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 Trump167
Joe Biden195
Jo Jorgensen168
Howie Hawkins22
Tulsi Gabbard23
Dan Crenshaw9
Justin Amash39
Amy Klobuchar7
Bernie Sanders122
Andrew Yang36
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul25
Ted Cruz9
TOTAL:859

The winner is Joe Biden with 22.7% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump239
Joe Biden337
Jo Jorgensen345
Howie Hawkins138
Tulsi Gabbard260
Dan Crenshaw112
Justin Amash259
Amy Klobuchar148
Bernie Sanders366
Andrew Yang376
Elizabeth Warren286
John Kasich106
Jeb Bush76
Rand Paul285
Ted Cruz166
Ballots Cast:859

The winner is Andrew Yang with 43.8% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 12 rounds:

Round 1:

Donald Trump143
Joe Biden63
Jo Jorgensen144
Howie Hawkins31
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash67
Amy Klobuchar11
Bernie Sanders168
Andrew Yang69
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul37
Ted Cruz19

Jeb Bush eliminated in this round.

Round 2:

Donald Trump143
Joe Biden63
Jo Jorgensen144
Howie Hawkins31
Tulsi Gabbard23
Dan Crenshaw11
Justin Amash68
Amy Klobuchar11
Bernie Sanders169
Andrew Yang69
Elizabeth Warren54
John Kasich14
Rand Paul37
Ted Cruz22

Eliminated in this round:

Round 3:

Donald Trump144
Joe Biden68
Jo Jorgensen149
Howie Hawkins33
Tulsi Gabbard24
Justin Amash68
Bernie Sanders170
Andrew Yang71
Elizabeth Warren55
John Kasich14
Rand Paul38
Ted Cruz25

John Kasich eliminated in this round.

Round 4:

Donald Trump144
Joe Biden70
Jo Jorgensen149
Howie Hawkins33
Tulsi Gabbard26
Justin Amash69
Bernie Sanders171
Andrew Yang73
Elizabeth Warren57
Rand Paul41
Ted Cruz26

Eliminated in this round:

Round 5:

Donald Trump153
Joe Biden74
Jo Jorgensen160
Howie Hawkins34
Justin Amash74
Bernie Sanders175
Andrew Yang77
Elizabeth Warren58
Rand Paul54

Howie Hawkins eliminated in this round.

Round 6:

Donald Trump153
Joe Biden78
Jo Jorgensen161
Justin Amash74
Bernie Sanders199
Andrew Yang80
Elizabeth Warren60
Rand Paul54

Rand Paul eliminated in this round.

Round 7:

Donald Trump172
Joe Biden78
Jo Jorgensen174
Justin Amash92
Bernie Sanders200
Andrew Yang82
Elizabeth Warren61

Elizabeth Warren eliminated in this round.

Round 8:

Donald Trump172
Joe Biden92
Jo Jorgensen176
Justin Amash93
Bernie Sanders233
Andrew Yang93

Joe Biden eliminated in this round.

Round 9:

Donald Trump175
Jo Jorgensen194
Justin Amash96
Bernie Sanders273
Andrew Yang121

Justin Amash eliminated in this round.

Round 10:

Donald Trump178
Jo Jorgensen275
Bernie Sanders276
Andrew Yang130

Andrew Yang eliminated in this round.

Round 11:

Donald Trump183
Jo Jorgensen306
Bernie Sanders370

Donald Trump eliminated in this round.

Round 12:

Jo Jorgensen448
Bernie Sanders411

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 Trump0/14/0 359 to
500		204 to
655		332 to
527		262 to
597		295 to
564		225 to
634		328 to
531		347 to
512		284 to
575		354 to
505		317 to
542		317 to
542		209 to
650		285 to
574
Joe Biden7/7/0500 to
359		 371 to
488		435 to
424		362 to
497		460 to
399		405 to
454		448 to
411		350 to
509		244 to
615		373 to
486		454 to
405		465 to
394		423 to
436		466 to
393
Jo Jorgensen13/1/0655 to
204		488 to
371		 560 to
299		486 to
373		612 to
247		518 to
341		512 to
347		448 to
411		424 to
435		476 to
383		587 to
272		618 to
241		587 to
272		634 to
225
Howie Hawkins6/8/0527 to
332		424 to
435		299 to
560		 334 to
525		469 to
390		390 to
469		425 to
434		355 to
504		285 to
574		431 to
428		443 to
416		469 to
390		422 to
437		493 to
366
Tulsi Gabbard12/2/0597 to
262		497 to
362		373 to
486		525 to
334		 596 to
263		491 to
368		577 to
282		446 to
413		416 to
443		503 to
356		614 to
245		621 to
238		502 to
357		588 to
271
Dan Crenshaw4/10/0564 to
295		399 to
460		247 to
612		390 to
469		263 to
596		 335 to
524		411 to
448		361 to
498		313 to
546		405 to
454		449 to
410		480 to
379		373 to
486		513 to
346
Justin Amash10/4/0634 to
225		454 to
405		341 to
518		469 to
390		368 to
491		524 to
335		 475 to
384		424 to
435		390 to
469		451 to
408		569 to
290		606 to
253		558 to
301		627 to
232
Amy Klobuchar7/7/0531 to
328		411 to
448		347 to
512		434 to
425		282 to
577		448 to
411		384 to
475		 373 to
486		256 to
603		427 to
432		527 to
332		529 to
330		448 to
411		518 to
341
Bernie Sanders11/3/0512 to
347		509 to
350		411 to
448		504 to
355		413 to
446		498 to
361		435 to
424		486 to
373		 376 to
483		497 to
362		513 to
346		515 to
344		464 to
395		509 to
350
Andrew Yang14/0/0575 to
284		615 to
244		435 to
424		574 to
285		443 to
416		546 to
313		469 to
390		603 to
256		483 to
376		 590 to
269		638 to
221		626 to
233		517 to
342		579 to
280
Elizabeth Warren8/6/0505 to
354		486 to
373		383 to
476		428 to
431		356 to
503		454 to
405		408 to
451		432 to
427		362 to
497		269 to
590		 488 to
371		504 to
355		445 to
414		498 to
361
John Kasich3/11/0542 to
317		405 to
454		272 to
587		416 to
443		245 to
614		410 to
449		290 to
569		332 to
527		346 to
513		221 to
638		371 to
488		 538 to
321		426 to
433		543 to
316
Jeb Bush2/12/0542 to
317		394 to
465		241 to
618		390 to
469		238 to
621		379 to
480		253 to
606		330 to
529		344 to
515		233 to
626		355 to
504		321 to
538		 373 to
486		517 to
342
Rand Paul7/7/0650 to
209		436 to
423		272 to
587		437 to
422		357 to
502		486 to
373		301 to
558		411 to
448		395 to
464		342 to
517		414 to
445		433 to
426		486 to
373		 654 to
205
Ted Cruz1/13/0574 to
285		393 to
466		225 to
634		366 to
493		271 to
588		346 to
513		232 to
627		341 to
518		350 to
509		280 to
579		361 to
498		316 to
543		342 to
517		205 to
654

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 Trump2431 2.8
Joe Biden2984 3.5
Jo Jorgensen3756 4.4
Howie Hawkins2165 2.5
Tulsi Gabbard3161 3.7
Dan Crenshaw2032 2.4
Justin Amash3205 3.7
Amy Klobuchar2260 2.6
Bernie Sanders3880 4.5
Andrew Yang4098 4.8
Elizabeth Warren3233 3.8
John Kasich1896 2.2
Jeb Bush1743 2.0
Rand Paul3133 3.6
Ted Cruz2218 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 Trump2431
Joe Biden2984
Jo Jorgensen3756
Howie Hawkins2165
Tulsi Gabbard3161
Dan Crenshaw2032
Justin Amash3205
Amy Klobuchar2260
Bernie Sanders3880
Andrew Yang4098
Elizabeth Warren3233
John Kasich1896
Jeb Bush1743
Rand Paul3133
Ted Cruz2218

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 Yang570
Bernie Sanders525

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 Trump0/14/0 305 to
437		189 to
532		307 to
359		239 to
457		245 to
265		209 to
457		308 to
385		311 to
467		254 to
529		320 to
427		303 to
327		299 to
312		180 to
402		224 to
235
Joe Biden9/5/0437 to
305		 353 to
391		387 to
255		322 to
411		440 to
268		379 to
332		356 to
172		196 to
372		177 to
475		225 to
304		409 to
199		430 to
208		400 to
382		433 to
297
Jo Jorgensen12/2/0532 to
189		391 to
353		 431 to
175		371 to
293		481 to
143		323 to
217		411 to
259		354 to
399		301 to
418		380 to
357		452 to
191		476 to
173		419 to
211		514 to
162
Howie Hawkins4/10/0359 to
307		255 to
387		175 to
431		 167 to
429		283 to
265		204 to
363		240 to
287		164 to
411		133 to
495		216 to
337		266 to
267		293 to
276		250 to
385		317 to
307
Tulsi Gabbard11/3/0457 to
239		411 to
322		293 to
371		429 to
167		 427 to
175		320 to
296		410 to
207		340 to
383		269 to
403		362 to
327		435 to
161		455 to
169		335 to
296		440 to
220
Dan Crenshaw2/12/0265 to
245		268 to
440		143 to
481		265 to
283		175 to
427		 146 to
375		238 to
329		259 to
456		203 to
500		265 to
403		243 to
265		254 to
263		152 to
362		234 to
223
Justin Amash8/6/0457 to
209		332 to
379		217 to
323		363 to
204		296 to
320		375 to
146		 324 to
280		316 to
410		261 to
430		322 to
376		355 to
191		394 to
179		334 to
222		424 to
176
Amy Klobuchar6/8/0385 to
308		172 to
356		259 to
411		287 to
240		207 to
410		329 to
238		280 to
324		 170 to
421		115 to
511		165 to
356		296 to
191		333 to
211		305 to
385		359 to
294
Bernie Sanders13/1/0467 to
311		372 to
196		399 to
354		411 to
164		383 to
340		456 to
259		410 to
316		421 to
170		 289 to
334		333 to
155		439 to
201		457 to
217		415 to
361		464 to
291
Andrew Yang14/0/0529 to
254		475 to
177		418 to
301		495 to
133		403 to
269		500 to
203		430 to
261		511 to
115		334 to
289		 407 to
192		522 to
133		538 to
148		433 to
305		504 to
243
Elizabeth Warren10/4/0427 to
320		304 to
225		357 to
380		337 to
216		327 to
362		403 to
265		376 to
322		356 to
165		155 to
333		192 to
407		 379 to
189		400 to
219		383 to
372		413 to
305
John Kasich5/9/0327 to
303		199 to
409		191 to
452		267 to
266		161 to
435		265 to
243		191 to
355		191 to
296		201 to
439		133 to
522		189 to
379		 238 to
164		231 to
365		290 to
268
Jeb Bush2/12/0312 to
299		208 to
430		173 to
476		276 to
293		169 to
455		263 to
254		179 to
394		211 to
333		217 to
457		148 to
538		219 to
400		164 to
238		 181 to
375		255 to
262
Rand Paul7/7/0402 to
180		382 to
400		211 to
419		385 to
250		296 to
335		362 to
152		222 to
334		385 to
305		361 to
415		305 to
433		372 to
383		365 to
231		375 to
181		 375 to
110
Ted Cruz2/12/0235 to
224		297 to
433		162 to
514		307 to
317		220 to
440		223 to
234		176 to
424		294 to
359		291 to
464		243 to
504		305 to
413		268 to
290		262 to
255		110 to
375

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
0486537.76%
19817.61%
28346.47%
38596.67%
48016.22%
59467.34%
67115.52%
77325.68%
86855.32%
95454.23%
109267.19%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump467362738303932342920107
Joe Biden29164495462716282542149
Jo Jorgensen219676266506538524658136
Howie Hawkins37981646155653729282139
Tulsi Gabbard22452638283987775463029
Dan Crenshaw39481655949613742331721
Justin Amash294695559465737384852104
Amy Klobuchar34762628266775746361311
Bernie Sanders290394534323934485976163
Andrew Yang18351445455787080836794
Elizabeth Warren32358472946404948697278
John Kasich3846969747283482916510
Jeb Bush36810280916967312214510
Rand Paul29271554542506365715253
Ted Cruz41079473144563942533622

Number of bullet votes: 19 (2.21%).
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.

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