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 Trump156
Joe Biden189
Jo Jorgensen164
Howie Hawkins21
Tulsi Gabbard22
Dan Crenshaw9
Justin Amash39
Amy Klobuchar6
Bernie Sanders116
Andrew Yang35
Elizabeth Warren24
John Kasich8
Jeb Bush5
Rand Paul24
Ted Cruz9
TOTAL:827

The winner is Joe Biden with 22.9% of the vote

Approval Vote Count

Approval vote totals:

CandidateNumber of Votes
Donald Trump226
Joe Biden323
Jo Jorgensen338
Howie Hawkins136
Tulsi Gabbard251
Dan Crenshaw110
Justin Amash256
Amy Klobuchar144
Bernie Sanders353
Andrew Yang366
Elizabeth Warren282
John Kasich103
Jeb Bush69
Rand Paul278
Ted Cruz158
Ballots Cast:827

The winner is Andrew Yang with 44.3% of the vote

Instant Runoff (Ranked Choice) Counts

Instant Runoff required 14 rounds:

Round 1:

Donald Trump133
Joe Biden61
Jo Jorgensen140
Howie Hawkins30
Tulsi Gabbard21
Dan Crenshaw11
Justin Amash67
Amy Klobuchar10
Bernie Sanders161
Andrew Yang66
Elizabeth Warren54
John Kasich13
Jeb Bush6
Rand Paul36
Ted Cruz18

Jeb Bush eliminated in this round.

Round 2:

Donald Trump133
Joe Biden61
Jo Jorgensen140
Howie Hawkins30
Tulsi Gabbard21
Dan Crenshaw11
Justin Amash68
Amy Klobuchar10
Bernie Sanders162
Andrew Yang66
Elizabeth Warren54
John Kasich14
Rand Paul36
Ted Cruz21

Amy Klobuchar eliminated in this round.

Round 3:

Donald Trump133
Joe Biden65
Jo Jorgensen141
Howie Hawkins32
Tulsi Gabbard21
Dan Crenshaw11
Justin Amash68
Bernie Sanders163
Andrew Yang67
Elizabeth Warren55
John Kasich14
Rand Paul36
Ted Cruz21

Dan Crenshaw eliminated in this round.

Round 4:

Donald Trump134
Joe Biden65
Jo Jorgensen145
Howie Hawkins32
Tulsi Gabbard22
Justin Amash68
Bernie Sanders163
Andrew Yang68
Elizabeth Warren55
John Kasich14
Rand Paul37
Ted Cruz24

John Kasich eliminated in this round.

Round 5:

Donald Trump134
Joe Biden67
Jo Jorgensen145
Howie Hawkins32
Tulsi Gabbard24
Justin Amash69
Bernie Sanders164
Andrew Yang70
Elizabeth Warren57
Rand Paul40
Ted Cruz25

Tulsi Gabbard eliminated in this round.

Round 6:

Donald Trump134
Joe Biden69
Jo Jorgensen153
Howie Hawkins32
Justin Amash74
Bernie Sanders166
Andrew Yang74
Elizabeth Warren58
Rand Paul42
Ted Cruz25

Ted Cruz eliminated in this round.

Round 7:

Donald Trump142
Joe Biden71
Jo Jorgensen156
Howie Hawkins33
Justin Amash74
Bernie Sanders167
Andrew Yang74
Elizabeth Warren58
Rand Paul52

Howie Hawkins eliminated in this round.

Round 8:

Donald Trump142
Joe Biden75
Jo Jorgensen157
Justin Amash74
Bernie Sanders191
Andrew Yang77
Elizabeth Warren59
Rand Paul52

Rand Paul eliminated in this round.

Round 9:

Donald Trump161
Joe Biden75
Jo Jorgensen169
Justin Amash91
Bernie Sanders192
Andrew Yang79
Elizabeth Warren60

Elizabeth Warren eliminated in this round.

Round 10:

Donald Trump161
Joe Biden88
Jo Jorgensen171
Justin Amash92
Bernie Sanders225
Andrew Yang90

Joe Biden eliminated in this round.

Round 11:

Donald Trump163
Jo Jorgensen188
Justin Amash95
Bernie Sanders264
Andrew Yang117

Justin Amash eliminated in this round.

Round 12:

Donald Trump166
Jo Jorgensen268
Bernie Sanders267
Andrew Yang126

Andrew Yang eliminated in this round.

Round 13:

Donald Trump171
Jo Jorgensen298
Bernie Sanders358

Donald Trump eliminated in this round.

Round 14:

Jo Jorgensen432
Bernie Sanders395

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 Trump0/14/0 344 to
483		191 to
636		316 to
511		248 to
579		277 to
550		209 to
618		313 to
514		331 to
496		270 to
557		338 to
489		300 to
527		300 to
527		193 to
634		267 to
560
Joe Biden7/7/0483 to
344		 358 to
469		420 to
407		349 to
478		443 to
384		389 to
438		431 to
396		338 to
489		234 to
593		354 to
473		437 to
390		448 to
379		407 to
420		448 to
379
Jo Jorgensen13/1/0636 to
191		469 to
358		 543 to
284		469 to
358		592 to
235		497 to
330		492 to
335		432 to
395		407 to
420		455 to
372		566 to
261		598 to
229		568 to
259		614 to
213
Howie Hawkins5/9/0511 to
316		407 to
420		284 to
543		 318 to
509		450 to
377		372 to
455		405 to
422		341 to
486		268 to
559		409 to
418		424 to
403		451 to
376		404 to
423		474 to
353
Tulsi Gabbard12/2/0579 to
248		478 to
349		358 to
469		509 to
318		 575 to
252		469 to
358		552 to
275		428 to
399		400 to
427		479 to
348		587 to
240		598 to
229		480 to
347		569 to
258
Dan Crenshaw4/10/0550 to
277		384 to
443		235 to
592		377 to
450		252 to
575		 316 to
511		396 to
431		349 to
478		298 to
529		388 to
439		430 to
397		463 to
364		356 to
471		496 to
331
Justin Amash10/4/0618 to
209		438 to
389		330 to
497		455 to
372		358 to
469		511 to
316		 460 to
367		411 to
416		375 to
452		433 to
394		548 to
279		587 to
240		540 to
287		610 to
217
Amy Klobuchar7/7/0514 to
313		396 to
431		335 to
492		422 to
405		275 to
552		431 to
396		367 to
460		 358 to
469		243 to
584		406 to
421		504 to
323		507 to
320		428 to
399		500 to
327
Bernie Sanders11/3/0496 to
331		489 to
338		395 to
432		486 to
341		399 to
428		478 to
349		416 to
411		469 to
358		 359 to
468		472 to
355		491 to
336		495 to
332		444 to
383		489 to
338
Andrew Yang14/0/0557 to
270		593 to
234		420 to
407		559 to
268		427 to
400		529 to
298		452 to
375		584 to
243		468 to
359		 567 to
260		615 to
212		605 to
222		494 to
333		559 to
268
Elizabeth Warren9/5/0489 to
338		473 to
354		372 to
455		418 to
409		348 to
479		439 to
388		394 to
433		421 to
406		355 to
472		260 to
567		 470 to
357		486 to
341		429 to
398		479 to
348
John Kasich3/11/0527 to
300		390 to
437		261 to
566		403 to
424		240 to
587		397 to
430		279 to
548		323 to
504		336 to
491		212 to
615		357 to
470		 518 to
309		408 to
419		523 to
304
Jeb Bush2/12/0527 to
300		379 to
448		229 to
598		376 to
451		229 to
598		364 to
463		240 to
587		320 to
507		332 to
495		222 to
605		341 to
486		309 to
518		 357 to
470		498 to
329
Rand Paul7/7/0634 to
193		420 to
407		259 to
568		423 to
404		347 to
480		471 to
356		287 to
540		399 to
428		383 to
444		333 to
494		398 to
429		419 to
408		470 to
357		 634 to
193
Ted Cruz1/13/0560 to
267		379 to
448		213 to
614		353 to
474		258 to
569		331 to
496		217 to
610		327 to
500		338 to
489		268 to
559		348 to
479		304 to
523		329 to
498		193 to
634

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 Trump2292 2.8
Joe Biden2875 3.5
Jo Jorgensen3645 4.4
Howie Hawkins2082 2.5
Tulsi Gabbard3028 3.7
Dan Crenshaw1956 2.4
Justin Amash3129 3.8
Amy Klobuchar2167 2.6
Bernie Sanders3738 4.5
Andrew Yang3963 4.8
Elizabeth Warren3135 3.8
John Kasich1814 2.2
Jeb Bush1646 2.0
Rand Paul3027 3.7
Ted Cruz2127 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 Trump2292
Joe Biden2875
Jo Jorgensen3645
Howie Hawkins2082
Tulsi Gabbard3028
Dan Crenshaw1956
Justin Amash3129
Amy Klobuchar2167
Bernie Sanders3738
Andrew Yang3963
Elizabeth Warren3135
John Kasich1814
Jeb Bush1646
Rand Paul3027
Ted Cruz2127

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 Yang552
Bernie Sanders503

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 Trump0/14/0 290 to
421		175 to
517		292 to
346		225 to
441		228 to
255		194 to
445		293 to
372		296 to
452		239 to
514		305 to
413		287 to
317		284 to
303		166 to
391		210 to
229
Joe Biden9/5/0421 to
290		 339 to
379		372 to
246		310 to
398		424 to
259		362 to
325		341 to
165		189 to
358		168 to
460		213 to
298		393 to
190		416 to
197		385 to
371		417 to
286
Jo Jorgensen12/2/0517 to
175		379 to
339		 419 to
169		363 to
281		469 to
132		309 to
212		399 to
250		345 to
382		294 to
407		366 to
346		440 to
181		463 to
160		405 to
199		497 to
150
Howie Hawkins4/9/1346 to
292		246 to
372		169 to
419		 163 to
416		275 to
256		196 to
357		230 to
278		157 to
393		127 to
483		207 to
326		258 to
258		282 to
264		242 to
373		305 to
294
Tulsi Gabbard11/3/0441 to
225		398 to
310		281 to
363		416 to
163		 411 to
169		306 to
292		395 to
204		328 to
368		260 to
392		349 to
319		422 to
158		438 to
161		321 to
287		423 to
209
Dan Crenshaw2/12/0255 to
228		259 to
424		132 to
469		256 to
275		169 to
411		 137 to
369		228 to
319		250 to
437		193 to
485		256 to
389		236 to
255		248 to
250		145 to
352		223 to
213
Justin Amash8/6/0445 to
194		325 to
362		212 to
309		357 to
196		292 to
306		369 to
137		 317 to
268		309 to
392		256 to
415		315 to
363		348 to
181		385 to
166		327 to
212		413 to
164
Amy Klobuchar6/8/0372 to
293		165 to
341		250 to
399		278 to
230		204 to
395		319 to
228		268 to
317		 163 to
403		109 to
495		158 to
344		288 to
182		321 to
200		296 to
373		344 to
282
Bernie Sanders13/1/0452 to
296		358 to
189		382 to
345		393 to
157		368 to
328		437 to
250		392 to
309		403 to
163		 275 to
324		317 to
149		421 to
191		441 to
205		397 to
350		447 to
280
Andrew Yang14/0/0514 to
239		460 to
168		407 to
294		483 to
127		392 to
260		485 to
193		415 to
256		495 to
109		324 to
275		 395 to
187		508 to
124		522 to
138		419 to
295		489 to
231
Elizabeth Warren10/4/0413 to
305		298 to
213		346 to
366		326 to
207		319 to
349		389 to
256		363 to
315		344 to
158		149 to
317		187 to
395		 366 to
179		388 to
207		371 to
361		399 to
292
John Kasich4/9/1317 to
287		190 to
393		181 to
440		258 to
258		158 to
422		255 to
236		181 to
348		182 to
288		191 to
421		124 to
508		179 to
366		 230 to
153		223 to
354		277 to
258
Jeb Bush2/12/0303 to
284		197 to
416		160 to
463		264 to
282		161 to
438		250 to
248		166 to
385		200 to
321		205 to
441		138 to
522		207 to
388		153 to
230		 170 to
363		244 to
254
Rand Paul7/7/0391 to
166		371 to
385		199 to
405		373 to
242		287 to
321		352 to
145		212 to
327		373 to
296		350 to
397		295 to
419		361 to
371		354 to
223		363 to
170		 360 to
102
Ted Cruz2/12/0229 to
210		286 to
417		150 to
497		294 to
305		209 to
423		213 to
223		164 to
413		282 to
344		280 to
447		231 to
489		292 to
399		258 to
277		254 to
244		102 to
360

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
0469037.81%
19487.64%
27996.44%
38406.77%
47546.08%
59017.26%
66845.51%
77035.67%
86585.30%
95324.29%
108967.22%

Now let's break down the above by candidate:

Candidate \ N Stars012345678910
Donald Trump455352537293831322618101
Joe Biden27862475462695778522048
Jo Jorgensen210635963476437514258133
Howie Hawkins36578626052613628281938
Tulsi Gabbard21551618279947471452827
Dan Crenshaw38378615743573741321721
Justin Amash278675258455336374752102
Amy Klobuchar33660597963735544351310
Bernie Sanders280394432303431475776157
Andrew Yang17349415452767078806490
Elizabeth Warren30956472943364547667178
John Kasich3726866716582462616510
Jeb Bush357997891636331181359
Rand Paul28069534439476163695052
Ted Cruz39974442942543742503620

Number of bullet votes: 18 (2.18%).
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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