Bernie Sanders146
Andrew Yang70
Elizabeth Warren53
Rand Paul49

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump129
Joe Biden60
Jo Jorgensen146
Justin Amash70
Bernie Sanders167
Andrew Yang73
Elizabeth Warren54
Rand Paul49

Rand Paul eliminated in this round.

Round 9:

Donald Trump148
Joe Biden60
Jo Jorgensen158
Justin Amash85
Bernie Sanders168
Andrew Yang75
Elizabeth Warren54

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump148
Joe Biden73
Jo Jorgensen159
Justin Amash86
Bernie Sanders198
Andrew Yang84

Joe Biden eliminated in this round.

Round 11:

Donald Trump150
Jo Jorgensen169
Justin Amash89
Bernie Sanders231
Andrew Yang109

Justin Amash eliminated in this round.

Round 12:

Donald Trump153
Jo Jorgensen243
Bernie Sanders234
Andrew Yang118

Andrew Yang eliminated in this round.

Round 13:

Donald Trump157
Jo Jorgensen272
Bernie Sanders319

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen397
Bernie Sanders351

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 Trump0/14/0 324 to
424
172 to
576
295 to
453
229 to
519
252 to
496
189 to
559
290 to
458
312 to
436
250 to
498
313 to
435
275 to
473
273 to
475
166 to
582
237 to
511
Joe Biden7/7/0424 to
324
313 to
435
381 to
367
310 to
438
386 to
362
340 to
408
387 to
361
307 to
441
200 to
548
314 to
434
386 to
362
391 to
357
355 to
393
388 to
360
Jo Jorgensen13/1/0576 to
172
435 to
313
506 to
242
433 to
315
536 to
212
450 to
298
449 to
299
397 to
351
368 to
380
414 to
334
516 to
232
541 to
207
511 to
237
554 to
194
Howie Hawkins4/9/1453 to
295
367 to
381
242 to
506
279 to
469
394 to
354
324 to
424
357 to
391
313 to
435
233 to
515
360 to
388
374 to
374
392 to
356
355 to
393
417 to
331
Tulsi Gabbard12/2/0519 to
229
438 to
310
315 to
433
469 to
279
514 to
234
412 to
336
499 to
249
393 to
355
360 to
388
433 to
315
527 to
221
535 to
213
421 to
327
506 to
242
Dan Crenshaw4/10/0496 to
252
362 to
386
212 to
536
354 to
394
234 to
514
287 to
461
366 to
382
327 to
421
273 to
475
360 to
388
396 to
352
424 to
324
315 to
433
442 to
306
Justin Amash11/3/0559 to
189
408 to
340
298 to
450
424 to
324
336 to
412
461 to
287
419 to
329
378 to
370
338 to
410
395 to
353
496 to
252
530 to
218
484 to
264
550 to
198
Amy Klobuchar7/7/0458 to
290
361 to
387
299 to
449
391 to
357
249 to
499
382 to
366
329 to
419
331 to
417
211 to
537
369 to
379
450 to
298
451 to
297
377 to
371
441 to
307
Bernie Sanders10/4/0436 to
312
441 to
307
351 to
397
435 to
313
355 to
393
421 to
327
370 to
378
417 to
331
311 to
437
415 to
333
437 to
311
436 to
312
389 to
359
433 to
315
Andrew Yang14/0/0498 to
250
548 to
200
380 to
368
515 to
233
388 to
360
475 to
273
410 to
338
537 to
211
437 to
311
518 to
230
558 to
190
542 to
206
438 to
310
498 to
250
Elizabeth Warren9/5/0435 to
313
434 to
314
334 to
414
388 to
360
315 to
433
388 to
360
353 to
395
379 to
369
333 to
415
230 to
518
420 to
328
430 to
318
377 to
371
425 to
323
John Kasich3/10/1473 to
275
362 to
386
232 to
516
374 to
374
221 to
527
352 to
396
252 to
496
298 to
450
311 to
437
190 to
558
328 to
420
462 to
286
357 to
391
464 to
284
Jeb Bush2/12/0475 to
273
357 to
391
207 to
541
356 to
392
213 to
535
324 to
424
218 to
530
297 to
451
312 to
436
206 to
542
318 to
430
286 to
462
315 to
433
436 to
312
Rand Paul7/7/0582 to
166
393 to
355
237 to
511
393 to
355
327 to
421
433 to
315
264 to
484
371 to
377
359 to
389
310 to
438
371 to
377
391 to
357
433 to
315
577 to
171
Ted Cruz1/13/0511 to
237
360 to
388
194 to
554
331 to
417
242 to
506
306 to
442
198 to
550
307 to
441
315 to
433
250 to
498
323 to
425
284 to
464
312 to
436
171 to
577

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 Trump2078 2.8
Joe Biden2541 3.4
Jo Jorgensen3353 4.5
Howie Hawkins1792 2.4
Tulsi Gabbard2679 3.6
Dan Crenshaw1762 2.4
Justin Amash2857 3.8
Amy Klobuchar1869 2.5
Bernie Sanders3279 4.4
Andrew Yang3562 4.8
Elizabeth Warren2804 3.7
John Kasich1591 2.1
Jeb Bush1447 1.9
Rand Paul2784 3.7
Ted Cruz1966 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 Trump2078
Joe Biden2541
Jo Jorgensen3353
Howie Hawkins1792
Tulsi Gabbard2679
Dan Crenshaw1762
Justin Amash2857
Amy Klobuchar1869
Bernie Sanders3279
Andrew Yang3562
Elizabeth Warren2804
John Kasich1591
Jeb Bush1447
Rand Paul2784
Ted Cruz1966

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 Yang473
Jo Jorgensen384

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 Trump0/14/0 271 to
372
156 to
468
271 to
299
208 to
388
206 to
229
173 to
401
272 to
323
276 to
395
222 to
459
283 to
364
262 to
281
261 to
266
144 to
362
185 to
213
Joe Biden8/6/0372 to
271
300 to
357
338 to
219
281 to
363
375 to
242
320 to
304
311 to
143
165 to
314
145 to
421
185 to
268
351 to
173
367 to
182
342 to
346
363 to
271
Jo Jorgensen12/2/0468 to
156
357 to
300
390 to
141
342 to
241
428 to
116
285 to
187
375 to
218
324 to
334
275 to
364
339 to
308
410 to
159
430 to
138
369 to
177
450 to
135
Howie Hawkins3/11/0299 to
271
219 to
338
141 to
390
145 to
376
237 to
235
169 to
330
208 to
247
145 to
346
107 to
444
180 to
295
226 to
234
246 to
241
207 to
347
260 to
277
Tulsi Gabbard10/4/0388 to
208
363 to
281
241 to
342
376 to
145
365 to
156
269 to
276
361 to
178
300 to
325
234 to
357
317 to
290
376 to
145
389 to
146
273 to
272
369 to
197
Dan Crenshaw2/12/0229 to
206
242 to
375
116 to
428
235 to
237
156 to
365
122 to
334
211 to
277
234 to
384
176 to
438
235 to
347
215 to
225
230 to
218
124 to
326
196 to
200
Justin Amash9/5/0401 to
173
304 to
320
187 to
285
330 to
169
276 to
269
334 to
122
296 to
234
287 to
347
238 to
371
290 to
325
320 to
156
353 to
140
295 to
193
371 to
148
Amy Klobuchar6/8/0323 to
272
143 to
311
218 to
375
247 to
208
178 to
361
277 to
211
234 to
296
145 to
355
91 to
453
137 to
316
254 to
165
282 to
184
256 to
352
294 to
265
Bernie Sanders13/1/0395 to
276
314 to
165
334 to
324
346 to
145
325 to
300
384 to
234
347 to
287
355 to
145
235 to
301
271 to
138
370 to
172
389 to
187
352 to
327
390 to
265
Andrew Yang14/0/0459 to
222
421 to
145
364 to
275
444 to
107
357 to
234
438 to
176
371 to
238
453 to
91
301 to
235
358 to
162
460 to
108
468 to
121
373 to
275
433 to
216
Elizabeth Warren9/5/0364 to
283
268 to
185
308 to
339
295 to
180
290 to
317
347 to
235
325 to
290
316 to
137
138 to
271
162 to
358
328 to
158
346 to
185
328 to
338
352 to
272
John Kasich5/9/0281 to
262
173 to
351
159 to
410
234 to
226
145 to
376
225 to
215
156 to
320
165 to
254
172 to
370
108 to
460
158 to
328
206 to
138
194 to
330
243 to
239
Jeb Bush1/13/0266 to
261
182 to
367
138 to
430
241 to
246
146 to
389
218 to
230
140 to
353
184 to
282
187 to
389
121 to
468
185 to
346
138 to
206
145 to
340
208 to
237
Rand Paul9/5/0362 to
144
346 to
342
177 to
369
347 to
207
272 to
273
326 to
124
193 to
295
352 to
256
327 to
352
275 to
373
338 to
328
330 to
194
340 to
145
330 to
92
Ted Cruz4/10/0213 to
185
271 to
363
135 to
450
277 to
260
197 to
369
200 to
196
148 to
371
265 to
294
265 to
390
216 to
433
272 to
352
239 to
243
237 to
208
92 to
330

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
0434938.76%
18307.40%
27266.47%
37326.52%
46625.90%
58097.21%
65945.29%
76325.63%
85895.25%
94774.25%
108207.31%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump41328203527363031231491
Joe Biden25857444955624971431644
Jo Jorgensen192545056415336483756125
Howie Hawkins34670585043562825211734
Tulsi Gabbard20347557267886665412123
Dan Crenshaw34968555040533437291617
Justin Amash25955464938483034435195
Amy Klobuchar3185556675566453630119
Bernie Sanders270364025263024375167142
Andrew Yang16442394948615873715984
Elizabeth Warren29443432537323936606475
John Kasich345586361587541231347
Jeb Bush331867280585726161327
Rand Paul25063483733425461674548
Ted Cruz35768372736503439473419

Number of bullet votes: 17 (2.27%).
Number of "approval" votes: 9 (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.