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 Trump211
Joe Biden227
Jo Jorgensen183
Howie Hawkins26
Tulsi Gabbard27
Dan Crenshaw12
Justin Amash49
Amy Klobuchar11
Bernie Sanders161
Andrew Yang45
Elizabeth Warren31
John Kasich13
Jeb Bush6
Rand Paul30
Ted Cruz16
TOTAL:1048

The winner is Joe Biden with 21.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump305
Joe Biden409
Jo Jorgensen393
Howie Hawkins176
Tulsi Gabbard314
Dan Crenshaw136
Justin Amash298
Amy Klobuchar183
Bernie Sanders452
Andrew Yang440
Elizabeth Warren344
John Kasich135
Jeb Bush101
Rand Paul337
Ted Cruz208
Ballots Cast:1048

The winner is Bernie Sanders with 43.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump186
Joe Biden85
Jo Jorgensen158
Howie Hawkins39
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash79
Amy Klobuchar14
Bernie Sanders206
Andrew Yang81
Elizabeth Warren65
John Kasich18
Jeb Bush6
Rand Paul42
Ted Cruz27

Jeb Bush eliminated in this round.

Round 2:

Donald Trump186
Joe Biden85
Jo Jorgensen158
Howie Hawkins39
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Amy Klobuchar14
Bernie Sanders207
Andrew Yang81
Elizabeth Warren65
John Kasich19
Rand Paul42
Ted Cruz30

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump186
Joe Biden92
Jo Jorgensen159
Howie Hawkins41
Tulsi Gabbard26
Dan Crenshaw16
Justin Amash80
Bernie Sanders208
Andrew Yang82
Elizabeth Warren66
John Kasich20
Rand Paul42
Ted Cruz30

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump187
Joe Biden93
Jo Jorgensen163
Howie Hawkins41
Tulsi Gabbard29
Justin Amash80
Bernie Sanders208
Andrew Yang83
Elizabeth Warren66
John Kasich20
Rand Paul44
Ted Cruz34

John Kasich eliminated in this round.

Round 5:

Donald Trump188
Joe Biden97
Jo Jorgensen163
Howie Hawkins41
Tulsi Gabbard33
Justin Amash81
Bernie Sanders210
Andrew Yang85
Elizabeth Warren68
Rand Paul47
Ted Cruz35

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump190
Joe Biden101
Jo Jorgensen171
Howie Hawkins42
Justin Amash88
Bernie Sanders213
Andrew Yang89
Elizabeth Warren69
Rand Paul50
Ted Cruz35

Ted Cruz eliminated in this round.

Round 7:

Donald Trump204
Joe Biden103
Jo Jorgensen174
Howie Hawkins43
Justin Amash88
Bernie Sanders214
Andrew Yang89
Elizabeth Warren69
Rand Paul64

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump204
Joe Biden109
Jo Jorgensen176
Justin Amash88
Bernie Sanders244
Andrew Yang92
Elizabeth Warren71
Rand Paul64

Rand Paul eliminated in this round.

Round 9:

Donald Trump225
Joe Biden109
Jo Jorgensen191
Justin Amash110
Bernie Sanders245
Andrew Yang96
Elizabeth Warren72

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump225
Joe Biden126
Jo Jorgensen195
Justin Amash111
Bernie Sanders282
Andrew Yang109

Andrew Yang eliminated in this round.

Round 11:

Donald Trump229
Joe Biden147
Jo Jorgensen211
Justin Amash125
Bernie Sanders336

Justin Amash eliminated in this round.

Round 12:

Donald Trump238
Joe Biden155
Jo Jorgensen312
Bernie Sanders343

Joe Biden eliminated in this round.

Round 13:

Donald Trump245
Jo Jorgensen350
Bernie Sanders453

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen543
Bernie Sanders505

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 Trump0/14/0 452 to
596		276 to
772		420 to
628		332 to
716		376 to
672		299 to
749		418 to
630		432 to
616		360 to
688		447 to
601		406 to
642		403 to
645		282 to
766		373 to
675
Joe Biden6/8/0596 to
452		 457 to
591		518 to
530		447 to
601		558 to
490		504 to
544		545 to
503		423 to
625		321 to
727		458 to
590		550 to
498		563 to
485		522 to
526		573 to
475
Jo Jorgensen13/1/0772 to
276		591 to
457		 679 to
369		592 to
456		736 to
312		638 to
410		625 to
423		543 to
505		520 to
528		583 to
465		715 to
333		751 to
297		712 to
336		760 to
288
Howie Hawkins9/5/0628 to
420		530 to
518		369 to
679		 418 to
630		585 to
463		504 to
544		541 to
507		448 to
600		375 to
673		538 to
510		561 to
487		589 to
459		535 to
513		607 to
441
Tulsi Gabbard12/1/1716 to
332		601 to
447		456 to
592		630 to
418		 728 to
320		620 to
428		705 to
343		541 to
507		524 to
524		618 to
430		752 to
296		762 to
286		626 to
422		715 to
333
Dan Crenshaw4/10/0672 to
376		490 to
558		312 to
736		463 to
585		320 to
728		 425 to
623		515 to
533		443 to
605		393 to
655		506 to
542		556 to
492		587 to
461		475 to
573		629 to
419
Justin Amash10/4/0749 to
299		544 to
504		410 to
638		544 to
504		428 to
620		623 to
425		 576 to
472		506 to
542		478 to
570		546 to
502		693 to
355		735 to
313		680 to
368		754 to
294
Amy Klobuchar6/7/1630 to
418		503 to
545		423 to
625		507 to
541		343 to
705		533 to
515		472 to
576		 460 to
588		339 to
709		524 to
524		641 to
407		646 to
402		559 to
489		633 to
415
Bernie Sanders11/3/0616 to
432		625 to
423		505 to
543		600 to
448		507 to
541		605 to
443		542 to
506		588 to
460		 477 to
571		622 to
426		637 to
411		638 to
410		582 to
466		627 to
421
Andrew Yang13/0/1688 to
360		727 to
321		528 to
520		673 to
375		524 to
524		655 to
393		570 to
478		709 to
339		571 to
477		 704 to
344		766 to
282		760 to
288		643 to
405		709 to
339
Elizabeth Warren7/6/1601 to
447		590 to
458		465 to
583		510 to
538		430 to
618		542 to
506		502 to
546		524 to
524		426 to
622		344 to
704		 599 to
449		620 to
428		553 to
495		609 to
439
John Kasich4/10/0642 to
406		498 to
550		333 to
715		487 to
561		296 to
752		492 to
556		355 to
693		407 to
641		411 to
637		282 to
766		449 to
599		 666 to
382		529 to
519		659 to
389
Jeb Bush2/12/0645 to
403		485 to
563		297 to
751		459 to
589		286 to
762		461 to
587		313 to
735		402 to
646		410 to
638		288 to
760		428 to
620		382 to
666		 467 to
581		631 to
417
Rand Paul5/9/0766 to
282		526 to
522		336 to
712		513 to
535		422 to
626		573 to
475		368 to
680		489 to
559		466 to
582		405 to
643		495 to
553		519 to
529		581 to
467		 784 to
264
Ted Cruz1/13/0675 to
373		475 to
573		288 to
760		441 to
607		333 to
715		419 to
629		294 to
754		415 to
633		421 to
627		339 to
709		439 to
609		389 to
659		417 to
631		264 to
784

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 Trump3074 2.9
Joe Biden3626 3.5
Jo Jorgensen4441 4.2
Howie Hawkins2725 2.6
Tulsi Gabbard3840 3.7
Dan Crenshaw2513 2.4
Justin Amash3804 3.6
Amy Klobuchar2809 2.7
Bernie Sanders4719 4.5
Andrew Yang4800 4.6
Elizabeth Warren3810 3.6
John Kasich2379 2.3
Jeb Bush2188 2.1
Rand Paul3758 3.6
Ted Cruz2724 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 Trump3074
Joe Biden3626
Jo Jorgensen4441
Howie Hawkins2725
Tulsi Gabbard3840
Dan Crenshaw2513
Justin Amash3804
Amy Klobuchar2809
Bernie Sanders4719
Andrew Yang4800
Elizabeth Warren3810
John Kasich2379
Jeb Bush2188
Rand Paul3758
Ted Cruz2724

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 Yang683
Bernie Sanders657

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 Trump1/13/0 386 to
531		255 to
624		395 to
433		301 to
547		319 to
327		279 to
543		390 to
466		389 to
560		324 to
628		406 to
504		381 to
392		375 to
384		237 to
482		295 to
281
Joe Biden9/5/0531 to
386		 443 to
468		463 to
320		392 to
499		531 to
329		465 to
397		428 to
227		244 to
461		237 to
560		293 to
364		495 to
261		519 to
261		492 to
457		534 to
364
Jo Jorgensen12/2/0624 to
255		468 to
443		 506 to
223		434 to
359		564 to
182		383 to
275		484 to
328		422 to
495		364 to
498		461 to
427		537 to
236		568 to
217		489 to
263		609 to
203
Howie Hawkins5/9/0433 to
395		320 to
463		223 to
506		 215 to
509		351 to
316		262 to
425		303 to
352		199 to
513		179 to
580		273 to
395		333 to
324		365 to
331		320 to
457		396 to
370
Tulsi Gabbard11/3/0547 to
301		499 to
392		359 to
434		509 to
215		 510 to
204		386 to
350		490 to
260		404 to
476		338 to
472		445 to
384		523 to
198		550 to
203		412 to
349		535 to
266
Dan Crenshaw2/12/0327 to
319		329 to
531		182 to
564		316 to
351		204 to
510		 184 to
442		295 to
401		313 to
561		247 to
595		330 to
478		296 to
317		310 to
323		193 to
428		295 to
268
Justin Amash8/6/0543 to
279		397 to
465		275 to
383		425 to
262		350 to
386		442 to
184		 379 to
349		372 to
510		316 to
511		384 to
446		422 to
230		469 to
225		399 to
275		507 to
222
Amy Klobuchar6/8/0466 to
390		227 to
428		328 to
484		352 to
303		260 to
490		401 to
295		349 to
379		 214 to
516		160 to
595		224 to
407		367 to
236		415 to
262		375 to
454		441 to
357
Bernie Sanders13/1/0560 to
389		461 to
244		495 to
422		513 to
199		476 to
404		561 to
313		510 to
372		516 to
214		 365 to
391		431 to
182		543 to
251		564 to
263		516 to
430		567 to
355
Andrew Yang14/0/0628 to
324		560 to
237		498 to
364		580 to
179		472 to
338		595 to
247		511 to
316		595 to
160		391 to
365		 485 to
244		620 to
175		637 to
190		518 to
366		604 to
294
Elizabeth Warren10/4/0504 to
406		364 to
293		427 to
461		395 to
273		384 to
445		478 to
330		446 to
384		407 to
224		182 to
431		244 to
485		 449 to
240		477 to
277		456 to
450		494 to
379
John Kasich4/10/0392 to
381		261 to
495		236 to
537		324 to
333		198 to
523		317 to
296		230 to
422		236 to
367		251 to
543		175 to
620		240 to
449		 297 to
206		279 to
431		358 to
324
Jeb Bush3/11/0384 to
375		261 to
519		217 to
568		331 to
365		203 to
550		323 to
310		225 to
469		262 to
415		263 to
564		190 to
637		277 to
477		206 to
297		 227 to
437		325 to
319
Rand Paul7/7/0482 to
237		457 to
492		263 to
489		457 to
320		349 to
412		428 to
193		275 to
399		454 to
375		430 to
516		366 to
518		450 to
456		431 to
279		437 to
227		 451 to
143
Ted Cruz0/14/0281 to
295		364 to
534		203 to
609		370 to
396		266 to
535		268 to
295		222 to
507		357 to
441		355 to
567		294 to
604		379 to
494		324 to
358		319 to
325		143 to
451

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
0579936.89%
112207.76%
210326.56%
311517.32%
410366.59%
512357.86%
68615.48%
78725.55%
88105.15%
96364.05%
1010686.79%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump542464355374839413630131
Joe Biden35178597085847893643155
Jo Jorgensen262857693709142595565150
Howie Hawkins44999737871834738392348
Tulsi Gabbard271667510310012110091523336
Dan Crenshaw47097817959844349392225
Justin Amash358836878598943415359117
Amy Klobuchar4107772105841027159381614
Bernie Sanders335555949484541607986191
Andrew Yang2296262707510187939574100
Elizabeth Warren39573604360506359827984
John Kasich45681829992109553221813
Jeb Bush433124971189284382715911
Rand Paul35094646651717278796162
Ted Cruz488100614553734252634031

Number of bullet votes: 25 (2.39%).
Number of "approval" votes: 14 (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.

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