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 Trump238
Joe Biden234
Jo Jorgensen187
Howie Hawkins28
Tulsi Gabbard28
Dan Crenshaw13
Justin Amash51
Amy Klobuchar11
Bernie Sanders176
Andrew Yang48
Elizabeth Warren32
John Kasich14
Jeb Bush7
Rand Paul31
Ted Cruz18
TOTAL:1116

The winner is Donald Trump with 21.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump338
Joe Biden428
Jo Jorgensen404
Howie Hawkins190
Tulsi Gabbard327
Dan Crenshaw148
Justin Amash309
Amy Klobuchar190
Bernie Sanders479
Andrew Yang453
Elizabeth Warren355
John Kasich146
Jeb Bush111
Rand Paul350
Ted Cruz232
Ballots Cast:1116

The winner is Bernie Sanders with 42.9% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump212
Joe Biden90
Jo Jorgensen162
Howie Hawkins41
Tulsi Gabbard27
Dan Crenshaw18
Justin Amash81
Amy Klobuchar14
Bernie Sanders219
Andrew Yang86
Elizabeth Warren66
John Kasich18
Jeb Bush7
Rand Paul44
Ted Cruz31

Jeb Bush eliminated in this round.

Round 2:

Donald Trump212
Joe Biden90
Jo Jorgensen162
Howie Hawkins41
Tulsi Gabbard27
Dan Crenshaw18
Justin Amash82
Amy Klobuchar14
Bernie Sanders220
Andrew Yang86
Elizabeth Warren66
John Kasich20
Rand Paul44
Ted Cruz34

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump212
Joe Biden97
Jo Jorgensen163
Howie Hawkins43
Tulsi Gabbard27
Dan Crenshaw18
Justin Amash82
Bernie Sanders221
Andrew Yang87
Elizabeth Warren67
John Kasich21
Rand Paul44
Ted Cruz34

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump213
Joe Biden98
Jo Jorgensen167
Howie Hawkins43
Tulsi Gabbard30
Justin Amash83
Bernie Sanders221
Andrew Yang88
Elizabeth Warren67
John Kasich21
Rand Paul46
Ted Cruz39

John Kasich eliminated in this round.

Round 5:

Donald Trump214
Joe Biden102
Jo Jorgensen167
Howie Hawkins43
Tulsi Gabbard34
Justin Amash85
Bernie Sanders223
Andrew Yang90
Elizabeth Warren69
Rand Paul49
Ted Cruz40

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump216
Joe Biden106
Jo Jorgensen175
Howie Hawkins44
Justin Amash92
Bernie Sanders227
Andrew Yang94
Elizabeth Warren70
Rand Paul52
Ted Cruz40

Ted Cruz eliminated in this round.

Round 7:

Donald Trump234
Joe Biden108
Jo Jorgensen178
Howie Hawkins45
Justin Amash92
Bernie Sanders229
Andrew Yang94
Elizabeth Warren70
Rand Paul66

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump234
Joe Biden114
Jo Jorgensen180
Justin Amash92
Bernie Sanders261
Andrew Yang97
Elizabeth Warren72
Rand Paul66

Rand Paul eliminated in this round.

Round 9:

Donald Trump255
Joe Biden114
Jo Jorgensen195
Justin Amash115
Bernie Sanders262
Andrew Yang101
Elizabeth Warren74

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump255
Joe Biden131
Jo Jorgensen199
Justin Amash116
Bernie Sanders300
Andrew Yang115

Andrew Yang eliminated in this round.

Round 11:

Donald Trump259
Joe Biden153
Jo Jorgensen217
Justin Amash130
Bernie Sanders357

Justin Amash eliminated in this round.

Round 12:

Donald Trump269
Joe Biden161
Jo Jorgensen320
Bernie Sanders366

Joe Biden eliminated in this round.

Round 13:

Donald Trump277
Jo Jorgensen361
Bernie Sanders478

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen573
Bernie Sanders543

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 Trump0/14/0 494 to
622
314 to
802
464 to
652
372 to
744
416 to
700
338 to
778
459 to
657
470 to
646
398 to
718
491 to
625
446 to
670
443 to
673
322 to
794
410 to
706
Joe Biden6/8/0622 to
494
484 to
632
545 to
571
474 to
642
591 to
525
530 to
586
574 to
542
443 to
673
338 to
778
489 to
627
580 to
536
593 to
523
552 to
564
606 to
510
Jo Jorgensen13/1/0802 to
314
632 to
484
717 to
399
630 to
486
780 to
336
680 to
436
670 to
446
573 to
543
555 to
561
626 to
490
761 to
355
793 to
323
756 to
360
797 to
319
Howie Hawkins9/5/0652 to
464
571 to
545
399 to
717
460 to
656
624 to
492
543 to
573
589 to
527
476 to
640
407 to
709
583 to
533
604 to
512
629 to
487
571 to
545
635 to
481
Tulsi Gabbard13/1/0744 to
372
642 to
474
486 to
630
656 to
460
775 to
341
663 to
453
757 to
359
573 to
543
562 to
554
663 to
453
800 to
316
807 to
309
673 to
443
750 to
366
Dan Crenshaw5/9/0700 to
416
525 to
591
336 to
780
492 to
624
341 to
775
462 to
654
559 to
557
474 to
642
429 to
687
550 to
566
601 to
515
630 to
486
515 to
601
666 to
450
Justin Amash10/4/0778 to
338
586 to
530
436 to
680
573 to
543
453 to
663
654 to
462
620 to
496
538 to
578
514 to
602
593 to
523
740 to
376
779 to
337
727 to
389
790 to
326
Amy Klobuchar6/8/0657 to
459
542 to
574
446 to
670
527 to
589
359 to
757
557 to
559
496 to
620
487 to
629
369 to
747
570 to
546
681 to
435
689 to
427
598 to
518
666 to
450
Bernie Sanders11/3/0646 to
470
673 to
443
543 to
573
640 to
476
543 to
573
642 to
474
578 to
538
629 to
487
514 to
602
666 to
450
677 to
439
679 to
437
624 to
492
660 to
456
Andrew Yang13/1/0718 to
398
778 to
338
561 to
555
709 to
407
554 to
562
687 to
429
602 to
514
747 to
369
602 to
514
752 to
364
811 to
305
805 to
311
685 to
431
741 to
375
Elizabeth Warren7/7/0625 to
491
627 to
489
490 to
626
533 to
583
453 to
663
566 to
550
523 to
593
546 to
570
450 to
666
364 to
752
626 to
490
650 to
466
587 to
529
636 to
480
John Kasich4/10/0670 to
446
536 to
580
355 to
761
512 to
604
316 to
800
515 to
601
376 to
740
435 to
681
439 to
677
305 to
811
490 to
626
708 to
408
567 to
549
692 to
424
Jeb Bush2/12/0673 to
443
523 to
593
323 to
793
487 to
629
309 to
807
486 to
630
337 to
779
427 to
689
437 to
679
311 to
805
466 to
650
408 to
708
502 to
614
663 to
453
Rand Paul5/9/0794 to
322
564 to
552
360 to
756
545 to
571
443 to
673
601 to
515
389 to
727
518 to
598
492 to
624
431 to
685
529 to
587
549 to
567
614 to
502
817 to
299
Ted Cruz1/13/0706 to
410
510 to
606
319 to
797
481 to
635
366 to
750
450 to
666
326 to
790
450 to
666
456 to
660
375 to
741
480 to
636
424 to
692
453 to
663
299 to
817

We have a tie! No candidate won every head to head contest.

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 Trump3386 3.0
Joe Biden3789 3.4
Jo Jorgensen4632 4.2
Howie Hawkins2913 2.6
Tulsi Gabbard4033 3.6
Dan Crenshaw2694 2.4
Justin Amash4001 3.6
Amy Klobuchar2964 2.7
Bernie Sanders5007 4.5
Andrew Yang5008 4.5
Elizabeth Warren3960 3.5
John Kasich2546 2.3
Jeb Bush2385 2.1
Rand Paul3958 3.5
Ted Cruz2961 2.7

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 Trump3386
Joe Biden3789
Jo Jorgensen4632
Howie Hawkins2913
Tulsi Gabbard4033
Dan Crenshaw2694
Justin Amash4001
Amy Klobuchar2964
Bernie Sanders5007
Andrew Yang5008
Elizabeth Warren3960
John Kasich2546
Jeb Bush2385
Rand Paul3958
Ted Cruz2961

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 Yang722
Bernie Sanders708

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 Trump4/10/0 424 to
554
290 to
645
435 to
453
338 to
567
355 to
345
314 to
564
426 to
487
423 to
587
360 to
651
446 to
522
417 to
412
409 to
402
273 to
498
325 to
298
Joe Biden9/5/0554 to
424
467 to
494
483 to
346
413 to
525
555 to
350
485 to
421
444 to
247
256 to
496
251 to
590
317 to
384
518 to
283
540 to
289
516 to
485
559 to
394
Jo Jorgensen12/2/0645 to
290
494 to
467
525 to
238
449 to
376
583 to
201
397 to
291
506 to
342
441 to
526
382 to
519
484 to
444
563 to
252
588 to
239
507 to
281
632 to
231
Howie Hawkins5/9/0453 to
435
346 to
483
238 to
525
228 to
527
369 to
338
278 to
443
319 to
367
210 to
545
195 to
601
293 to
406
353 to
340
381 to
353
335 to
480
417 to
404
Tulsi Gabbard11/3/0567 to
338
525 to
413
376 to
449
527 to
228
530 to
218
402 to
363
510 to
271
422 to
506
353 to
491
467 to
397
546 to
211
569 to
223
431 to
364
555 to
294
Dan Crenshaw1/13/0345 to
355
350 to
555
201 to
583
338 to
369
218 to
530
200 to
460
315 to
414
333 to
593
264 to
618
353 to
489
316 to
330
330 to
339
212 to
445
312 to
293
Justin Amash8/6/0564 to
314
421 to
485
291 to
397
443 to
278
363 to
402
460 to
200
398 to
362
390 to
538
334 to
528
406 to
460
443 to
244
486 to
247
415 to
288
529 to
249
Amy Klobuchar6/8/0487 to
426
247 to
444
342 to
506
367 to
319
271 to
510
414 to
315
362 to
398
228 to
550
169 to
617
242 to
422
386 to
250
429 to
284
389 to
476
463 to
385
Bernie Sanders13/1/0587 to
423
496 to
256
526 to
441
545 to
210
506 to
422
593 to
333
538 to
390
550 to
228
394 to
408
468 to
190
576 to
269
595 to
283
546 to
450
598 to
382
Andrew Yang14/0/0651 to
360
590 to
251
519 to
382
601 to
195
491 to
353
618 to
264
528 to
334
617 to
169
408 to
394
508 to
257
643 to
188
656 to
210
540 to
386
628 to
325
Elizabeth Warren9/5/0522 to
446
384 to
317
444 to
484
406 to
293
397 to
467
489 to
353
460 to
406
422 to
242
190 to
468
257 to
508
464 to
261
491 to
304
470 to
475
511 to
413
John Kasich3/11/0412 to
417
283 to
518
252 to
563
340 to
353
211 to
546
330 to
316
244 to
443
250 to
386
269 to
576
188 to
643
261 to
464
307 to
225
292 to
451
377 to
353
Jeb Bush1/13/0402 to
409
289 to
540
239 to
588
353 to
381
223 to
569
339 to
330
247 to
486
284 to
429
283 to
595
210 to
656
304 to
491
225 to
307
243 to
451
341 to
344
Rand Paul8/6/0498 to
273
485 to
516
281 to
507
480 to
335
364 to
431
445 to
212
288 to
415
476 to
389
450 to
546
386 to
540
475 to
470
451 to
292
451 to
243
469 to
168
Ted Cruz1/13/0298 to
325
394 to
559
231 to
632
404 to
417
294 to
555
293 to
312
249 to
529
385 to
463
382 to
598
325 to
628
413 to
511
353 to
377
344 to
341
168 to
469

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
0617836.91%
113207.89%
210886.50%
312297.34%
411366.79%
513297.94%
69025.39%
79145.46%
88585.13%
96694.00%
1011176.67%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump563494757395441493837142
Joe Biden37688647991878195663257
Jo Jorgensen288908099789946605666154
Howie Hawkins476106788375904842432451
Tulsi Gabbard299727710610712810792553538
Dan Crenshaw497103838765904952402426
Justin Amash384877085699744435959119
Amy Klobuchar4378476116881117162401714
Bernie Sanders357616252494945678290202
Andrew Yang25366687587104899410177102
Elizabeth Warren42579674867556659848185
John Kasich482908610699114573524914
Jeb Bush45813299121104903930191014
Rand Paul375101676959817480836364
Ted Cruz508112644659804554684535

Number of bullet votes: 29 (2.60%).
Number of "approval" votes: 16 (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.