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 Trump187
Joe Biden207
Jo Jorgensen170
Howie Hawkins24
Tulsi Gabbard23
Dan Crenshaw10
Justin Amash47
Amy Klobuchar10
Bernie Sanders135
Andrew Yang38
Elizabeth Warren25
John Kasich10
Jeb Bush5
Rand Paul27
Ted Cruz12
TOTAL:930

The winner is Joe Biden with 22.3% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump267
Joe Biden363
Jo Jorgensen362
Howie Hawkins149
Tulsi Gabbard279
Dan Crenshaw122
Justin Amash274
Amy Klobuchar157
Bernie Sanders395
Andrew Yang393
Elizabeth Warren302
John Kasich113
Jeb Bush82
Rand Paul305
Ted Cruz184
Ballots Cast:930

The winner is Bernie Sanders with 42.5% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump162
Joe Biden73
Jo Jorgensen146
Howie Hawkins34
Tulsi Gabbard23
Dan Crenshaw12
Justin Amash75
Amy Klobuchar14
Bernie Sanders180
Andrew Yang70
Elizabeth Warren58
John Kasich15
Jeb Bush6
Rand Paul39
Ted Cruz23

Jeb Bush eliminated in this round.

Round 2:

Donald Trump162
Joe Biden73
Jo Jorgensen146
Howie Hawkins34
Tulsi Gabbard23
Dan Crenshaw12
Justin Amash76
Amy Klobuchar14
Bernie Sanders181
Andrew Yang70
Elizabeth Warren58
John Kasich16
Rand Paul39
Ted Cruz26

Dan Crenshaw eliminated in this round.

Round 3:

Donald Trump163
Joe Biden73
Jo Jorgensen150
Howie Hawkins34
Tulsi Gabbard25
Justin Amash76
Amy Klobuchar14
Bernie Sanders181
Andrew Yang71
Elizabeth Warren58
John Kasich16
Rand Paul40
Ted Cruz29

Amy Klobuchar eliminated in this round.

Round 4:

Donald Trump163
Joe Biden80
Jo Jorgensen151
Howie Hawkins36
Tulsi Gabbard25
Justin Amash76
Bernie Sanders182
Andrew Yang72
Elizabeth Warren59
John Kasich17
Rand Paul40
Ted Cruz29

John Kasich eliminated in this round.

Round 5:

Donald Trump163
Joe Biden83
Jo Jorgensen151
Howie Hawkins36
Tulsi Gabbard28
Justin Amash77
Bernie Sanders184
Andrew Yang74
Elizabeth Warren61
Rand Paul43
Ted Cruz30

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump164
Joe Biden86
Jo Jorgensen159
Howie Hawkins36
Justin Amash82
Bernie Sanders187
Andrew Yang78
Elizabeth Warren62
Rand Paul46
Ted Cruz30

Ted Cruz eliminated in this round.

Round 7:

Donald Trump176
Joe Biden88
Jo Jorgensen162
Howie Hawkins37
Justin Amash82
Bernie Sanders188
Andrew Yang78
Elizabeth Warren62
Rand Paul57

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump176
Joe Biden92
Jo Jorgensen163
Justin Amash82
Bernie Sanders215
Andrew Yang81
Elizabeth Warren64
Rand Paul57

Rand Paul eliminated in this round.

Round 9:

Donald Trump195
Joe Biden92
Jo Jorgensen177
Justin Amash101
Bernie Sanders216
Andrew Yang84
Elizabeth Warren65

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump195
Joe Biden107
Jo Jorgensen181
Justin Amash102
Bernie Sanders250
Andrew Yang95

Andrew Yang eliminated in this round.

Round 11:

Donald Trump198
Joe Biden125
Jo Jorgensen196
Justin Amash114
Bernie Sanders297

Justin Amash eliminated in this round.

Round 12:

Donald Trump205
Joe Biden133
Jo Jorgensen289
Bernie Sanders303

Joe Biden eliminated in this round.

Round 13:

Donald Trump211
Jo Jorgensen321
Bernie Sanders398

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen485
Bernie Sanders445

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 Trump0/14/0 396 to
534		237 to
693		371 to
559		293 to
637		330 to
600		257 to
673		365 to
565		382 to
548		317 to
613		391 to
539		355 to
575		355 to
575		242 to
688		321 to
609
Joe Biden7/7/0534 to
396		 402 to
528		469 to
461		391 to
539		496 to
434		441 to
489		485 to
445		378 to
552		275 to
655		406 to
524		488 to
442		498 to
432		459 to
471		503 to
427
Jo Jorgensen13/1/0693 to
237		528 to
402		 604 to
326		526 to
404		659 to
271		562 to
368		557 to
373		485 to
445		463 to
467		517 to
413		636 to
294		672 to
258		631 to
299		679 to
251
Howie Hawkins7/7/0559 to
371		461 to
469		326 to
604		 365 to
565		512 to
418		433 to
497		469 to
461		392 to
538		322 to
608		476 to
454		489 to
441		518 to
412		464 to
466		533 to
397
Tulsi Gabbard12/2/0637 to
293		539 to
391		404 to
526		565 to
365		 648 to
282		538 to
392		627 to
303		486 to
444		460 to
470		549 to
381		670 to
260		679 to
251		549 to
381		632 to
298
Dan Crenshaw4/10/0600 to
330		434 to
496		271 to
659		418 to
512		282 to
648		 375 to
555		453 to
477		396 to
534		350 to
580		448 to
482		496 to
434		527 to
403		410 to
520		551 to
379
Justin Amash10/4/0673 to
257		489 to
441		368 to
562		497 to
433		392 to
538		555 to
375		 518 to
412		460 to
470		427 to
503		492 to
438		621 to
309		659 to
271		606 to
324		671 to
259
Amy Klobuchar7/7/0565 to
365		445 to
485		373 to
557		461 to
469		303 to
627		477 to
453		412 to
518		 410 to
520		288 to
642		469 to
461		570 to
360		574 to
356		490 to
440		556 to
374
Bernie Sanders11/3/0548 to
382		552 to
378		445 to
485		538 to
392		444 to
486		534 to
396		470 to
460		520 to
410		 421 to
509		546 to
384		559 to
371		561 to
369		507 to
423		549 to
381
Andrew Yang14/0/0613 to
317		655 to
275		467 to
463		608 to
322		470 to
460		580 to
350		503 to
427		642 to
288		509 to
421		 634 to
296		686 to
244		676 to
254		560 to
370		623 to
307
Elizabeth Warren7/7/0539 to
391		524 to
406		413 to
517		454 to
476		381 to
549		482 to
448		438 to
492		461 to
469		384 to
546		296 to
634		 530 to
400		548 to
382		485 to
445		534 to
396
John Kasich3/11/0575 to
355		442 to
488		294 to
636		441 to
489		260 to
670		434 to
496		309 to
621		360 to
570		371 to
559		244 to
686		400 to
530		 586 to
344		461 to
469		579 to
351
Jeb Bush2/12/0575 to
355		432 to
498		258 to
672		412 to
518		251 to
679		403 to
527		271 to
659		356 to
574		369 to
561		254 to
676		382 to
548		344 to
586		 404 to
526		549 to
381
Rand Paul7/7/0688 to
242		471 to
459		299 to
631		466 to
464		381 to
549		520 to
410		324 to
606		440 to
490		423 to
507		370 to
560		445 to
485		469 to
461		526 to
404		 699 to
231
Ted Cruz1/13/0609 to
321		427 to
503		251 to
679		397 to
533		298 to
632		379 to
551		259 to
671		374 to
556		381 to
549		307 to
623		396 to
534		351 to
579		381 to
549		231 to
699

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 Trump2696 2.9
Joe Biden3219 3.5
Jo Jorgensen4005 4.3
Howie Hawkins2340 2.5
Tulsi Gabbard3395 3.7
Dan Crenshaw2200 2.4
Justin Amash3444 3.7
Amy Klobuchar2445 2.6
Bernie Sanders4171 4.5
Andrew Yang4331 4.7
Elizabeth Warren3413 3.7
John Kasich2062 2.2
Jeb Bush1898 2.0
Rand Paul3392 3.6
Ted Cruz2430 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 Trump2696
Joe Biden3219
Jo Jorgensen4005
Howie Hawkins2340
Tulsi Gabbard3395
Dan Crenshaw2200
Justin Amash3444
Amy Klobuchar2445
Bernie Sanders4171
Andrew Yang4331
Elizabeth Warren3413
John Kasich2062
Jeb Bush1898
Rand Paul3392
Ted Cruz2430

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 Yang612
Bernie Sanders581

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 Trump1/13/0 335 to
469		220 to
563		342 to
385		266 to
489		276 to
283		239 to
489		343 to
411		341 to
501		284 to
561		352 to
455		336 to
349		331 to
334		204 to
429		253 to
252
Joe Biden9/5/0469 to
335		 386 to
420		417 to
273		347 to
443		473 to
289		409 to
359		384 to
192		215 to
404		202 to
505		253 to
324		438 to
220		461 to
227		432 to
414		469 to
325
Jo Jorgensen12/2/0563 to
220		420 to
386		 461 to
192		398 to
317		513 to
160		342 to
242		439 to
284		377 to
436		327 to
447		410 to
381		486 to
207		511 to
191		441 to
235		546 to
179
Howie Hawkins5/9/0385 to
342		273 to
417		192 to
461		 185 to
460		307 to
284		221 to
391		262 to
313		173 to
451		145 to
530		231 to
360		289 to
287		318 to
297		274 to
417		345 to
334
Tulsi Gabbard11/3/0489 to
266		443 to
347		317 to
398		460 to
185		 457 to
187		339 to
323		441 to
227		361 to
418		296 to
430		393 to
347		465 to
174		490 to
182		363 to
319		474 to
241
Dan Crenshaw2/12/0283 to
276		289 to
473		160 to
513		284 to
307		187 to
457		 160 to
405		260 to
354		277 to
495		220 to
534		287 to
429		264 to
283		275 to
284		165 to
391		254 to
242
Justin Amash8/6/0489 to
239		359 to
409		242 to
342		391 to
221		323 to
339		405 to
160		 347 to
301		336 to
446		284 to
460		347 to
398		382 to
202		425 to
194		358 to
241		455 to
195
Amy Klobuchar6/8/0411 to
343		192 to
384		284 to
439		313 to
262		227 to
441		354 to
260		301 to
347		 186 to
455		133 to
540		188 to
372		322 to
206		362 to
230		328 to
414		386 to
322
Bernie Sanders13/1/0501 to
341		404 to
215		436 to
377		451 to
173		418 to
361		495 to
277		446 to
336		455 to
186		 318 to
349		368 to
163		476 to
216		496 to
232		450 to
387		499 to
317
Andrew Yang14/0/0561 to
284		505 to
202		447 to
327		530 to
145		430 to
296		534 to
220		460 to
284		540 to
133		349 to
318		 435 to
209		558 to
148		576 to
163		461 to
332		538 to
265
Elizabeth Warren10/4/0455 to
352		324 to
253		381 to
410		360 to
231		347 to
393		429 to
287		398 to
347		372 to
188		163 to
368		209 to
435		 402 to
205		425 to
240		406 to
403		442 to
334
John Kasich4/10/0349 to
336		220 to
438		207 to
486		287 to
289		174 to
465		283 to
264		202 to
382		206 to
322		216 to
476		148 to
558		205 to
402		 258 to
181		249 to
393		312 to
292
Jeb Bush2/12/0334 to
331		227 to
461		191 to
511		297 to
318		182 to
490		284 to
275		194 to
425		230 to
362		232 to
496		163 to
576		240 to
425		181 to
258		 198 to
402		281 to
285
Rand Paul7/7/0429 to
204		414 to
432		235 to
441		417 to
274		319 to
363		391 to
165		241 to
358		414 to
328		387 to
450		332 to
461		403 to
406		393 to
249		402 to
198		 405 to
124
Ted Cruz1/13/0252 to
253		325 to
469		179 to
546		334 to
345		241 to
474		242 to
254		195 to
455		322 to
386		317 to
499		265 to
538		334 to
442		292 to
312		285 to
281		124 to
405

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
0524137.57%
110867.78%
29106.52%
39606.88%
48786.29%
510337.41%
67615.46%
77845.62%
87335.25%
95804.16%
109847.05%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump497373145314335373124119
Joe Biden31968506170736885562852
Jo Jorgensen234786775567539545161140
Howie Hawkins40889706759724031312142
Tulsi Gabbard242616791871039081463131
Dan Crenshaw42490716357643845362022
Justin Amash318765963516839395256109
Amy Klobuchar37468689171846050361414
Bernie Sanders310464941354036566878171
Andrew Yang20256525863877885886794
Elizabeth Warren35366503849435252757478
John Kasich4157376808092483018513
Jeb Bush395111861027573332314711
Rand Paul31279615244576570755659
Ted Cruz43888533350594046563829

Number of bullet votes: 23 (2.47%).
Number of "approval" votes: 13 (1%).

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