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 Trump169
Joe Biden195
Jo Jorgensen168
Howie Hawkins23
Tulsi Gabbard23
Dan Crenshaw9
Justin Amash39
Amy Klobuchar7
Bernie Sanders123
Andrew Yang36
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul25
Ted Cruz9
TOTAL:863

The winner is Joe Biden with 22.6% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump241
Joe Biden340
Jo Jorgensen345
Howie Hawkins139
Tulsi Gabbard262
Dan Crenshaw112
Justin Amash259
Amy Klobuchar148
Bernie Sanders368
Andrew Yang378
Elizabeth Warren287
John Kasich106
Jeb Bush76
Rand Paul285
Ted Cruz166
Ballots Cast:863

The winner is Andrew Yang with 43.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump145
Joe Biden63
Jo Jorgensen144
Howie Hawkins32
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash67
Amy Klobuchar11
Bernie Sanders169
Andrew Yang69
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul37
Ted Cruz19

Jeb Bush eliminated in this round.

Round 2:

Donald Trump145
Joe Biden63
Jo Jorgensen144
Howie Hawkins32
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash68
Amy Klobuchar11
Bernie Sanders170
Andrew Yang69
Elizabeth Warren54
John Kasich14
Rand Paul37
Ted Cruz22

Eliminated in this round:

Round 3:

Donald Trump146
Joe Biden68
Jo Jorgensen149
Howie Hawkins34
Tulsi Gabbard24
Justin Amash68
Bernie Sanders171
Andrew Yang71
Elizabeth Warren55
John Kasich14
Rand Paul38
Ted Cruz25

John Kasich eliminated in this round.

Round 4:

Donald Trump146
Joe Biden70
Jo Jorgensen149
Howie Hawkins34
Tulsi Gabbard26
Justin Amash69
Bernie Sanders172
Andrew Yang73
Elizabeth Warren57
Rand Paul41
Ted Cruz26

Eliminated in this round:

Round 5:

Donald Trump155
Joe Biden74
Jo Jorgensen160
Howie Hawkins35
Justin Amash74
Bernie Sanders176
Andrew Yang77
Elizabeth Warren58
Rand Paul54

Howie Hawkins eliminated in this round.

Round 6:

Donald Trump155
Joe Biden78
Jo Jorgensen161
Justin Amash74
Bernie Sanders201
Andrew Yang80
Elizabeth Warren60
Rand Paul54

Rand Paul eliminated in this round.

Round 7:

Donald Trump174
Joe Biden78
Jo Jorgensen174
Justin Amash92
Bernie Sanders202
Andrew Yang82
Elizabeth Warren61

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump174
Joe Biden92
Jo Jorgensen176
Justin Amash93
Bernie Sanders235
Andrew Yang93

Joe Biden eliminated in this round.

Round 9:

Donald Trump177
Jo Jorgensen194
Justin Amash96
Bernie Sanders275
Andrew Yang121

Justin Amash eliminated in this round.

Round 10:

Donald Trump180
Jo Jorgensen275
Bernie Sanders278
Andrew Yang130

Andrew Yang eliminated in this round.

Round 11:

Donald Trump185
Jo Jorgensen306
Bernie Sanders372

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen449
Bernie Sanders414

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 Trump0/14/0 361 to
502		206 to
657		334 to
529		264 to
599		297 to
566		227 to
636		330 to
533		349 to
514		286 to
577		356 to
507		319 to
544		319 to
544		211 to
652		288 to
575
Joe Biden7/7/0502 to
361		 373 to
490		436 to
427		363 to
500		462 to
401		408 to
455		451 to
412		351 to
512		245 to
618		375 to
488		457 to
406		468 to
395		427 to
436		469 to
394
Jo Jorgensen13/1/0657 to
206		490 to
373		 562 to
301		487 to
376		615 to
248		521 to
342		514 to
349		449 to
414		425 to
438		478 to
385		590 to
273		621 to
242		590 to
273		636 to
227
Howie Hawkins6/8/0529 to
334		427 to
436		301 to
562		 336 to
527		473 to
390		394 to
469		429 to
434		358 to
505		288 to
575		435 to
428		447 to
416		473 to
390		426 to
437		496 to
367
Tulsi Gabbard12/2/0599 to
264		500 to
363		376 to
487		527 to
336		 600 to
263		495 to
368		581 to
282		448 to
415		418 to
445		506 to
357		618 to
245		625 to
238		506 to
357		591 to
272
Dan Crenshaw4/10/0566 to
297		401 to
462		248 to
615		390 to
473		263 to
600		 336 to
527		413 to
450		362 to
501		315 to
548		408 to
455		452 to
411		483 to
380		376 to
487		516 to
347
Justin Amash10/4/0636 to
227		455 to
408		342 to
521		469 to
394		368 to
495		527 to
336		 478 to
385		426 to
437		392 to
471		454 to
409		573 to
290		610 to
253		562 to
301		630 to
233
Amy Klobuchar7/7/0533 to
330		412 to
451		349 to
514		434 to
429		282 to
581		450 to
413		385 to
478		 374 to
489		258 to
605		430 to
433		531 to
332		533 to
330		452 to
411		521 to
342
Bernie Sanders11/3/0514 to
349		512 to
351		414 to
449		505 to
358		415 to
448		501 to
362		437 to
426		489 to
374		 380 to
483		501 to
362		517 to
346		519 to
344		468 to
395		512 to
351
Andrew Yang14/0/0577 to
286		618 to
245		438 to
425		575 to
288		445 to
418		548 to
315		471 to
392		605 to
258		483 to
380		 592 to
271		642 to
221		630 to
233		520 to
343		582 to
281
Elizabeth Warren8/6/0507 to
356		488 to
375		385 to
478		428 to
435		357 to
506		455 to
408		409 to
454		433 to
430		362 to
501		271 to
592		 491 to
372		507 to
356		448 to
415		500 to
363
John Kasich3/11/0544 to
319		406 to
457		273 to
590		416 to
447		245 to
618		411 to
452		290 to
573		332 to
531		346 to
517		221 to
642		372 to
491		 542 to
321		428 to
435		546 to
317
Jeb Bush2/12/0544 to
319		395 to
468		242 to
621		390 to
473		238 to
625		380 to
483		253 to
610		330 to
533		344 to
519		233 to
630		356 to
507		321 to
542		 375 to
488		519 to
344
Rand Paul7/7/0652 to
211		436 to
427		273 to
590		437 to
426		357 to
506		487 to
376		301 to
562		411 to
452		395 to
468		343 to
520		415 to
448		435 to
428		488 to
375		 657 to
206
Ted Cruz1/13/0575 to
288		394 to
469		227 to
636		367 to
496		272 to
591		347 to
516		233 to
630		342 to
521		351 to
512		281 to
582		363 to
500		317 to
546		344 to
519		206 to
657

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 Trump2453 2.8
Joe Biden3001 3.5
Jo Jorgensen3771 4.4
Howie Hawkins2184 2.5
Tulsi Gabbard3177 3.7
Dan Crenshaw2041 2.4
Justin Amash3216 3.7
Amy Klobuchar2270 2.6
Bernie Sanders3902 4.5
Andrew Yang4114 4.8
Elizabeth Warren3248 3.8
John Kasich1901 2.2
Jeb Bush1749 2.0
Rand Paul3141 3.6
Ted Cruz2222 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 Trump2453
Joe Biden3001
Jo Jorgensen3771
Howie Hawkins2184
Tulsi Gabbard3177
Dan Crenshaw2041
Justin Amash3216
Amy Klobuchar2270
Bernie Sanders3902
Andrew Yang4114
Elizabeth Warren3248
John Kasich1901
Jeb Bush1749
Rand Paul3141
Ted Cruz2222

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 Yang572
Bernie Sanders528

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 Trump0/14/0 307 to
439		191 to
533		309 to
360		241 to
459		247 to
266		211 to
459		310 to
387		313 to
469		256 to
531		322 to
429		305 to
328		301 to
312		182 to
403		227 to
235
Joe Biden9/5/0439 to
307		 356 to
392		389 to
257		323 to
413		443 to
269		381 to
333		358 to
173		197 to
374		178 to
478		227 to
306		412 to
200		433 to
209		402 to
383		436 to
298
Jo Jorgensen12/2/0533 to
191		392 to
356		 433 to
176		373 to
295		484 to
144		325 to
218		413 to
261		355 to
402		303 to
420		382 to
359		455 to
192		479 to
173		422 to
212		518 to
162
Howie Hawkins5/9/0360 to
309		257 to
389		176 to
433		 169 to
430		285 to
266		206 to
364		243 to
288		166 to
413		135 to
497		218 to
339		269 to
268		296 to
276		253 to
386		321 to
307
Tulsi Gabbard11/3/0459 to
241		413 to
323		295 to
373		430 to
169		 429 to
175		322 to
297		413 to
207		341 to
386		271 to
405		364 to
329		439 to
161		459 to
169		338 to
296		444 to
220
Dan Crenshaw2/12/0266 to
247		269 to
443		144 to
484		266 to
285		175 to
429		 147 to
378		240 to
331		260 to
459		204 to
503		266 to
405		245 to
265		257 to
263		154 to
363		237 to
223
Justin Amash8/6/0459 to
211		333 to
381		218 to
325		364 to
206		297 to
322		378 to
147		 325 to
281		317 to
413		262 to
433		324 to
378		358 to
191		397 to
179		336 to
222		427 to
176
Amy Klobuchar6/8/0387 to
310		173 to
358		261 to
413		288 to
243		207 to
413		331 to
240		281 to
325		 171 to
424		116 to
514		167 to
358		299 to
191		335 to
212		306 to
386		361 to
294
Bernie Sanders13/1/0469 to
313		374 to
197		402 to
355		413 to
166		386 to
341		459 to
260		413 to
317		424 to
171		 291 to
335		336 to
156		442 to
202		460 to
218		418 to
362		467 to
292
Andrew Yang14/0/0531 to
256		478 to
178		420 to
303		497 to
135		405 to
271		503 to
204		433 to
262		514 to
116		335 to
291		 408 to
193		525 to
133		541 to
149		436 to
306		507 to
244
Elizabeth Warren10/4/0429 to
322		306 to
227		359 to
382		339 to
218		329 to
364		405 to
266		378 to
324		358 to
167		156 to
336		193 to
408		 381 to
189		403 to
220		385 to
374		416 to
306
John Kasich4/10/0328 to
305		200 to
412		192 to
455		268 to
269		161 to
439		265 to
245		191 to
358		191 to
299		202 to
442		133 to
525		189 to
381		 239 to
165		231 to
367		291 to
269
Jeb Bush2/12/0312 to
301		209 to
433		173 to
479		276 to
296		169 to
459		263 to
257		179 to
397		212 to
335		218 to
460		149 to
541		220 to
403		165 to
239		 181 to
376		257 to
262
Rand Paul7/7/0403 to
182		383 to
402		212 to
422		386 to
253		296 to
338		363 to
154		222 to
336		386 to
306		362 to
418		306 to
436		374 to
385		367 to
231		376 to
181		 377 to
110
Ted Cruz2/12/0235 to
227		298 to
436		162 to
518		307 to
321		220 to
444		223 to
237		176 to
427		294 to
361		292 to
467		244 to
507		306 to
416		269 to
291		262 to
257		110 to
377

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
0487937.69%
19897.64%
28376.47%
38686.71%
48076.23%
59557.38%
67135.51%
77365.69%
86875.31%
95464.22%
109287.17%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump468362739303932342921108
Joe Biden29264495463726282552149
Jo Jorgensen219686267506639524658136
Howie Hawkins37982646255663729282140
Tulsi Gabbard22453638284997875463029
Dan Crenshaw39582655951613742331721
Justin Amash295705559465937384852104
Amy Klobuchar34862638366785746361311
Bernie Sanders291394534323934506076163
Andrew Yang18352445555797081836794
Elizabeth Warren32359473047404949697278
John Kasich3867069747383482916510
Jeb Bush37010280936967312214510
Rand Paul29471554642516365715253
Ted Cruz41279493144563942533622

Number of bullet votes: 19 (2.20%).
Number of "approval" votes: 11 (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.

Quiz2D Home | Presidential Poll | Blog | Third Party Strategy | Silly Radio Ads | Privacy | About/Contact