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 Trump196
Joe Biden211
Jo Jorgensen170
Howie Hawkins24
Tulsi Gabbard25
Dan Crenshaw10
Justin Amash48
Amy Klobuchar10
Bernie Sanders143
Andrew Yang39
Elizabeth Warren28
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz14
TOTAL:960

The winner is Joe Biden with 22.0% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump280
Joe Biden376
Jo Jorgensen370
Howie Hawkins157
Tulsi Gabbard293
Dan Crenshaw130
Justin Amash280
Amy Klobuchar166
Bernie Sanders411
Andrew Yang407
Elizabeth Warren314
John Kasich120
Jeb Bush89
Rand Paul317
Ted Cruz193
Ballots Cast:960

The winner is Bernie Sanders with 42.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 13 rounds:

Round 1:

Donald Trump171
Joe Biden75
Jo Jorgensen147
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash75
Amy Klobuchar14
Bernie Sanders188
Andrew Yang73
Elizabeth Warren60
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz25

Jeb Bush eliminated in this round.

Round 2:

Donald Trump171
Joe Biden75
Jo Jorgensen147
Howie Hawkins34
Tulsi Gabbard24
Dan Crenshaw14
Justin Amash76
Amy Klobuchar14
Bernie Sanders189
Andrew Yang73
Elizabeth Warren60
John Kasich16
Rand Paul39
Ted Cruz28

Eliminated in this round:

Round 3:

Donald Trump172
Joe Biden83
Jo Jorgensen152
Howie Hawkins36
Tulsi Gabbard27
Justin Amash76
Bernie Sanders190
Andrew Yang75
Elizabeth Warren61
John Kasich17
Rand Paul40
Ted Cruz31

John Kasich eliminated in this round.

Round 4:

Donald Trump172
Joe Biden86
Jo Jorgensen152
Howie Hawkins36
Tulsi Gabbard30
Justin Amash77
Bernie Sanders192
Andrew Yang77
Elizabeth Warren63
Rand Paul43
Ted Cruz32

Tulsi Gabbard eliminated in this round.

Round 5:

Donald Trump173
Joe Biden90
Jo Jorgensen160
Howie Hawkins37
Justin Amash82
Bernie Sanders195
Andrew Yang81
Elizabeth Warren64
Rand Paul46
Ted Cruz32

Ted Cruz eliminated in this round.

Round 6:

Donald Trump186
Joe Biden92
Jo Jorgensen163
Howie Hawkins38
Justin Amash82
Bernie Sanders196
Andrew Yang81
Elizabeth Warren64
Rand Paul58

Howie Hawkins eliminated in this round.

Round 7:

Donald Trump186
Joe Biden97
Jo Jorgensen164
Justin Amash82
Bernie Sanders223
Andrew Yang84
Elizabeth Warren66
Rand Paul58

Rand Paul eliminated in this round.

Round 8:

Donald Trump205
Joe Biden97
Jo Jorgensen178
Justin Amash102
Bernie Sanders224
Andrew Yang87
Elizabeth Warren67

Elizabeth Warren eliminated in this round.

Round 9:

Donald Trump205
Joe Biden112
Jo Jorgensen182
Justin Amash103
Bernie Sanders259
Andrew Yang99

Andrew Yang eliminated in this round.

Round 10:

Donald Trump208
Joe Biden130
Jo Jorgensen197
Justin Amash117
Bernie Sanders308

Justin Amash eliminated in this round.

Round 11:

Donald Trump215
Joe Biden138
Jo Jorgensen292
Bernie Sanders315

Joe Biden eliminated in this round.

Round 12:

Donald Trump221
Jo Jorgensen326
Bernie Sanders413

Donald Trump eliminated in this round.

Round 13:

Jo Jorgensen497
Bernie Sanders463

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 Trump0/14/0 412 to
548		250 to
710		384 to
576		304 to
656		343 to
617		271 to
689		381 to
579		396 to
564		331 to
629		406 to
554		373 to
587		369 to
591		255 to
705		335 to
625
Joe Biden7/7/0548 to
412		 416 to
544		483 to
477		403 to
557		509 to
451		457 to
503		501 to
459		388 to
572		287 to
673		416 to
544		505 to
455		514 to
446		474 to
486		521 to
439
Jo Jorgensen13/1/0710 to
250		544 to
416		 624 to
336		545 to
415		674 to
286		584 to
376		578 to
382		497 to
463		478 to
482		533 to
427		656 to
304		688 to
272		648 to
312		697 to
263
Howie Hawkins8/6/0576 to
384		477 to
483		336 to
624		 378 to
582		529 to
431		452 to
508		491 to
469		404 to
556		336 to
624		490 to
470		510 to
450		536 to
424		481 to
479		553 to
407
Tulsi Gabbard12/2/0656 to
304		557 to
403		415 to
545		582 to
378		 665 to
295		559 to
401		652 to
308		501 to
459		477 to
483		567 to
393		692 to
268		698 to
262		567 to
393		652 to
308
Dan Crenshaw4/10/0617 to
343		451 to
509		286 to
674		431 to
529		295 to
665		 395 to
565		476 to
484		409 to
551		366 to
594		463 to
497		518 to
442		545 to
415		428 to
532		571 to
389
Justin Amash10/4/0689 to
271		503 to
457		376 to
584		508 to
452		401 to
559		565 to
395		 536 to
424		472 to
488		440 to
520		503 to
457		641 to
319		676 to
284		621 to
339		691 to
269
Amy Klobuchar6/7/1579 to
381		459 to
501		382 to
578		469 to
491		308 to
652		484 to
476		424 to
536		 421 to
539		302 to
658		480 to
480		589 to
371		589 to
371		505 to
455		575 to
385
Bernie Sanders11/3/0564 to
396		572 to
388		463 to
497		556 to
404		459 to
501		551 to
409		488 to
472		539 to
421		 438 to
522		566 to
394		581 to
379		583 to
377		529 to
431		571 to
389
Andrew Yang14/0/0629 to
331		673 to
287		482 to
478		624 to
336		483 to
477		594 to
366		520 to
440		658 to
302		522 to
438		 655 to
305		710 to
250		699 to
261		583 to
377		646 to
314
Elizabeth Warren7/6/1554 to
406		544 to
416		427 to
533		470 to
490		393 to
567		497 to
463		457 to
503		480 to
480		394 to
566		305 to
655		 549 to
411		568 to
392		501 to
459		554 to
406
John Kasich3/11/0587 to
373		455 to
505		304 to
656		450 to
510		268 to
692		442 to
518		319 to
641		371 to
589		379 to
581		250 to
710		411 to
549		 607 to
353		475 to
485		597 to
363
Jeb Bush2/12/0591 to
369		446 to
514		272 to
688		424 to
536		262 to
698		415 to
545		284 to
676		371 to
589		377 to
583		261 to
699		392 to
568		353 to
607		 419 to
541		569 to
391
Rand Paul6/8/0705 to
255		486 to
474		312 to
648		479 to
481		393 to
567		532 to
428		339 to
621		455 to
505		431 to
529		377 to
583		459 to
501		485 to
475		541 to
419		 720 to
240
Ted Cruz1/13/0625 to
335		439 to
521		263 to
697		407 to
553		308 to
652		389 to
571		269 to
691		385 to
575		389 to
571		314 to
646		406 to
554		363 to
597		391 to
569		240 to
720

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 Trump2818 2.9
Joe Biden3311 3.4
Jo Jorgensen4095 4.3
Howie Hawkins2421 2.5
Tulsi Gabbard3514 3.7
Dan Crenshaw2304 2.4
Justin Amash3523 3.7
Amy Klobuchar2529 2.6
Bernie Sanders4307 4.5
Andrew Yang4457 4.6
Elizabeth Warren3509 3.7
John Kasich2136 2.2
Jeb Bush1964 2.0
Rand Paul3489 3.6
Ted Cruz2503 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 Trump2818
Joe Biden3311
Jo Jorgensen4095
Howie Hawkins2421
Tulsi Gabbard3514
Dan Crenshaw2304
Justin Amash3523
Amy Klobuchar2529
Bernie Sanders4307
Andrew Yang4457
Elizabeth Warren3509
John Kasich2136
Jeb Bush1964
Rand Paul3489
Ted Cruz2503

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 Yang634
Bernie Sanders604

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 Trump2/12/0 349 to
482		231 to
573		357 to
393		275 to
501		286 to
295		252 to
499		356 to
423		353 to
513		295 to
576		368 to
464		350 to
357		344 to
343		215 to
441		264 to
258
Joe Biden9/5/0482 to
349		 398 to
431		429 to
282		354 to
457		483 to
302		422 to
368		396 to
201		222 to
418		209 to
518		262 to
335		449 to
231		473 to
233		442 to
424		483 to
334
Jo Jorgensen12/2/0573 to
231		431 to
398		 471 to
195		404 to
329		519 to
170		349 to
248		449 to
294		385 to
452		333 to
459		422 to
389		497 to
211		524 to
196		446 to
245		558 to
185
Howie Hawkins5/9/0393 to
357		282 to
429		195 to
471		 188 to
474		312 to
294		228 to
397		271 to
324		179 to
467		149 to
542		240 to
368		298 to
294		328 to
304		280 to
426		356 to
341
Tulsi Gabbard11/3/0501 to
275		457 to
354		329 to
404		474 to
188		 465 to
193		349 to
328		455 to
232		373 to
430		306 to
439		405 to
353		478 to
178		503 to
186		373 to
326		487 to
245
Dan Crenshaw2/12/0295 to
286		302 to
483		170 to
519		294 to
312		193 to
465		 169 to
410		273 to
361		288 to
510		231 to
545		300 to
438		276 to
287		286 to
291		173 to
397		265 to
246
Justin Amash8/6/0499 to
252		368 to
422		248 to
349		397 to
228		328 to
349		410 to
169		 355 to
313		345 to
461		289 to
473		355 to
408		392 to
206		434 to
201		363 to
251		465 to
201
Amy Klobuchar6/8/0423 to
356		201 to
396		294 to
449		324 to
271		232 to
455		361 to
273		313 to
355		 193 to
472		138 to
554		198 to
381		332 to
214		371 to
240		335 to
425		398 to
329
Bernie Sanders13/1/0513 to
353		418 to
222		452 to
385		467 to
179		430 to
373		510 to
288		461 to
345		472 to
193		 326 to
356		383 to
169		492 to
225		512 to
240		465 to
396		515 to
324
Andrew Yang14/0/0576 to
295		518 to
209		459 to
333		542 to
149		439 to
306		545 to
231		473 to
289		554 to
138		356 to
326		 446 to
215		572 to
155		589 to
169		473 to
340		551 to
270
Elizabeth Warren9/4/1464 to
368		335 to
262		389 to
422		368 to
240		353 to
405		438 to
300		408 to
355		381 to
198		169 to
383		215 to
446		 412 to
214		437 to
249		415 to
415		453 to
344
John Kasich4/10/0357 to
350		231 to
449		211 to
497		294 to
298		178 to
478		287 to
276		206 to
392		214 to
332		225 to
492		155 to
572		214 to
412		 267 to
186		251 to
404		322 to
298
Jeb Bush1/13/0343 to
344		233 to
473		196 to
524		304 to
328		186 to
503		291 to
286		201 to
434		240 to
371		240 to
512		169 to
589		249 to
437		186 to
267		 201 to
411		291 to
292
Rand Paul7/6/1441 to
215		424 to
442		245 to
446		426 to
280		326 to
373		397 to
173		251 to
363		425 to
335		396 to
465		340 to
473		415 to
415		404 to
251		411 to
201		 416 to
128
Ted Cruz1/13/0258 to
264		334 to
483		185 to
558		341 to
356		245 to
487		246 to
265		201 to
465		329 to
398		324 to
515		270 to
551		344 to
453		298 to
322		292 to
291		128 to
416

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
0539137.44%
111287.83%
29406.53%
39956.91%
49106.32%
510937.59%
67885.47%
77985.54%
87565.25%
95904.10%
1010117.02%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump506393546334536373227124
Joe Biden32770536575766986592852
Jo Jorgensen245797075598241565161141
Howie Hawkins42093706961774133322143
Tulsi Gabbard251646892891059384493134
Dan Crenshaw43593716557704046382025
Justin Amash330796166527439395257111
Amy Klobuchar38372699573906152371414
Bernie Sanders315495146384237566980177
Andrew Yang21157536164928085907097
Elizabeth Warren36269553953435453777580
John Kasich4257779828396513019513
Jeb Bush406114901047878352314711
Rand Paul32382615444617072785659
Ted Cruz45291543651624146593830

Number of bullet votes: 25 (2.60%).
Number of "approval" votes: 13 (1%).

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