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 Trump167
Joe Biden195
Jo Jorgensen168
Howie Hawkins22
Tulsi Gabbard23
Dan Crenshaw9
Justin Amash39
Amy Klobuchar7
Bernie Sanders122
Andrew Yang36
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul25
Ted Cruz9
TOTAL:859

The winner is Joe Biden with 22.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump239
Joe Biden337
Jo Jorgensen345
Howie Hawkins138
Tulsi Gabbard260
Dan Crenshaw112
Justin Amash259
Amy Klobuchar148
Bernie Sanders366
Andrew Yang376
Elizabeth Warren286
John Kasich106
Jeb Bush76
Rand Paul285
Ted Cruz166
Ballots Cast:859

The winner is Andrew Yang with 43.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump143
Joe Biden63
Jo Jorgensen144
Howie Hawkins31
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash67
Amy Klobuchar11
Bernie Sanders168
Andrew Yang69
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul37
Ted Cruz19

Jeb Bush eliminated in this round.

Round 2:

Donald Trump143
Joe Biden63
Jo Jorgensen144
Howie Hawkins31
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash68
Amy Klobuchar11
Bernie Sanders169
Andrew Yang69
Elizabeth Warren54
John Kasich14
Rand Paul37
Ted Cruz22

Eliminated in this round:

Round 3:

Donald Trump144
Joe Biden68
Jo Jorgensen149
Howie Hawkins33
Tulsi Gabbard24
Justin Amash68
Bernie Sanders170
Andrew Yang71
Elizabeth Warren55
John Kasich14
Rand Paul38
Ted Cruz25

John Kasich eliminated in this round.

Round 4:

Donald Trump144
Joe Biden70
Jo Jorgensen149
Howie Hawkins33
Tulsi Gabbard26
Justin Amash69
Bernie Sanders171
Andrew Yang73
Elizabeth Warren57
Rand Paul41
Ted Cruz26

Eliminated in this round:

Round 5:

Donald Trump153
Joe Biden74
Jo Jorgensen160
Howie Hawkins34
Justin Amash74
Bernie Sanders175
Andrew Yang77
Elizabeth Warren58
Rand Paul54

Howie Hawkins eliminated in this round.

Round 6:

Donald Trump153
Joe Biden78
Jo Jorgensen161
Justin Amash74
Bernie Sanders199
Andrew Yang80
Elizabeth Warren60
Rand Paul54

Rand Paul eliminated in this round.

Round 7:

Donald Trump172
Joe Biden78
Jo Jorgensen174
Justin Amash92
Bernie Sanders200
Andrew Yang82
Elizabeth Warren61

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump172
Joe Biden92
Jo Jorgensen176
Justin Amash93
Bernie Sanders233
Andrew Yang93

Joe Biden eliminated in this round.

Round 9:

Donald Trump175
Jo Jorgensen194
Justin Amash96
Bernie Sanders273
Andrew Yang121

Justin Amash eliminated in this round.

Round 10:

Donald Trump178
Jo Jorgensen275
Bernie Sanders276
Andrew Yang130

Andrew Yang eliminated in this round.

Round 11:

Donald Trump183
Jo Jorgensen306
Bernie Sanders370

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen448
Bernie Sanders411

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 Trump0/14/0 359 to
500
204 to
655
332 to
527
262 to
597
295 to
564
225 to
634
328 to
531
347 to
512
284 to
575
354 to
505
317 to
542
317 to
542
209 to
650
285 to
574
Joe Biden7/7/0500 to
359
371 to
488
435 to
424
362 to
497
460 to
399
405 to
454
448 to
411
350 to
509
244 to
615
373 to
486
454 to
405
465 to
394
423 to
436
466 to
393
Jo Jorgensen13/1/0655 to
204
488 to
371
560 to
299
486 to
373
612 to
247
518 to
341
512 to
347
448 to
411
424 to
435
476 to
383
587 to
272
618 to
241
587 to
272
634 to
225
Howie Hawkins6/8/0527 to
332
424 to
435
299 to
560
334 to
525
469 to
390
390 to
469
425 to
434
355 to
504
285 to
574
431 to
428
443 to
416
469 to
390
422 to
437
493 to
366
Tulsi Gabbard12/2/0597 to
262
497 to
362
373 to
486
525 to
334
596 to
263
491 to
368
577 to
282
446 to
413
416 to
443
503 to
356
614 to
245
621 to
238
502 to
357
588 to
271
Dan Crenshaw4/10/0564 to
295
399 to
460
247 to
612
390 to
469
263 to
596
335 to
524
411 to
448
361 to
498
313 to
546
405 to
454
449 to
410
480 to
379
373 to
486
513 to
346
Justin Amash10/4/0634 to
225
454 to
405
341 to
518
469 to
390
368 to
491
524 to
335
475 to
384
424 to
435
390 to
469
451 to
408
569 to
290
606 to
253
558 to
301
627 to
232
Amy Klobuchar7/7/0531 to
328
411 to
448
347 to
512
434 to
425
282 to
577
448 to
411
384 to
475
373 to
486
256 to
603
427 to
432
527 to
332
529 to
330
448 to
411
518 to
341
Bernie Sanders11/3/0512 to
347
509 to
350
411 to
448
504 to
355
413 to
446
498 to
361
435 to
424
486 to
373
376 to
483
497 to
362
513 to
346
515 to
344
464 to
395
509 to
350
Andrew Yang14/0/0575 to
284
615 to
244
435 to
424
574 to
285
443 to
416
546 to
313
469 to
390
603 to
256
483 to
376
590 to
269
638 to
221
626 to
233
517 to
342
579 to
280
Elizabeth Warren8/6/0505 to
354
486 to
373
383 to
476
428 to
431
356 to
503
454 to
405
408 to
451
432 to
427
362 to
497
269 to
590
488 to
371
504 to
355
445 to
414
498 to
361
John Kasich3/11/0542 to
317
405 to
454
272 to
587
416 to
443
245 to
614
410 to
449
290 to
569
332 to
527
346 to
513
221 to
638
371 to
488
538 to
321
426 to
433
543 to
316
Jeb Bush2/12/0542 to
317
394 to
465
241 to
618
390 to
469
238 to
621
379 to
480
253 to
606
330 to
529
344 to
515
233 to
626
355 to
504
321 to
538
373 to
486
517 to
342
Rand Paul7/7/0650 to
209
436 to
423
272 to
587
437 to
422
357 to
502
486 to
373
301 to
558
411 to
448
395 to
464
342 to
517
414 to
445
433 to
426
486 to
373
654 to
205
Ted Cruz1/13/0574 to
285
393 to
466
225 to
634
366 to
493
271 to
588
346 to
513
232 to
627
341 to
518
350 to
509
280 to
579
361 to
498
316 to
543
342 to
517
205 to
654

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 Trump2431 2.8
Joe Biden2984 3.5
Jo Jorgensen3756 4.4
Howie Hawkins2165 2.5
Tulsi Gabbard3161 3.7
Dan Crenshaw2032 2.4
Justin Amash3205 3.7
Amy Klobuchar2260 2.6
Bernie Sanders3880 4.5
Andrew Yang4098 4.8
Elizabeth Warren3233 3.8
John Kasich1896 2.2
Jeb Bush1743 2.0
Rand Paul3133 3.6
Ted Cruz2218 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 Trump2431
Joe Biden2984
Jo Jorgensen3756
Howie Hawkins2165
Tulsi Gabbard3161
Dan Crenshaw2032
Justin Amash3205
Amy Klobuchar2260
Bernie Sanders3880
Andrew Yang4098
Elizabeth Warren3233
John Kasich1896
Jeb Bush1743
Rand Paul3133
Ted Cruz2218

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 Yang570
Bernie Sanders525

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 Trump0/14/0 305 to
437
189 to
532
307 to
359
239 to
457
245 to
265
209 to
457
308 to
385
311 to
467
254 to
529
320 to
427
303 to
327
299 to
312
180 to
402
224 to
235
Joe Biden9/5/0437 to
305
353 to
391
387 to
255
322 to
411
440 to
268
379 to
332
356 to
172
196 to
372
177 to
475
225 to
304
409 to
199
430 to
208
400 to
382
433 to
297
Jo Jorgensen12/2/0532 to
189
391 to
353
431 to
175
371 to
293
481 to
143
323 to
217
411 to
259
354 to
399
301 to
418
380 to
357
452 to
191
476 to
173
419 to
211
514 to
162
Howie Hawkins4/10/0359 to
307
255 to
387
175 to
431
167 to
429
283 to
265
204 to
363
240 to
287
164 to
411
133 to
495
216 to
337
266 to
267
293 to
276
250 to
385
317 to
307
Tulsi Gabbard11/3/0457 to
239
411 to
322
293 to
371
429 to
167
427 to
175
320 to
296
410 to
207
340 to
383
269 to
403
362 to
327
435 to
161
455 to
169
335 to
296
440 to
220
Dan Crenshaw2/12/0265 to
245
268 to
440
143 to
481
265 to
283
175 to
427
146 to
375
238 to
329
259 to
456
203 to
500
265 to
403
243 to
265
254 to
263
152 to
362
234 to
223
Justin Amash8/6/0457 to
209
332 to
379
217 to
323
363 to
204
296 to
320
375 to
146
324 to
280
316 to
410
261 to
430
322 to
376
355 to
191
394 to
179
334 to
222
424 to
176
Amy Klobuchar6/8/0385 to
308
172 to
356
259 to
411
287 to
240
207 to
410
329 to
238
280 to
324
170 to
421
115 to
511
165 to
356
296 to
191
333 to
211
305 to
385
359 to
294
Bernie Sanders13/1/0467 to
311
372 to
196
399 to
354
411 to
164
383 to
340
456 to
259
410 to
316
421 to
170
289 to
334
333 to
155
439 to
201
457 to
217
415 to
361
464 to
291
Andrew Yang14/0/0529 to
254
475 to
177
418 to
301
495 to
133
403 to
269
500 to
203
430 to
261
511 to
115
334 to
289
407 to
192
522 to
133
538 to
148
433 to
305
504 to
243
Elizabeth Warren10/4/0427 to
320
304 to
225
357 to
380
337 to
216
327 to
362
403 to
265
376 to
322
356 to
165
155 to
333
192 to
407
379 to
189
400 to
219
383 to
372
413 to
305
John Kasich5/9/0327 to
303
199 to
409
191 to
452
267 to
266
161 to
435
265 to
243
191 to
355
191 to
296
201 to
439
133 to
522
189 to
379
238 to
164
231 to
365
290 to
268
Jeb Bush2/12/0312 to
299
208 to
430
173 to
476
276 to
293
169 to
455
263 to
254
179 to
394
211 to
333
217 to
457
148 to
538
219 to
400
164 to
238
181 to
375
255 to
262
Rand Paul7/7/0402 to
180
382 to
400
211 to
419
385 to
250
296 to
335
362 to
152
222 to
334
385 to
305
361 to
415
305 to
433
372 to
383
365 to
231
375 to
181
375 to
110
Ted Cruz2/12/0235 to
224
297 to
433
162 to
514
307 to
317
220 to
440
223 to
234
176 to
424
294 to
359
291 to
464
243 to
504
305 to
413
268 to
290
262 to
255
110 to
375

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
0486537.76%
19817.61%
28346.47%
38596.67%
48016.22%
59467.34%
67115.52%
77325.68%
86855.32%
95454.23%
109267.19%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump467362738303932342920107
Joe Biden29164495462716282542149
Jo Jorgensen219676266506538524658136
Howie Hawkins37981646155653729282139
Tulsi Gabbard22452638283987775463029
Dan Crenshaw39481655949613742331721
Justin Amash294695559465737384852104
Amy Klobuchar34762628266775746361311
Bernie Sanders290394534323934485976163
Andrew Yang18351445455787080836794
Elizabeth Warren32358472946404948697278
John Kasich3846969747283482916510
Jeb Bush36810280916967312214510
Rand Paul29271554542506365715253
Ted Cruz41079473144563942533622

Number of bullet votes: 19 (2.21%).
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.