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%).

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