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 Trump137
Joe Biden174
Jo Jorgensen153
Howie Hawkins15
Tulsi Gabbard18
Dan Crenshaw8
Justin Amash37
Amy Klobuchar5
Bernie Sanders96
Andrew Yang33
Elizabeth Warren21
John Kasich8
Jeb Bush4
Rand Paul22
Ted Cruz8
TOTAL:739

The winner is Joe Biden with 23.5% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump200
Joe Biden283
Jo Jorgensen317
Howie Hawkins118
Tulsi Gabbard229
Dan Crenshaw102
Justin Amash241
Amy Klobuchar128
Bernie Sanders307
Andrew Yang333
Elizabeth Warren254
John Kasich90
Jeb Bush58
Rand Paul260
Ted Cruz146
Ballots Cast:739

The winner is Andrew Yang with 45.1% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump116
Joe Biden51
Jo Jorgensen130
Howie Hawkins24
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash64
Amy Klobuchar8
Bernie Sanders139
Andrew Yang62
Elizabeth Warren50
John Kasich12
Jeb Bush4
Rand Paul34
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump116
Joe Biden51
Jo Jorgensen130
Howie Hawkins24
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Amy Klobuchar8
Bernie Sanders140
Andrew Yang62
Elizabeth Warren50
John Kasich12
Rand Paul34
Ted Cruz20

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump116
Joe Biden54
Jo Jorgensen131
Howie Hawkins25
Tulsi Gabbard17
Dan Crenshaw10
Justin Amash65
Bernie Sanders141
Andrew Yang63
Elizabeth Warren51
John Kasich12
Rand Paul34
Ted Cruz20

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump116
Joe Biden54
Jo Jorgensen135
Howie Hawkins25
Tulsi Gabbard18
Justin Amash65
Bernie Sanders141
Andrew Yang64
Elizabeth Warren51
John Kasich12
Rand Paul35
Ted Cruz23

John Kasich eliminated in this round.

Round 5:

Donald Trump116
Joe Biden55
Jo Jorgensen135
Howie Hawkins25
Tulsi Gabbard20
Justin Amash66
Bernie Sanders142
Andrew Yang66
Elizabeth Warren52
Rand Paul38
Ted Cruz24

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump116
Joe Biden55
Jo Jorgensen143
Howie Hawkins25
Justin Amash70
Bernie Sanders143
Andrew Yang70
Elizabeth Warren53
Rand Paul40
Ted Cruz24

Ted Cruz eliminated in this round.

Round 7:

Donald Trump124
Joe Biden57
Jo Jorgensen146
Howie Hawkins26
Justin Amash70
Bernie Sanders144
Andrew Yang70
Elizabeth Warren53
Rand Paul49

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump124
Joe Biden59
Jo Jorgensen146
Justin Amash70
Bernie Sanders165
Andrew Yang72
Elizabeth Warren54
Rand Paul49

Rand Paul eliminated in this round.

Round 9:

Donald Trump143
Joe Biden59
Jo Jorgensen158
Justin Amash85
Bernie Sanders166
Andrew Yang74
Elizabeth Warren54

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump143
Joe Biden72
Jo Jorgensen159
Justin Amash86
Bernie Sanders196
Andrew Yang83

Joe Biden eliminated in this round.

Round 11:

Donald Trump145
Jo Jorgensen169
Justin Amash89
Bernie Sanders228
Andrew Yang108

Justin Amash eliminated in this round.

Round 12:

Donald Trump148
Jo Jorgensen243
Bernie Sanders231
Andrew Yang117

Andrew Yang eliminated in this round.

Round 13:

Donald Trump152
Jo Jorgensen272
Bernie Sanders315

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen395
Bernie Sanders344

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 Trump0/14/0 319 to
420		167 to
572		290 to
449		223 to
516		246 to
493		183 to
556		284 to
455		307 to
432		244 to
495		307 to
432		269 to
470		267 to
472		160 to
579		231 to
508
Joe Biden7/7/0420 to
319		 309 to
430		376 to
363		306 to
433		381 to
358		335 to
404		381 to
358		304 to
435		196 to
543		308 to
431		381 to
358		386 to
353		350 to
389		383 to
356
Jo Jorgensen13/1/0572 to
167		430 to
309		 502 to
237		430 to
309		531 to
208		444 to
295		444 to
295		395 to
344		363 to
376		409 to
330		510 to
229		535 to
204		506 to
233		549 to
190
Howie Hawkins4/10/0449 to
290		363 to
376		237 to
502		 275 to
464		390 to
349		318 to
421		353 to
386		311 to
428		228 to
511		355 to
384		369 to
370		387 to
352		350 to
389		412 to
327
Tulsi Gabbard12/2/0516 to
223		433 to
306		309 to
430		464 to
275		 508 to
231		403 to
336		491 to
248		389 to
350		353 to
386		426 to
313		520 to
219		528 to
211		416 to
323		500 to
239
Dan Crenshaw4/10/0493 to
246		358 to
381		208 to
531		349 to
390		231 to
508		 281 to
458		361 to
378		324 to
415		267 to
472		355 to
384		390 to
349		419 to
320		309 to
430		436 to
303
Justin Amash11/3/0556 to
183		404 to
335		295 to
444		421 to
318		336 to
403		458 to
281		 416 to
323		376 to
363		333 to
406		391 to
348		491 to
248		524 to
215		479 to
260		545 to
194
Amy Klobuchar7/7/0455 to
284		358 to
381		295 to
444		386 to
353		248 to
491		378 to
361		323 to
416		 328 to
411		206 to
533		364 to
375		445 to
294		446 to
293		372 to
367		435 to
304
Bernie Sanders10/4/0432 to
307		435 to
304		344 to
395		428 to
311		350 to
389		415 to
324		363 to
376		411 to
328		 306 to
433		408 to
331		431 to
308		431 to
308		384 to
355		427 to
312
Andrew Yang14/0/0495 to
244		543 to
196		376 to
363		511 to
228		386 to
353		472 to
267		406 to
333		533 to
206		433 to
306		 512 to
227		554 to
185		537 to
202		433 to
306		492 to
247
Elizabeth Warren9/5/0432 to
307		431 to
308		330 to
409		384 to
355		313 to
426		384 to
355		348 to
391		375 to
364		331 to
408		227 to
512		 415 to
324		425 to
314		372 to
367		419 to
320
John Kasich4/10/0470 to
269		358 to
381		229 to
510		370 to
369		219 to
520		349 to
390		248 to
491		294 to
445		308 to
431		185 to
554		324 to
415		 457 to
282		352 to
387		458 to
281
Jeb Bush2/12/0472 to
267		353 to
386		204 to
535		352 to
387		211 to
528		320 to
419		215 to
524		293 to
446		308 to
431		202 to
537		314 to
425		282 to
457		 309 to
430		430 to
309
Rand Paul7/7/0579 to
160		389 to
350		233 to
506		389 to
350		323 to
416		430 to
309		260 to
479		367 to
372		355 to
384		306 to
433		367 to
372		387 to
352		430 to
309		 571 to
168
Ted Cruz1/13/0508 to
231		356 to
383		190 to
549		327 to
412		239 to
500		303 to
436		194 to
545		304 to
435		312 to
427		247 to
492		320 to
419		281 to
458		309 to
430		168 to
571

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 Trump2026 2.7
Joe Biden2505 3.4
Jo Jorgensen3330 4.5
Howie Hawkins1768 2.4
Tulsi Gabbard2646 3.6
Dan Crenshaw1730 2.3
Justin Amash2846 3.9
Amy Klobuchar1849 2.5
Bernie Sanders3232 4.4
Andrew Yang3538 4.8
Elizabeth Warren2780 3.8
John Kasich1565 2.1
Jeb Bush1423 1.9
Rand Paul2750 3.7
Ted Cruz1934 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 Trump2026
Joe Biden2505
Jo Jorgensen3330
Howie Hawkins1768
Tulsi Gabbard2646
Dan Crenshaw1730
Justin Amash2846
Amy Klobuchar1849
Bernie Sanders3232
Andrew Yang3538
Elizabeth Warren2780
John Kasich1565
Jeb Bush1423
Rand Paul2750
Ted Cruz1934

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 Yang466
Jo Jorgensen378

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 Trump0/14/0 266 to
368		150 to
465		265 to
296		202 to
385		200 to
227		167 to
399		266 to
320		271 to
391		216 to
456		277 to
361		256 to
279		255 to
263		138 to
360		179 to
211
Joe Biden8/6/0368 to
266		 296 to
356		335 to
218		277 to
361		370 to
239		315 to
303		306 to
142		164 to
310		142 to
417		182 to
266		346 to
170		362 to
179		337 to
342		358 to
268
Jo Jorgensen12/2/0465 to
150		356 to
296		 388 to
139		342 to
238		425 to
113		282 to
187		373 to
218		323 to
328		273 to
361		337 to
305		407 to
156		427 to
136		366 to
173		447 to
131
Howie Hawkins3/11/0296 to
265		218 to
335		139 to
388		 143 to
373		234 to
232		166 to
329		206 to
245		145 to
341		105 to
441		179 to
293		223 to
231		243 to
238		204 to
343		257 to
273
Tulsi Gabbard9/4/1385 to
202		361 to
277		238 to
342		373 to
143		 361 to
153		264 to
276		357 to
178		298 to
320		231 to
355		314 to
288		372 to
143		384 to
145		269 to
269		366 to
193
Dan Crenshaw2/12/0227 to
200		239 to
370		113 to
425		232 to
234		153 to
361		 117 to
333		208 to
274		231 to
378		173 to
435		232 to
343		212 to
224		226 to
215		121 to
323		193 to
196
Justin Amash9/5/0399 to
167		303 to
315		187 to
282		329 to
166		276 to
264		333 to
117		 295 to
231		286 to
341		237 to
367		289 to
321		318 to
152		353 to
137		294 to
188		369 to
143
Amy Klobuchar6/8/0320 to
266		142 to
306		218 to
373		245 to
206		178 to
357		274 to
208		231 to
295		 144 to
349		89 to
450		136 to
313		252 to
162		279 to
181		253 to
348		291 to
261
Bernie Sanders13/1/0391 to
271		310 to
164		328 to
323		341 to
145		320 to
298		378 to
231		341 to
286		349 to
144		 230 to
299		266 to
138		364 to
169		384 to
184		347 to
323		385 to
262
Andrew Yang14/0/0456 to
216		417 to
142		361 to
273		441 to
105		355 to
231		435 to
173		367 to
237		450 to
89		299 to
230		 356 to
161		457 to
105		465 to
118		370 to
271		430 to
212
Elizabeth Warren9/5/0361 to
277		266 to
182		305 to
337		293 to
179		288 to
314		343 to
232		321 to
289		313 to
136		138 to
266		161 to
356		 324 to
155		343 to
182		325 to
334		349 to
268
John Kasich5/9/0279 to
256		170 to
346		156 to
407		231 to
223		143 to
372		224 to
212		152 to
318		162 to
252		169 to
364		105 to
457		155 to
324		 203 to
134		192 to
326		240 to
235
Jeb Bush1/13/0263 to
255		179 to
362		136 to
427		238 to
243		145 to
384		215 to
226		137 to
353		181 to
279		184 to
384		118 to
465		182 to
343		134 to
203		 143 to
337		206 to
233
Rand Paul9/4/1360 to
138		342 to
337		173 to
366		343 to
204		269 to
269		323 to
121		188 to
294		348 to
253		323 to
347		271 to
370		334 to
325		326 to
192		337 to
143		 328 to
89
Ted Cruz4/10/0211 to
179		268 to
358		131 to
447		273 to
257		193 to
366		196 to
193		143 to
369		261 to
291		262 to
385		212 to
430		268 to
349		235 to
240		233 to
206		89 to
328

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
0430338.82%
18187.38%
27136.43%
37246.53%
46515.87%
58037.24%
65855.28%
76265.65%
85775.21%
94714.25%
108147.34%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump41127203427363031221487
Joe Biden25556444954614971411643
Jo Jorgensen188544955405335483656125
Howie Hawkins34269575043552825191734
Tulsi Gabbard20047547167886563402123
Dan Crenshaw34668545039523336281617
Justin Amash25454454936483034435195
Amy Klobuchar3145555655566433630119
Bernie Sanders268354024263024365065141
Andrew Yang16141374947615773715884
Elizabeth Warren29141422537323736596475
John Kasich342586260577341221347
Jeb Bush329847180555726161227
Rand Paul24862473732415360674448
Ted Cruz35467362636503439463219

Number of bullet votes: 17 (2.30%).
Number of "approval" votes: 9 (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.

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