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 Trump156
Joe Biden189
Jo Jorgensen164
Howie Hawkins21
Tulsi Gabbard22
Dan Crenshaw9
Justin Amash39
Amy Klobuchar6
Bernie Sanders116
Andrew Yang35
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul24
Ted Cruz9
TOTAL:827

The winner is Joe Biden with 22.9% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump226
Joe Biden323
Jo Jorgensen338
Howie Hawkins136
Tulsi Gabbard251
Dan Crenshaw110
Justin Amash256
Amy Klobuchar144
Bernie Sanders353
Andrew Yang366
Elizabeth Warren282
John Kasich103
Jeb Bush69
Rand Paul278
Ted Cruz158
Ballots Cast:827

The winner is Andrew Yang with 44.3% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump133
Joe Biden61
Jo Jorgensen140
Howie Hawkins30
Tulsi Gabbard21
Dan Crenshaw11
Justin Amash67
Amy Klobuchar10
Bernie Sanders161
Andrew Yang66
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul36
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump133
Joe Biden61
Jo Jorgensen140
Howie Hawkins30
Tulsi Gabbard21
Dan Crenshaw11
Justin Amash68
Amy Klobuchar10
Bernie Sanders162
Andrew Yang66
Elizabeth Warren54
John Kasich14
Rand Paul36
Ted Cruz21

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump133
Joe Biden65
Jo Jorgensen141
Howie Hawkins32
Tulsi Gabbard21
Dan Crenshaw11
Justin Amash68
Bernie Sanders163
Andrew Yang67
Elizabeth Warren55
John Kasich14
Rand Paul36
Ted Cruz21

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump134
Joe Biden65
Jo Jorgensen145
Howie Hawkins32
Tulsi Gabbard22
Justin Amash68
Bernie Sanders163
Andrew Yang68
Elizabeth Warren55
John Kasich14
Rand Paul37
Ted Cruz24

John Kasich eliminated in this round.

Round 5:

Donald Trump134
Joe Biden67
Jo Jorgensen145
Howie Hawkins32
Tulsi Gabbard24
Justin Amash69
Bernie Sanders164
Andrew Yang70
Elizabeth Warren57
Rand Paul40
Ted Cruz25

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump134
Joe Biden69
Jo Jorgensen153
Howie Hawkins32
Justin Amash74
Bernie Sanders166
Andrew Yang74
Elizabeth Warren58
Rand Paul42
Ted Cruz25

Ted Cruz eliminated in this round.

Round 7:

Donald Trump142
Joe Biden71
Jo Jorgensen156
Howie Hawkins33
Justin Amash74
Bernie Sanders167
Andrew Yang74
Elizabeth Warren58
Rand Paul52

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump142
Joe Biden75
Jo Jorgensen157
Justin Amash74
Bernie Sanders191
Andrew Yang77
Elizabeth Warren59
Rand Paul52

Rand Paul eliminated in this round.

Round 9:

Donald Trump161
Joe Biden75
Jo Jorgensen169
Justin Amash91
Bernie Sanders192
Andrew Yang79
Elizabeth Warren60

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump161
Joe Biden88
Jo Jorgensen171
Justin Amash92
Bernie Sanders225
Andrew Yang90

Joe Biden eliminated in this round.

Round 11:

Donald Trump163
Jo Jorgensen188
Justin Amash95
Bernie Sanders264
Andrew Yang117

Justin Amash eliminated in this round.

Round 12:

Donald Trump166
Jo Jorgensen268
Bernie Sanders267
Andrew Yang126

Andrew Yang eliminated in this round.

Round 13:

Donald Trump171
Jo Jorgensen298
Bernie Sanders358

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen432
Bernie Sanders395

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 Trump0/14/0 344 to
483
191 to
636
316 to
511
248 to
579
277 to
550
209 to
618
313 to
514
331 to
496
270 to
557
338 to
489
300 to
527
300 to
527
193 to
634
267 to
560
Joe Biden7/7/0483 to
344
358 to
469
420 to
407
349 to
478
443 to
384
389 to
438
431 to
396
338 to
489
234 to
593
354 to
473
437 to
390
448 to
379
407 to
420
448 to
379
Jo Jorgensen13/1/0636 to
191
469 to
358
543 to
284
469 to
358
592 to
235
497 to
330
492 to
335
432 to
395
407 to
420
455 to
372
566 to
261
598 to
229
568 to
259
614 to
213
Howie Hawkins5/9/0511 to
316
407 to
420
284 to
543
318 to
509
450 to
377
372 to
455
405 to
422
341 to
486
268 to
559
409 to
418
424 to
403
451 to
376
404 to
423
474 to
353
Tulsi Gabbard12/2/0579 to
248
478 to
349
358 to
469
509 to
318
575 to
252
469 to
358
552 to
275
428 to
399
400 to
427
479 to
348
587 to
240
598 to
229
480 to
347
569 to
258
Dan Crenshaw4/10/0550 to
277
384 to
443
235 to
592
377 to
450
252 to
575
316 to
511
396 to
431
349 to
478
298 to
529
388 to
439
430 to
397
463 to
364
356 to
471
496 to
331
Justin Amash10/4/0618 to
209
438 to
389
330 to
497
455 to
372
358 to
469
511 to
316
460 to
367
411 to
416
375 to
452
433 to
394
548 to
279
587 to
240
540 to
287
610 to
217
Amy Klobuchar7/7/0514 to
313
396 to
431
335 to
492
422 to
405
275 to
552
431 to
396
367 to
460
358 to
469
243 to
584
406 to
421
504 to
323
507 to
320
428 to
399
500 to
327
Bernie Sanders11/3/0496 to
331
489 to
338
395 to
432
486 to
341
399 to
428
478 to
349
416 to
411
469 to
358
359 to
468
472 to
355
491 to
336
495 to
332
444 to
383
489 to
338
Andrew Yang14/0/0557 to
270
593 to
234
420 to
407
559 to
268
427 to
400
529 to
298
452 to
375
584 to
243
468 to
359
567 to
260
615 to
212
605 to
222
494 to
333
559 to
268
Elizabeth Warren9/5/0489 to
338
473 to
354
372 to
455
418 to
409
348 to
479
439 to
388
394 to
433
421 to
406
355 to
472
260 to
567
470 to
357
486 to
341
429 to
398
479 to
348
John Kasich3/11/0527 to
300
390 to
437
261 to
566
403 to
424
240 to
587
397 to
430
279 to
548
323 to
504
336 to
491
212 to
615
357 to
470
518 to
309
408 to
419
523 to
304
Jeb Bush2/12/0527 to
300
379 to
448
229 to
598
376 to
451
229 to
598
364 to
463
240 to
587
320 to
507
332 to
495
222 to
605
341 to
486
309 to
518
357 to
470
498 to
329
Rand Paul7/7/0634 to
193
420 to
407
259 to
568
423 to
404
347 to
480
471 to
356
287 to
540
399 to
428
383 to
444
333 to
494
398 to
429
419 to
408
470 to
357
634 to
193
Ted Cruz1/13/0560 to
267
379 to
448
213 to
614
353 to
474
258 to
569
331 to
496
217 to
610
327 to
500
338 to
489
268 to
559
348 to
479
304 to
523
329 to
498
193 to
634

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 Trump2292 2.8
Joe Biden2875 3.5
Jo Jorgensen3645 4.4
Howie Hawkins2082 2.5
Tulsi Gabbard3028 3.7
Dan Crenshaw1956 2.4
Justin Amash3129 3.8
Amy Klobuchar2167 2.6
Bernie Sanders3738 4.5
Andrew Yang3963 4.8
Elizabeth Warren3135 3.8
John Kasich1814 2.2
Jeb Bush1646 2.0
Rand Paul3027 3.7
Ted Cruz2127 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 Trump2292
Joe Biden2875
Jo Jorgensen3645
Howie Hawkins2082
Tulsi Gabbard3028
Dan Crenshaw1956
Justin Amash3129
Amy Klobuchar2167
Bernie Sanders3738
Andrew Yang3963
Elizabeth Warren3135
John Kasich1814
Jeb Bush1646
Rand Paul3027
Ted Cruz2127

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 Yang552
Bernie Sanders503

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 Trump0/14/0 290 to
421
175 to
517
292 to
346
225 to
441
228 to
255
194 to
445
293 to
372
296 to
452
239 to
514
305 to
413
287 to
317
284 to
303
166 to
391
210 to
229
Joe Biden9/5/0421 to
290
339 to
379
372 to
246
310 to
398
424 to
259
362 to
325
341 to
165
189 to
358
168 to
460
213 to
298
393 to
190
416 to
197
385 to
371
417 to
286
Jo Jorgensen12/2/0517 to
175
379 to
339
419 to
169
363 to
281
469 to
132
309 to
212
399 to
250
345 to
382
294 to
407
366 to
346
440 to
181
463 to
160
405 to
199
497 to
150
Howie Hawkins4/9/1346 to
292
246 to
372
169 to
419
163 to
416
275 to
256
196 to
357
230 to
278
157 to
393
127 to
483
207 to
326
258 to
258
282 to
264
242 to
373
305 to
294
Tulsi Gabbard11/3/0441 to
225
398 to
310
281 to
363
416 to
163
411 to
169
306 to
292
395 to
204
328 to
368
260 to
392
349 to
319
422 to
158
438 to
161
321 to
287
423 to
209
Dan Crenshaw2/12/0255 to
228
259 to
424
132 to
469
256 to
275
169 to
411
137 to
369
228 to
319
250 to
437
193 to
485
256 to
389
236 to
255
248 to
250
145 to
352
223 to
213
Justin Amash8/6/0445 to
194
325 to
362
212 to
309
357 to
196
292 to
306
369 to
137
317 to
268
309 to
392
256 to
415
315 to
363
348 to
181
385 to
166
327 to
212
413 to
164
Amy Klobuchar6/8/0372 to
293
165 to
341
250 to
399
278 to
230
204 to
395
319 to
228
268 to
317
163 to
403
109 to
495
158 to
344
288 to
182
321 to
200
296 to
373
344 to
282
Bernie Sanders13/1/0452 to
296
358 to
189
382 to
345
393 to
157
368 to
328
437 to
250
392 to
309
403 to
163
275 to
324
317 to
149
421 to
191
441 to
205
397 to
350
447 to
280
Andrew Yang14/0/0514 to
239
460 to
168
407 to
294
483 to
127
392 to
260
485 to
193
415 to
256
495 to
109
324 to
275
395 to
187
508 to
124
522 to
138
419 to
295
489 to
231
Elizabeth Warren10/4/0413 to
305
298 to
213
346 to
366
326 to
207
319 to
349
389 to
256
363 to
315
344 to
158
149 to
317
187 to
395
366 to
179
388 to
207
371 to
361
399 to
292
John Kasich4/9/1317 to
287
190 to
393
181 to
440
258 to
258
158 to
422
255 to
236
181 to
348
182 to
288
191 to
421
124 to
508
179 to
366
230 to
153
223 to
354
277 to
258
Jeb Bush2/12/0303 to
284
197 to
416
160 to
463
264 to
282
161 to
438
250 to
248
166 to
385
200 to
321
205 to
441
138 to
522
207 to
388
153 to
230
170 to
363
244 to
254
Rand Paul7/7/0391 to
166
371 to
385
199 to
405
373 to
242
287 to
321
352 to
145
212 to
327
373 to
296
350 to
397
295 to
419
361 to
371
354 to
223
363 to
170
360 to
102
Ted Cruz2/12/0229 to
210
286 to
417
150 to
497
294 to
305
209 to
423
213 to
223
164 to
413
282 to
344
280 to
447
231 to
489
292 to
399
258 to
277
254 to
244
102 to
360

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
0469037.81%
19487.64%
27996.44%
38406.77%
47546.08%
59017.26%
66845.51%
77035.67%
86585.30%
95324.29%
108967.22%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump455352537293831322618101
Joe Biden27862475462695778522048
Jo Jorgensen210635963476437514258133
Howie Hawkins36578626052613628281938
Tulsi Gabbard21551618279947471452827
Dan Crenshaw38378615743573741321721
Justin Amash278675258455336374752102
Amy Klobuchar33660597963735544351310
Bernie Sanders280394432303431475776157
Andrew Yang17349415452767078806490
Elizabeth Warren30956472943364547667178
John Kasich3726866716582462616510
Jeb Bush357997891636331181359
Rand Paul28069534439476163695052
Ted Cruz39974442942543742503620

Number of bullet votes: 18 (2.18%).
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.