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 Trump142
Joe Biden175
Jo Jorgensen153
Howie Hawkins16
Tulsi Gabbard18
Dan Crenshaw8
Justin Amash37
Amy Klobuchar5
Bernie Sanders98
Andrew Yang33
Elizabeth Warren21
John Kasich8
Jeb Bush4
Rand Paul22
Ted Cruz8
TOTAL:748

The winner is Joe Biden with 23.4% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump205
Joe Biden286
Jo Jorgensen319
Howie Hawkins120
Tulsi Gabbard230
Dan Crenshaw105
Justin Amash241
Amy Klobuchar128
Bernie Sanders311
Andrew Yang333
Elizabeth Warren254
John Kasich92
Jeb Bush59
Rand Paul263
Ted Cruz148
Ballots Cast:748

The winner is Andrew Yang with 44.5% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump121
Joe Biden52
Jo Jorgensen130
Howie Hawkins25
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash64
Amy Klobuchar8
Bernie Sanders141
Andrew Yang62
Elizabeth Warren50
John Kasich12
Jeb Bush4
Rand Paul34
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump121
Joe Biden52
Jo Jorgensen130
Howie Hawkins25
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Amy Klobuchar8
Bernie Sanders142
Andrew Yang62
Elizabeth Warren50
John Kasich12
Rand Paul34
Ted Cruz20

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump121
Joe Biden55
Jo Jorgensen131
Howie Hawkins26
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Bernie Sanders143
Andrew Yang63
Elizabeth Warren51
John Kasich12
Rand Paul34
Ted Cruz20

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump121
Joe Biden55
Jo Jorgensen135
Howie Hawkins26
Tulsi Gabbard18
Justin Amash65
Bernie Sanders143
Andrew Yang64
Elizabeth Warren51
John Kasich12
Rand Paul35
Ted Cruz23

John Kasich eliminated in this round.

Round 5:

Donald Trump121
Joe Biden56
Jo Jorgensen135
Howie Hawkins26
Tulsi Gabbard20
Justin Amash66
Bernie Sanders144
Andrew Yang66
Elizabeth Warren52
Rand Paul38
Ted Cruz24

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump121
Joe Biden56
Jo Jorgensen143
Howie Hawkins26
Justin Amash70
Bernie Sanders145
Andrew Yang70
Elizabeth Warren53
Rand Paul40
Ted Cruz24

Ted Cruz eliminated in this round.

Round 7:

Donald Trump129
Joe Biden58
Jo Jorgensen146
Howie Hawkins27
Justin Amash70
Bernie Sanders146
Andrew Yang70
Elizabeth Warren53
Rand Paul49

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump129
Joe Biden60
Jo Jorgensen146
Justin Amash70
Bernie Sanders167
Andrew Yang73
Elizabeth Warren54
Rand Paul49

Rand Paul eliminated in this round.

Round 9:

Donald Trump148
Joe Biden60
Jo Jorgensen158
Justin Amash85
Bernie Sanders168
Andrew Yang75
Elizabeth Warren54

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump148
Joe Biden73
Jo Jorgensen159
Justin Amash86
Bernie Sanders198
Andrew Yang84

Joe Biden eliminated in this round.

Round 11:

Donald Trump150
Jo Jorgensen169
Justin Amash89
Bernie Sanders231
Andrew Yang109

Justin Amash eliminated in this round.

Round 12:

Donald Trump153
Jo Jorgensen243
Bernie Sanders234
Andrew Yang118

Andrew Yang eliminated in this round.

Round 13:

Donald Trump157
Jo Jorgensen272
Bernie Sanders319

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen397
Bernie Sanders351

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 Trump0/14/0 324 to
424		172 to
576		295 to
453		229 to
519		252 to
496		189 to
559		290 to
458		312 to
436		250 to
498		313 to
435		275 to
473		273 to
475		166 to
582		237 to
511
Joe Biden7/7/0424 to
324		 313 to
435		381 to
367		310 to
438		386 to
362		340 to
408		387 to
361		307 to
441		200 to
548		314 to
434		386 to
362		391 to
357		355 to
393		388 to
360
Jo Jorgensen13/1/0576 to
172		435 to
313		 506 to
242		433 to
315		536 to
212		450 to
298		449 to
299		397 to
351		368 to
380		414 to
334		516 to
232		541 to
207		511 to
237		554 to
194
Howie Hawkins4/9/1453 to
295		367 to
381		242 to
506		 279 to
469		394 to
354		324 to
424		357 to
391		313 to
435		233 to
515		360 to
388		374 to
374		392 to
356		355 to
393		417 to
331
Tulsi Gabbard12/2/0519 to
229		438 to
310		315 to
433		469 to
279		 514 to
234		412 to
336		499 to
249		393 to
355		360 to
388		433 to
315		527 to
221		535 to
213		421 to
327		506 to
242
Dan Crenshaw4/10/0496 to
252		362 to
386		212 to
536		354 to
394		234 to
514		 287 to
461		366 to
382		327 to
421		273 to
475		360 to
388		396 to
352		424 to
324		315 to
433		442 to
306
Justin Amash11/3/0559 to
189		408 to
340		298 to
450		424 to
324		336 to
412		461 to
287		 419 to
329		378 to
370		338 to
410		395 to
353		496 to
252		530 to
218		484 to
264		550 to
198
Amy Klobuchar7/7/0458 to
290		361 to
387		299 to
449		391 to
357		249 to
499		382 to
366		329 to
419		 331 to
417		211 to
537		369 to
379		450 to
298		451 to
297		377 to
371		441 to
307
Bernie Sanders10/4/0436 to
312		441 to
307		351 to
397		435 to
313		355 to
393		421 to
327		370 to
378		417 to
331		 311 to
437		415 to
333		437 to
311		436 to
312		389 to
359		433 to
315
Andrew Yang14/0/0498 to
250		548 to
200		380 to
368		515 to
233		388 to
360		475 to
273		410 to
338		537 to
211		437 to
311		 518 to
230		558 to
190		542 to
206		438 to
310		498 to
250
Elizabeth Warren9/5/0435 to
313		434 to
314		334 to
414		388 to
360		315 to
433		388 to
360		353 to
395		379 to
369		333 to
415		230 to
518		 420 to
328		430 to
318		377 to
371		425 to
323
John Kasich3/10/1473 to
275		362 to
386		232 to
516		374 to
374		221 to
527		352 to
396		252 to
496		298 to
450		311 to
437		190 to
558		328 to
420		 462 to
286		357 to
391		464 to
284
Jeb Bush2/12/0475 to
273		357 to
391		207 to
541		356 to
392		213 to
535		324 to
424		218 to
530		297 to
451		312 to
436		206 to
542		318 to
430		286 to
462		 315 to
433		436 to
312
Rand Paul7/7/0582 to
166		393 to
355		237 to
511		393 to
355		327 to
421		433 to
315		264 to
484		371 to
377		359 to
389		310 to
438		371 to
377		391 to
357		433 to
315		 577 to
171
Ted Cruz1/13/0511 to
237		360 to
388		194 to
554		331 to
417		242 to
506		306 to
442		198 to
550		307 to
441		315 to
433		250 to
498		323 to
425		284 to
464		312 to
436		171 to
577

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 Trump2078 2.8
Joe Biden2541 3.4
Jo Jorgensen3353 4.5
Howie Hawkins1792 2.4
Tulsi Gabbard2679 3.6
Dan Crenshaw1762 2.4
Justin Amash2857 3.8
Amy Klobuchar1869 2.5
Bernie Sanders3279 4.4
Andrew Yang3562 4.8
Elizabeth Warren2804 3.7
John Kasich1591 2.1
Jeb Bush1447 1.9
Rand Paul2784 3.7
Ted Cruz1966 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 Trump2078
Joe Biden2541
Jo Jorgensen3353
Howie Hawkins1792
Tulsi Gabbard2679
Dan Crenshaw1762
Justin Amash2857
Amy Klobuchar1869
Bernie Sanders3279
Andrew Yang3562
Elizabeth Warren2804
John Kasich1591
Jeb Bush1447
Rand Paul2784
Ted Cruz1966

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 Yang473
Jo Jorgensen384

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 Trump0/14/0 271 to
372		156 to
468		271 to
299		208 to
388		206 to
229		173 to
401		272 to
323		276 to
395		222 to
459		283 to
364		262 to
281		261 to
266		144 to
362		185 to
213
Joe Biden8/6/0372 to
271		 300 to
357		338 to
219		281 to
363		375 to
242		320 to
304		311 to
143		165 to
314		145 to
421		185 to
268		351 to
173		367 to
182		342 to
346		363 to
271
Jo Jorgensen12/2/0468 to
156		357 to
300		 390 to
141		342 to
241		428 to
116		285 to
187		375 to
218		324 to
334		275 to
364		339 to
308		410 to
159		430 to
138		369 to
177		450 to
135
Howie Hawkins3/11/0299 to
271		219 to
338		141 to
390		 145 to
376		237 to
235		169 to
330		208 to
247		145 to
346		107 to
444		180 to
295		226 to
234		246 to
241		207 to
347		260 to
277
Tulsi Gabbard10/4/0388 to
208		363 to
281		241 to
342		376 to
145		 365 to
156		269 to
276		361 to
178		300 to
325		234 to
357		317 to
290		376 to
145		389 to
146		273 to
272		369 to
197
Dan Crenshaw2/12/0229 to
206		242 to
375		116 to
428		235 to
237		156 to
365		 122 to
334		211 to
277		234 to
384		176 to
438		235 to
347		215 to
225		230 to
218		124 to
326		196 to
200
Justin Amash9/5/0401 to
173		304 to
320		187 to
285		330 to
169		276 to
269		334 to
122		 296 to
234		287 to
347		238 to
371		290 to
325		320 to
156		353 to
140		295 to
193		371 to
148
Amy Klobuchar6/8/0323 to
272		143 to
311		218 to
375		247 to
208		178 to
361		277 to
211		234 to
296		 145 to
355		91 to
453		137 to
316		254 to
165		282 to
184		256 to
352		294 to
265
Bernie Sanders13/1/0395 to
276		314 to
165		334 to
324		346 to
145		325 to
300		384 to
234		347 to
287		355 to
145		 235 to
301		271 to
138		370 to
172		389 to
187		352 to
327		390 to
265
Andrew Yang14/0/0459 to
222		421 to
145		364 to
275		444 to
107		357 to
234		438 to
176		371 to
238		453 to
91		301 to
235		 358 to
162		460 to
108		468 to
121		373 to
275		433 to
216
Elizabeth Warren9/5/0364 to
283		268 to
185		308 to
339		295 to
180		290 to
317		347 to
235		325 to
290		316 to
137		138 to
271		162 to
358		 328 to
158		346 to
185		328 to
338		352 to
272
John Kasich5/9/0281 to
262		173 to
351		159 to
410		234 to
226		145 to
376		225 to
215		156 to
320		165 to
254		172 to
370		108 to
460		158 to
328		 206 to
138		194 to
330		243 to
239
Jeb Bush1/13/0266 to
261		182 to
367		138 to
430		241 to
246		146 to
389		218 to
230		140 to
353		184 to
282		187 to
389		121 to
468		185 to
346		138 to
206		 145 to
340		208 to
237
Rand Paul9/5/0362 to
144		346 to
342		177 to
369		347 to
207		272 to
273		326 to
124		193 to
295		352 to
256		327 to
352		275 to
373		338 to
328		330 to
194		340 to
145		 330 to
92
Ted Cruz4/10/0213 to
185		271 to
363		135 to
450		277 to
260		197 to
369		200 to
196		148 to
371		265 to
294		265 to
390		216 to
433		272 to
352		239 to
243		237 to
208		92 to
330

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
0434938.76%
18307.40%
27266.47%
37326.52%
46625.90%
58097.21%
65945.29%
76325.63%
85895.25%
94774.25%
108207.31%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump41328203527363031231491
Joe Biden25857444955624971431644
Jo Jorgensen192545056415336483756125
Howie Hawkins34670585043562825211734
Tulsi Gabbard20347557267886665412123
Dan Crenshaw34968555040533437291617
Justin Amash25955464938483034435195
Amy Klobuchar3185556675566453630119
Bernie Sanders270364025263024375167142
Andrew Yang16442394948615873715984
Elizabeth Warren29443432537323936606475
John Kasich345586361587541231347
Jeb Bush331867280585726161327
Rand Paul25063483733425461674548
Ted Cruz35768372736503439473419

Number of bullet votes: 17 (2.27%).
Number of "approval" votes: 9 (1%).

Look at Other Results?

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