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 Trump137
Joe Biden174
Jo Jorgensen153
Howie Hawkins15
Tulsi Gabbard18
Dan Crenshaw8
Justin Amash37
Amy Klobuchar5
Bernie Sanders96
Andrew Yang33
Elizabeth Warren21
John Kasich8
Jeb Bush4
Rand Paul22
Ted Cruz8
TOTAL:739

The winner is Joe Biden with 23.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump200
Joe Biden283
Jo Jorgensen317
Howie Hawkins118
Tulsi Gabbard229
Dan Crenshaw102
Justin Amash241
Amy Klobuchar128
Bernie Sanders307
Andrew Yang333
Elizabeth Warren254
John Kasich90
Jeb Bush58
Rand Paul260
Ted Cruz146
Ballots Cast:739

The winner is Andrew Yang with 45.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump116
Joe Biden51
Jo Jorgensen130
Howie Hawkins24
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash64
Amy Klobuchar8
Bernie Sanders139
Andrew Yang62
Elizabeth Warren50
John Kasich12
Jeb Bush4
Rand Paul34
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump116
Joe Biden51
Jo Jorgensen130
Howie Hawkins24
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Amy Klobuchar8
Bernie Sanders140
Andrew Yang62
Elizabeth Warren50
John Kasich12
Rand Paul34
Ted Cruz20

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump116
Joe Biden54
Jo Jorgensen131
Howie Hawkins25
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Bernie Sanders141
Andrew Yang63
Elizabeth Warren51
John Kasich12
Rand Paul34
Ted Cruz20

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump116
Joe Biden54
Jo Jorgensen135
Howie Hawkins25
Tulsi Gabbard18
Justin Amash65
Bernie Sanders141
Andrew Yang64
Elizabeth Warren51
John Kasich12
Rand Paul35
Ted Cruz23

John Kasich eliminated in this round.

Round 5:

Donald Trump116
Joe Biden55
Jo Jorgensen135
Howie Hawkins25
Tulsi Gabbard20
Justin Amash66
Bernie Sanders142
Andrew Yang66
Elizabeth Warren52
Rand Paul38
Ted Cruz24

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump116
Joe Biden55
Jo Jorgensen143
Howie Hawkins25
Justin Amash70
Bernie Sanders143
Andrew Yang70
Elizabeth Warren53
Rand Paul40
Ted Cruz24

Ted Cruz eliminated in this round.

Round 7:

Donald Trump124
Joe Biden57
Jo Jorgensen146
Howie Hawkins26
Justin Amash70
Bernie Sanders144
Andrew Yang70
Elizabeth Warren53
Rand Paul49

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump124
Joe Biden59
Jo Jorgensen146
Justin Amash70
Bernie Sanders165
Andrew Yang72
Elizabeth Warren54
Rand Paul49

Rand Paul eliminated in this round.

Round 9:

Donald Trump143
Joe Biden59
Jo Jorgensen158
Justin Amash85
Bernie Sanders166
Andrew Yang74
Elizabeth Warren54

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump143
Joe Biden72
Jo Jorgensen159
Justin Amash86
Bernie Sanders196
Andrew Yang83

Joe Biden eliminated in this round.

Round 11:

Donald Trump145
Jo Jorgensen169
Justin Amash89
Bernie Sanders228
Andrew Yang108

Justin Amash eliminated in this round.

Round 12:

Donald Trump148
Jo Jorgensen243
Bernie Sanders231
Andrew Yang117

Andrew Yang eliminated in this round.

Round 13:

Donald Trump152
Jo Jorgensen272
Bernie Sanders315

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen395
Bernie Sanders344

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 Trump0/14/0 319 to
420
167 to
572
290 to
449
223 to
516
246 to
493
183 to
556
284 to
455
307 to
432
244 to
495
307 to
432
269 to
470
267 to
472
160 to
579
231 to
508
Joe Biden7/7/0420 to
319
309 to
430
376 to
363
306 to
433
381 to
358
335 to
404
381 to
358
304 to
435
196 to
543
308 to
431
381 to
358
386 to
353
350 to
389
383 to
356
Jo Jorgensen13/1/0572 to
167
430 to
309
502 to
237
430 to
309
531 to
208
444 to
295
444 to
295
395 to
344
363 to
376
409 to
330
510 to
229
535 to
204
506 to
233
549 to
190
Howie Hawkins4/10/0449 to
290
363 to
376
237 to
502
275 to
464
390 to
349
318 to
421
353 to
386
311 to
428
228 to
511
355 to
384
369 to
370
387 to
352
350 to
389
412 to
327
Tulsi Gabbard12/2/0516 to
223
433 to
306
309 to
430
464 to
275
508 to
231
403 to
336
491 to
248
389 to
350
353 to
386
426 to
313
520 to
219
528 to
211
416 to
323
500 to
239
Dan Crenshaw4/10/0493 to
246
358 to
381
208 to
531
349 to
390
231 to
508
281 to
458
361 to
378
324 to
415
267 to
472
355 to
384
390 to
349
419 to
320
309 to
430
436 to
303
Justin Amash11/3/0556 to
183
404 to
335
295 to
444
421 to
318
336 to
403
458 to
281
416 to
323
376 to
363
333 to
406
391 to
348
491 to
248
524 to
215
479 to
260
545 to
194
Amy Klobuchar7/7/0455 to
284
358 to
381
295 to
444
386 to
353
248 to
491
378 to
361
323 to
416
328 to
411
206 to
533
364 to
375
445 to
294
446 to
293
372 to
367
435 to
304
Bernie Sanders10/4/0432 to
307
435 to
304
344 to
395
428 to
311
350 to
389
415 to
324
363 to
376
411 to
328
306 to
433
408 to
331
431 to
308
431 to
308
384 to
355
427 to
312
Andrew Yang14/0/0495 to
244
543 to
196
376 to
363
511 to
228
386 to
353
472 to
267
406 to
333
533 to
206
433 to
306
512 to
227
554 to
185
537 to
202
433 to
306
492 to
247
Elizabeth Warren9/5/0432 to
307
431 to
308
330 to
409
384 to
355
313 to
426
384 to
355
348 to
391
375 to
364
331 to
408
227 to
512
415 to
324
425 to
314
372 to
367
419 to
320
John Kasich4/10/0470 to
269
358 to
381
229 to
510
370 to
369
219 to
520
349 to
390
248 to
491
294 to
445
308 to
431
185 to
554
324 to
415
457 to
282
352 to
387
458 to
281
Jeb Bush2/12/0472 to
267
353 to
386
204 to
535
352 to
387
211 to
528
320 to
419
215 to
524
293 to
446
308 to
431
202 to
537
314 to
425
282 to
457
309 to
430
430 to
309
Rand Paul7/7/0579 to
160
389 to
350
233 to
506
389 to
350
323 to
416
430 to
309
260 to
479
367 to
372
355 to
384
306 to
433
367 to
372
387 to
352
430 to
309
571 to
168
Ted Cruz1/13/0508 to
231
356 to
383
190 to
549
327 to
412
239 to
500
303 to
436
194 to
545
304 to
435
312 to
427
247 to
492
320 to
419
281 to
458
309 to
430
168 to
571

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 Trump2026 2.7
Joe Biden2505 3.4
Jo Jorgensen3330 4.5
Howie Hawkins1768 2.4
Tulsi Gabbard2646 3.6
Dan Crenshaw1730 2.3
Justin Amash2846 3.9
Amy Klobuchar1849 2.5
Bernie Sanders3232 4.4
Andrew Yang3538 4.8
Elizabeth Warren2780 3.8
John Kasich1565 2.1
Jeb Bush1423 1.9
Rand Paul2750 3.7
Ted Cruz1934 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 Trump2026
Joe Biden2505
Jo Jorgensen3330
Howie Hawkins1768
Tulsi Gabbard2646
Dan Crenshaw1730
Justin Amash2846
Amy Klobuchar1849
Bernie Sanders3232
Andrew Yang3538
Elizabeth Warren2780
John Kasich1565
Jeb Bush1423
Rand Paul2750
Ted Cruz1934

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 Yang466
Jo Jorgensen378

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 Trump0/14/0 266 to
368
150 to
465
265 to
296
202 to
385
200 to
227
167 to
399
266 to
320
271 to
391
216 to
456
277 to
361
256 to
279
255 to
263
138 to
360
179 to
211
Joe Biden8/6/0368 to
266
296 to
356
335 to
218
277 to
361
370 to
239
315 to
303
306 to
142
164 to
310
142 to
417
182 to
266
346 to
170
362 to
179
337 to
342
358 to
268
Jo Jorgensen12/2/0465 to
150
356 to
296
388 to
139
342 to
238
425 to
113
282 to
187
373 to
218
323 to
328
273 to
361
337 to
305
407 to
156
427 to
136
366 to
173
447 to
131
Howie Hawkins3/11/0296 to
265
218 to
335
139 to
388
143 to
373
234 to
232
166 to
329
206 to
245
145 to
341
105 to
441
179 to
293
223 to
231
243 to
238
204 to
343
257 to
273
Tulsi Gabbard9/4/1385 to
202
361 to
277
238 to
342
373 to
143
361 to
153
264 to
276
357 to
178
298 to
320
231 to
355
314 to
288
372 to
143
384 to
145
269 to
269
366 to
193
Dan Crenshaw2/12/0227 to
200
239 to
370
113 to
425
232 to
234
153 to
361
117 to
333
208 to
274
231 to
378
173 to
435
232 to
343
212 to
224
226 to
215
121 to
323
193 to
196
Justin Amash9/5/0399 to
167
303 to
315
187 to
282
329 to
166
276 to
264
333 to
117
295 to
231
286 to
341
237 to
367
289 to
321
318 to
152
353 to
137
294 to
188
369 to
143
Amy Klobuchar6/8/0320 to
266
142 to
306
218 to
373
245 to
206
178 to
357
274 to
208
231 to
295
144 to
349
89 to
450
136 to
313
252 to
162
279 to
181
253 to
348
291 to
261
Bernie Sanders13/1/0391 to
271
310 to
164
328 to
323
341 to
145
320 to
298
378 to
231
341 to
286
349 to
144
230 to
299
266 to
138
364 to
169
384 to
184
347 to
323
385 to
262
Andrew Yang14/0/0456 to
216
417 to
142
361 to
273
441 to
105
355 to
231
435 to
173
367 to
237
450 to
89
299 to
230
356 to
161
457 to
105
465 to
118
370 to
271
430 to
212
Elizabeth Warren9/5/0361 to
277
266 to
182
305 to
337
293 to
179
288 to
314
343 to
232
321 to
289
313 to
136
138 to
266
161 to
356
324 to
155
343 to
182
325 to
334
349 to
268
John Kasich5/9/0279 to
256
170 to
346
156 to
407
231 to
223
143 to
372
224 to
212
152 to
318
162 to
252
169 to
364
105 to
457
155 to
324
203 to
134
192 to
326
240 to
235
Jeb Bush1/13/0263 to
255
179 to
362
136 to
427
238 to
243
145 to
384
215 to
226
137 to
353
181 to
279
184 to
384
118 to
465
182 to
343
134 to
203
143 to
337
206 to
233
Rand Paul9/4/1360 to
138
342 to
337
173 to
366
343 to
204
269 to
269
323 to
121
188 to
294
348 to
253
323 to
347
271 to
370
334 to
325
326 to
192
337 to
143
328 to
89
Ted Cruz4/10/0211 to
179
268 to
358
131 to
447
273 to
257
193 to
366
196 to
193
143 to
369
261 to
291
262 to
385
212 to
430
268 to
349
235 to
240
233 to
206
89 to
328

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
0430338.82%
18187.38%
27136.43%
37246.53%
46515.87%
58037.24%
65855.28%
76265.65%
85775.21%
94714.25%
108147.34%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump41127203427363031221487
Joe Biden25556444954614971411643
Jo Jorgensen188544955405335483656125
Howie Hawkins34269575043552825191734
Tulsi Gabbard20047547167886563402123
Dan Crenshaw34668545039523336281617
Justin Amash25454454936483034435195
Amy Klobuchar3145555655566433630119
Bernie Sanders268354024263024365065141
Andrew Yang16141374947615773715884
Elizabeth Warren29141422537323736596475
John Kasich342586260577341221347
Jeb Bush329847180555726161227
Rand Paul24862473732415360674448
Ted Cruz35467362636503439463219

Number of bullet votes: 17 (2.30%).
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.