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 Trump153
Joe Biden188
Jo Jorgensen163
Howie Hawkins20
Tulsi Gabbard20
Dan Crenshaw9
Justin Amash39
Amy Klobuchar6
Bernie Sanders113
Andrew Yang34
Elizabeth Warren23
John Kasich8
Jeb Bush5
Rand Paul24
Ted Cruz8
TOTAL:813

The winner is Joe Biden with 23.1% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump222
Joe Biden316
Jo Jorgensen336
Howie Hawkins135
Tulsi Gabbard247
Dan Crenshaw108
Justin Amash254
Amy Klobuchar144
Bernie Sanders345
Andrew Yang360
Elizabeth Warren276
John Kasich101
Jeb Bush67
Rand Paul274
Ted Cruz156
Ballots Cast:813

The winner is Andrew Yang with 44.3% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump130
Joe Biden61
Jo Jorgensen140
Howie Hawkins29
Tulsi Gabbard19
Dan Crenshaw11
Justin Amash66
Amy Klobuchar10
Bernie Sanders156
Andrew Yang66
Elizabeth Warren53
John Kasich13
Jeb Bush5
Rand Paul36
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump130
Joe Biden61
Jo Jorgensen140
Howie Hawkins29
Tulsi Gabbard19
Dan Crenshaw11
Justin Amash67
Amy Klobuchar10
Bernie Sanders157
Andrew Yang66
Elizabeth Warren53
John Kasich14
Rand Paul36
Ted Cruz20

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump130
Joe Biden65
Jo Jorgensen141
Howie Hawkins31
Tulsi Gabbard19
Dan Crenshaw11
Justin Amash67
Bernie Sanders158
Andrew Yang67
Elizabeth Warren54
John Kasich14
Rand Paul36
Ted Cruz20

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump131
Joe Biden65
Jo Jorgensen145
Howie Hawkins31
Tulsi Gabbard20
Justin Amash67
Bernie Sanders158
Andrew Yang68
Elizabeth Warren54
John Kasich14
Rand Paul37
Ted Cruz23

John Kasich eliminated in this round.

Round 5:

Donald Trump131
Joe Biden67
Jo Jorgensen145
Howie Hawkins31
Tulsi Gabbard22
Justin Amash68
Bernie Sanders159
Andrew Yang70
Elizabeth Warren56
Rand Paul40
Ted Cruz24

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump131
Joe Biden68
Jo Jorgensen153
Howie Hawkins31
Justin Amash72
Bernie Sanders161
Andrew Yang74
Elizabeth Warren57
Rand Paul42
Ted Cruz24

Ted Cruz eliminated in this round.

Round 7:

Donald Trump139
Joe Biden70
Jo Jorgensen156
Howie Hawkins32
Justin Amash72
Bernie Sanders162
Andrew Yang74
Elizabeth Warren57
Rand Paul51

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump139
Joe Biden74
Jo Jorgensen156
Justin Amash72
Bernie Sanders186
Andrew Yang77
Elizabeth Warren58
Rand Paul51

Rand Paul eliminated in this round.

Round 9:

Donald Trump158
Joe Biden74
Jo Jorgensen168
Justin Amash89
Bernie Sanders187
Andrew Yang79
Elizabeth Warren58

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump158
Joe Biden87
Jo Jorgensen170
Justin Amash90
Bernie Sanders219
Andrew Yang89

Joe Biden eliminated in this round.

Round 11:

Donald Trump160
Jo Jorgensen187
Justin Amash93
Bernie Sanders257
Andrew Yang116

Justin Amash eliminated in this round.

Round 12:

Donald Trump163
Jo Jorgensen265
Bernie Sanders260
Andrew Yang125

Andrew Yang eliminated in this round.

Round 13:

Donald Trump168
Jo Jorgensen295
Bernie Sanders350

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen426
Bernie Sanders387

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 Trump0/14/0 340 to
473
186 to
627
311 to
502
244 to
569
274 to
539
206 to
607
310 to
503
328 to
485
267 to
546
335 to
478
296 to
517
297 to
516
190 to
623
263 to
550
Joe Biden7/7/0473 to
340
349 to
464
413 to
400
343 to
470
434 to
379
382 to
431
423 to
390
333 to
480
230 to
583
349 to
464
429 to
384
439 to
374
399 to
414
438 to
375
Jo Jorgensen13/1/0627 to
186
464 to
349
536 to
277
463 to
350
584 to
229
490 to
323
484 to
329
426 to
387
400 to
413
449 to
364
558 to
255
590 to
223
560 to
253
606 to
207
Howie Hawkins5/9/0502 to
311
400 to
413
277 to
536
312 to
501
444 to
369
367 to
446
399 to
414
336 to
477
264 to
549
402 to
411
420 to
393
445 to
368
399 to
414
466 to
347
Tulsi Gabbard12/2/0569 to
244
470 to
343
350 to
463
501 to
312
565 to
248
459 to
354
542 to
271
421 to
392
394 to
419
471 to
342
578 to
235
588 to
225
470 to
343
559 to
254
Dan Crenshaw4/10/0539 to
274
379 to
434
229 to
584
369 to
444
248 to
565
311 to
502
391 to
422
344 to
469
294 to
519
383 to
430
426 to
387
458 to
355
351 to
462
488 to
325
Justin Amash10/4/0607 to
206
431 to
382
323 to
490
446 to
367
354 to
459
502 to
311
454 to
359
406 to
407
371 to
442
428 to
385
543 to
270
580 to
233
532 to
281
602 to
211
Amy Klobuchar7/7/0503 to
310
390 to
423
329 to
484
414 to
399
271 to
542
422 to
391
359 to
454
353 to
460
239 to
574
400 to
413
496 to
317
499 to
314
420 to
393
490 to
323
Bernie Sanders11/3/0485 to
328
480 to
333
387 to
426
477 to
336
392 to
421
469 to
344
407 to
406
460 to
353
351 to
462
463 to
350
483 to
330
487 to
326
436 to
377
479 to
334
Andrew Yang14/0/0546 to
267
583 to
230
413 to
400
549 to
264
419 to
394
519 to
294
442 to
371
574 to
239
462 to
351
560 to
253
607 to
206
596 to
217
486 to
327
550 to
263
Elizabeth Warren9/5/0478 to
335
464 to
349
364 to
449
411 to
402
342 to
471
430 to
383
385 to
428
413 to
400
350 to
463
253 to
560
462 to
351
478 to
335
421 to
392
470 to
343
John Kasich3/11/0517 to
296
384 to
429
255 to
558
393 to
420
235 to
578
387 to
426
270 to
543
317 to
496
330 to
483
206 to
607
351 to
462
508 to
305
401 to
412
513 to
300
Jeb Bush2/12/0516 to
297
374 to
439
223 to
590
368 to
445
225 to
588
355 to
458
233 to
580
314 to
499
326 to
487
217 to
596
335 to
478
305 to
508
350 to
463
486 to
327
Rand Paul7/7/0623 to
190
414 to
399
253 to
560
414 to
399
343 to
470
462 to
351
281 to
532
393 to
420
377 to
436
327 to
486
392 to
421
412 to
401
463 to
350
623 to
190
Ted Cruz1/13/0550 to
263
375 to
438
207 to
606
347 to
466
254 to
559
325 to
488
211 to
602
323 to
490
334 to
479
263 to
550
343 to
470
300 to
513
327 to
486
190 to
623

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 Trump2253 2.8
Joe Biden2822 3.5
Jo Jorgensen3604 4.4
Howie Hawkins2039 2.5
Tulsi Gabbard2960 3.6
Dan Crenshaw1914 2.4
Justin Amash3090 3.8
Amy Klobuchar2121 2.6
Bernie Sanders3656 4.5
Andrew Yang3899 4.8
Elizabeth Warren3070 3.8
John Kasich1771 2.2
Jeb Bush1600 2.0
Rand Paul2976 3.7
Ted Cruz2089 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 Trump2253
Joe Biden2822
Jo Jorgensen3604
Howie Hawkins2039
Tulsi Gabbard2960
Dan Crenshaw1914
Justin Amash3090
Amy Klobuchar2121
Bernie Sanders3656
Andrew Yang3899
Elizabeth Warren3070
John Kasich1771
Jeb Bush1600
Rand Paul2976
Ted Cruz2089

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 Yang546
Bernie Sanders491

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 Trump0/14/0 286 to
411
171 to
509
287 to
339
221 to
431
225 to
250
190 to
437
288 to
363
292 to
442
235 to
504
300 to
404
281 to
311
281 to
294
162 to
384
207 to
224
Joe Biden9/5/0411 to
286
332 to
376
365 to
243
306 to
389
416 to
255
355 to
321
334 to
163
185 to
351
164 to
453
209 to
292
385 to
186
409 to
193
379 to
365
407 to
282
Jo Jorgensen12/2/0509 to
171
376 to
332
415 to
165
361 to
272
463 to
128
305 to
208
397 to
244
342 to
374
292 to
399
363 to
338
435 to
175
458 to
155
400 to
194
490 to
146
Howie Hawkins5/9/0339 to
287
243 to
365
165 to
415
159 to
408
269 to
251
191 to
352
228 to
272
156 to
386
123 to
476
203 to
320
254 to
251
278 to
257
237 to
365
299 to
288
Tulsi Gabbard11/3/0431 to
221
389 to
306
272 to
361
408 to
159
401 to
167
296 to
291
387 to
199
322 to
361
253 to
386
342 to
313
413 to
155
427 to
158
310 to
285
412 to
207
Dan Crenshaw3/11/0250 to
225
255 to
416
128 to
463
251 to
269
167 to
401
134 to
364
224 to
311
246 to
429
189 to
478
252 to
381
232 to
248
244 to
243
141 to
346
218 to
210
Justin Amash8/6/0437 to
190
321 to
355
208 to
305
352 to
191
291 to
296
364 to
134
314 to
262
305 to
384
252 to
408
311 to
355
345 to
172
381 to
159
323 to
207
407 to
160
Amy Klobuchar6/8/0363 to
288
163 to
334
244 to
397
272 to
228
199 to
387
311 to
224
262 to
314
161 to
395
106 to
487
155 to
337
283 to
176
315 to
195
291 to
367
335 to
277
Bernie Sanders13/1/0442 to
292
351 to
185
374 to
342
386 to
156
361 to
322
429 to
246
384 to
305
395 to
161
267 to
322
310 to
149
413 to
187
434 to
199
390 to
345
437 to
276
Andrew Yang14/0/0504 to
235
453 to
164
399 to
292
476 to
123
386 to
253
478 to
189
408 to
252
487 to
106
322 to
267
390 to
181
500 to
119
513 to
133
412 to
290
480 to
226
Elizabeth Warren10/4/0404 to
300
292 to
209
338 to
363
320 to
203
313 to
342
381 to
252
355 to
311
337 to
155
149 to
310
181 to
390
358 to
175
381 to
201
364 to
356
390 to
287
John Kasich4/10/0311 to
281
186 to
385
175 to
435
251 to
254
155 to
413
248 to
232
172 to
345
176 to
283
187 to
413
119 to
500
175 to
358
226 to
150
218 to
349
271 to
253
Jeb Bush1/13/0294 to
281
193 to
409
155 to
458
257 to
278
158 to
427
243 to
244
159 to
381
195 to
315
199 to
434
133 to
513
201 to
381
150 to
226
165 to
357
237 to
250
Rand Paul7/7/0384 to
162
365 to
379
194 to
400
365 to
237
285 to
310
346 to
141
207 to
323
367 to
291
345 to
390
290 to
412
356 to
364
349 to
218
357 to
165
353 to
100
Ted Cruz2/12/0224 to
207
282 to
407
146 to
490
288 to
299
207 to
412
210 to
218
160 to
407
277 to
335
276 to
437
226 to
480
287 to
390
253 to
271
250 to
237
100 to
353

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
0464138.06%
19267.59%
27796.39%
38176.70%
47396.06%
58827.23%
66645.44%
76905.66%
86475.31%
95274.32%
108837.24%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump44833243729383032261799
Joe Biden27660475259685676512048
Jo Jorgensen206625860476037514257133
Howie Hawkins36077615850613528281936
Tulsi Gabbard21550578178937468442627
Dan Crenshaw37876595742573739311720
Justin Amash275654956445235374752101
Amy Klobuchar33359597662695344351310
Bernie Sanders278384331293430465775152
Andrew Yang17147405452746776796489
Elizabeth Warren30754462842364347627177
John Kasich3686666696481432615510
Jeb Bush355977788626129171359
Rand Paul27768524238465862685052
Ted Cruz39474412841523741493620

Number of bullet votes: 18 (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.