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As the 2016 election results continue to come in, it looks pretty clear that Hillary Clinton will win the popular vote but will lose the electoral college. I know this has happened before and usually by very small margins but I was wondering is what the least amount of popular votes a candidate could get but still have enough states to win the electoral college?
Assume we are talking roughly 125,000,000 votes (about how many were cast this election)

Ekadh Singh - Reinstate Monica
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celeriko
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    Unless there are additional rules I don't know about, you could lose the popular vote by literally 100% and end up as president if you could somehow convince the electors to vote for you "faithlessly". – Samthere Nov 10 '16 at 10:26
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    The electors in some States are bound by law to vote faithfully, but in theory your comment seems plausible. – Craig Tullis Nov 11 '16 at 08:44
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    http://www.npr.org/2016/11/02/500112248/how-to-win-the-presidency-with-27-percent-of-the-popular-vote – a25bedc5-3d09-41b8-82fb-ea6c353d75ae Nov 11 '16 at 12:14
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    Keep in mind however that even in the states where there is a law on the books that the Electoral members must vote the popular vote, there is little penalty for them not doing so. https://www.archives.gov/federal-register/electoral-college/electors.html#restrictions – JVC Nov 11 '16 at 19:56
  • I'm not sure you will get the exact answer, but, since cows vote, if you sort states by population and select the smallest N states that garner you more than half the electoral votes you should come close. You only need get a plurality in those states for the "loser" to win. – Hot Licks Nov 11 '16 at 22:31
  • https://www.quora.com/What-is-the-smallest-total-land-area-in-the-United-States-whose-100-vote-would-be-sufficient-to-elect-a-president doesn't answer this question, but presents a similar calculation to the ones below. –  Aug 19 '17 at 19:31

10 Answers10

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I don't know the exact number but, as a proportion of the votes cast, it's essentially 100%.

Here's how to calculate it. Find the set of states with the largest population of possible voters but no more than 268 electoral college votes. In all of those states, let candidate A win 100% of the vote, with 100% turnout. In every other state, have just one person vote, and have that person vote for candidate B.

This gives candidate A approximately 62,500,000 votes (assuming your electorate of 125M* and that A's states are about half the population) and candidate B gets at most 50 votes. So, in this admittedly highly contrived scenario, B wins the electoral college with something in the ballpark of 0.0001% of the popular vote.

Note that a tied electoral college allows an even lower proportion of the popular vote since the House could choose resolve the tie in favour of the third-place candidate. That candidate could, in principle, have won a single state by getting the only vote that was cast there, and not got any other votes in the rest of the country.

* It seems that the actual number of people who are eligible to vote is around 232 million though, of course, many of them don't vote at all.

David Richerby
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    Since electoral votes are not evenly distributed among the population, you could easily boost A’s portion to well above 62,500,000. But determining precisely what the highest you could get would be very tedious to do (start with California, then... —which incidentally is basically what Clinton did, without the B side being nearly as contrived), since brute force is the only approach available. – KRyan Nov 09 '16 at 23:22
  • Back in 2000, I did the math, and came out with 10 votes as the minimum (at the time, the ten largest states controlled just over 50% of the electoral vote). – Mark Nov 10 '16 at 00:55
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    @Mark The other answers seem to be saying you now need to win the eleven states for a college majority, so that would work if you want the minimum possible number of votes. If you want the minimum possible proportion of the vote, you don't necessarily want California. California wins you 55 EC votes but eats up a population of 40 million people. Winning WY, VT, DC, AK, ND, RI, SD, DE, NH, ME, MT, HI, WV, NE, ID gets you 54 EC votes for only about 15 million people. But, it required fifteen times as many people to vote for you while only giving three times as many votes to your opponent. – David Richerby Nov 10 '16 at 09:22
  • So that also wrecks your ratio, which means there's a trade-off to be made. This is one of the reasons why I didn't actually run the numbers myself. – David Richerby Nov 10 '16 at 09:22
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    But to win CA you dont need 40 million votes - you can do it with only one, as long as its the only vote recorded. So you could win 10 states withonly 10 votes, as long as no-one else votes in those states. – pauljwilliams Nov 10 '16 at 11:11
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    @PaulJWilliams My point is that, by winning California with only one vote, you deny your opponent the opportunity to get some large number of votes (40M if we imagine that everybody who lives in the state can vote). If your goal is to lose the popular vote by as big a margin as possible, you probably want to give those votes to your opponent. By winning Wyoming through Idaho with one vote each, you only deny your opponent fifteen million votes. – David Richerby Nov 10 '16 at 11:48
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    If you go the tied electoral college route, you might as well have a lot more political parties all winning different states. – David Starkey Nov 10 '16 at 15:17
  • @DavidStarkey Does that help? If nobody gets a majority of the college, Congress picks between the top three candidates. If there are only three parties, you can come in last place and still be in the top three; if there are many parties, you have to beat all but two of them, which seems harder. For example, if party A wins California, B wins Texas and C wins Florida, I need at least 30 college votes to beat C. But, with only three parties, I only need one college vote to get into the top three (e.g., one of the three districts of Nebraska.) – David Richerby Nov 10 '16 at 16:24
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    @DavidRicherby Perhaps I'm wrong, but if 50 parties each win 1 state, then the ones with the highest number of electoral votes will be potential options. If the scenario in this answer occurs for a state with very low electoral votes, then you could have the popular vote and not even be an option for Congress. Sure, 50 parties is unrealistic, but so is the scenario described in this answer. – David Starkey Nov 10 '16 at 16:38
  • @DavidStarkey OK but if 50 parties each win one state with one vote, then the winning party has one fiftieth (i.e., 2%) of the winning vote. In my solution, the winning party has much, much less than 1%. I totally agree that the scenarios we're discussing are completely unrealistic; they represent the worst possible cases, which are ridiculously unlikely. – David Richerby Nov 10 '16 at 18:22
  • @DavidRicherby The idea would be that you can ramp up the number of votes in that one specific state to virtually any number. 10 million votes for candidate A in Delaware to win 3 points, against the 1 vote for the party that ends up winning a higher point state and being the choice from Congress. It's not any different percent-wise, it's just an interesting alternative where the popular vote could even be excluded from a tie. – David Starkey Nov 10 '16 at 18:28
  • @DavidStarkey OK -- I see where you're going. – David Richerby Nov 10 '16 at 18:30
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CGP Grey has done the math in November 2011.

In the extreme case, assuming a constant turnout across all 50 states (and with the electoral votes distributed as in 2011)*, it could take only 22% of the popular vote to win the electoral college. This is theoretically achievable by winning with a one-vote margin the states with the highest ratio of electoral votes per capita.

* The number of electoral votes for each state changes after each census. They changed in December 2010 and will not change again until after the 2020 census.

Brythan
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Federico
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    Specifically if you win the states where the electoral vote per capital is the lowest with 50.0001% of the vote until you win the electoral college. Then assume the rest of the votes were cast for the other candidate. The advantage goes to smaller sates because of the default 2 delegates each state gets for their senators and minimum of one representative. Every representative after that waters down the value of each delegate. With Texas being about 750k per electoral vote, and Wyoming with a little less than 200k per vote. – QueueHammer Nov 09 '16 at 18:16
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    Seems legit and fair – PlasmaHH Nov 09 '16 at 19:28
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    You need the states with highest electoral votes per capita, to make each individual person's vote worth more of an electoral college vote. – Nij Nov 09 '16 at 21:02
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    David Richerby's answer and this answer should be combined as they both provide good answers but with different assumptions. This answer makes the more reasonable assumption that there is a significant number of people voting in each state while the other answer truly minimizes the popular vote. – Readin Nov 10 '16 at 04:11
  • @Nij: indeed. And related to this answer: https://politics.stackexchange.com/questions/26669/does-the-electoral-college-system-really-favor-low-population-areas?noredirect=1&lq=1 – the gods from engineering May 04 '19 at 19:07
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I've recalculated the data for the Electoral College stats as of 2016, taken from Wikipedia. The result is 22%, full explanation below.

You only need 270 Electoral Votes to become President. This can be achieved by winning the bottom 40 states (sorted by their population per EV) + DC, with 50.1% of the vote:

+----------------+-----+------------+------------+------------------------------+------------------------------------+---------------------+
|     State      | EVs | Population | Persons/EV | Minimum Votes To Win (50.1%) | Votes received by second candidate | Total EVs after win |
+----------------+-----+------------+------------+------------------------------+------------------------------------+---------------------+
| Wyoming        |   3 | 584,153    |     194718 |                       292661 |                             291492 |                   3 |
| Vermont        |   3 | 626,011    |     208670 |                       313632 |                             312379 |                   6 |
| Washington DC  |   3 | 658,893    |     219631 |                       330105 |                             328788 |                   9 |
| Alaska         |   3 | 737,732    |     245911 |                       369604 |                             368128 |                  12 |
| North Dakota   |   3 | 739,482    |     246494 |                       370480 |                             369002 |                  15 |
| Rhode Island   |   4 | 1,055,173  |     263793 |                       528642 |                             526531 |                  19 |
| South Dakota   |   3 | 853,175    |     284392 |                       427441 |                             425734 |                  22 |
| Delaware       |   3 | 935,614    |     311871 |                       468743 |                             466871 |                  25 |
| New Hampshire  |   4 | 1,326,813  |     331703 |                       664733 |                             662080 |                  29 |
| Maine          |   4 | 1,330,089  |     332522 |                       666375 |                             663714 |                  33 |
| Montana        |   3 | 1,023,579  |     341193 |                       512813 |                             510766 |                  36 |
| Hawaii         |   4 | 1,419,561  |     354890 |                       711200 |                             708361 |                  40 |
| West Virginia  |   5 | 1,850,326  |     370065 |                       927013 |                             923313 |                  45 |
| Nebraska       |   5 | 1,881,503  |     376301 |                       942633 |                             938870 |                  50 |
| Idaho          |   4 | 1,634,464  |     408616 |                       818866 |                             815598 |                  54 |
| New Mexico     |   5 | 2,085,572  |     417114 |                      1044872 |                            1040700 |                  59 |
| Nevada         |   6 | 2,839,099  |     473183 |                      1422389 |                            1416710 |                  65 |
| Kansas         |   6 | 2,904,021  |     484004 |                      1454915 |                            1449106 |                  71 |
| Utah           |   6 | 2,942,902  |     490484 |                      1474394 |                            1468508 |                  77 |
| Mississippi    |   6 | 2,984,926  |     497488 |                      1495448 |                            1489478 |                  83 |
| Arkansas       |   6 | 2,994,079  |     499013 |                      1500034 |                            1494045 |                  89 |
| Connecticut    |   7 | 3,596,677  |     513811 |                      1801935 |                            1794742 |                  96 |
| Iowa           |   6 | 3,107,126  |     517854 |                      1556670 |                            1550456 |                 102 |
| South Carolina |   9 | 4,832,482  |     536942 |                      2421073 |                            2411409 |                 111 |
| Alabama        |   9 | 4,849,377  |     538820 |                      2429538 |                            2419839 |                 120 |
| Minnesota      |  10 | 5,457,173  |     545717 |                      2734044 |                            2723129 |                 130 |
| Kentucky       |   8 | 4,413,457  |     551682 |                      2211142 |                            2202315 |                 138 |
| Oklahoma       |   7 | 3,878,051  |     554007 |                      1942904 |                            1935147 |                 145 |
| Oregon         |   7 | 3,970,239  |     567177 |                      1989090 |                            1981149 |                 152 |
| Wisconsin      |  10 | 5,757,564  |     575756 |                      2884540 |                            2873024 |                 162 |
| Louisiana      |   8 | 4,649,676  |     581210 |                      2329488 |                            2320188 |                 170 |
| Washington     |  12 | 7,061,530  |     588461 |                      3537827 |                            3523703 |                 182 |
| Colorado       |   9 | 5,355,856  |     595095 |                      2683284 |                            2672572 |                 191 |
| Tennessee      |  11 | 6,549,352  |     595396 |                      3281225 |                            3268127 |                 202 |
| Maryland       |  10 | 5,976,407  |     597641 |                      2994180 |                            2982227 |                 212 |
| Indiana        |  11 | 6,596,855  |     599714 |                      3305024 |                            3291831 |                 223 |
| Missouri       |  10 | 6,063,589  |     606359 |                      3037858 |                            3025731 |                 233 |
| Arizona        |  11 | 6,731,484  |     611953 |                      3372473 |                            3359011 |                 244 |
| Massachusetts  |  11 | 6,745,408  |     613219 |                      3379449 |                            3365959 |                 255 |
| Michigan       |  16 | 9,909,877  |     619367 |                      4964848 |                            4945029 |                 271 |
| Total votes    |     |            |            |                     69593583 |                           69315764 |                     |
+----------------+-----+------------+------------+------------------------------+------------------------------------+---------------------+

The candidate in the second place can then receive 100% of the vote in the 11 remaining states:

+----------------+-----+------------+------------+-----------------------+---------------------------------+
|     State      | EVs | Population | Persons/EV | Votes cast for winner | Votes cast for second candidate |
+----------------+-----+------------+------------+-----------------------+---------------------------------+
| Georgia        |  16 | 10,097,343 |     631084 |                     0 | 10097343                        |
| New Jersey     |  14 | 8,938,175  |     638441 |                     0 | 8,938,175                       |
| Pennsylvania   |  20 | 12,787,209 |     639360 |                     0 | 12,787,209                      |
| Virginia       |  13 | 8,326,289  |     640484 |                     0 | 8,326,289                       |
| Illinois       |  20 | 12,880,580 |     644029 |                     0 | 12,880,580                      |
| Ohio           |  18 | 11,594,163 |     644120 |                     0 | 11,594,163                      |
| North Carolina |  15 | 9,943,964  |     662931 |                     0 | 9,943,964                       |
| New York       |  29 | 19,746,227 |     680904 |                     0 | 19,746,227                      |
| Florida        |  29 | 19,893,297 |     685976 |                     0 | 19,893,297                      |
| California     |  55 | 38,802,500 |     705500 |                     0 | 38,802,500                      |
| Texas          |  38 | 26,956,958 |     709394 |                     0 | 26,956,958                      |
| Total votes    |     |            |            |                     0 | 179,966,705                     |
+----------------+-----+------------+------------+-----------------------+---------------------------------+
  • Total number of voters: 318,876,052
  • Total votes for winner: 69,593,583
  • Percentage of votes received by the winner: 22%

The numbers are skewed by the fact that not every resident is a citizen and not every citizen is over the age of 18. However the share of foreigners and non-adults is similar in most states, so the total percentage should be approximately correct. Also note that this scenario assumes that 100% of the population is going to vote.

@DavidRicherby correctly points out a an even more extreme scenario where only 1 person votes in the 40 states + DC. The reader may decide which option they find more probable :)

JonathanReez
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  • This answer seems to be assuming that every single person in the USA, including under-18s votes. (Or, equivalently, the final percentage assumes that the same percentage of the population votes in every state.) But this doesn't work out: for example, one would expect states with different racial compositions to have different proportions of people under 18 because of different family sizes (e.g., 24.2% of white people are under 20, compared to 31.6% of black people, according to Wikipedia). – David Richerby Nov 09 '16 at 18:56
  • But +1 for running the analysis. I'm not sure if your scenario, which features lots of illegal voting by under-18s is more or less realistic than my scenario. They're both pretty ridiculous. :-) – David Richerby Nov 09 '16 at 18:57
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    @DavidRicherby I agree, but I couldn't quickly find the data for the number of registered voters per state. I'll remove the part about your scenario being less realistic :) – JonathanReez Nov 09 '16 at 19:01
  • Fair enough. :-) – David Richerby Nov 09 '16 at 19:03
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    This also assumes that A. Each state hands out electoral votes using popular vote, and B. The popular vote gets 100% of the state's electoral votes. IIRC those are both true in most states, but not all. – BlueRaja - Danny Pflughoeft Nov 09 '16 at 21:32
  • @BlueRaja-DannyPflughoeft some states give out Votes based on Congressional districts. In that case you need to make sure you get 50.1% of the vote in each of them, which doesn't change the result. – JonathanReez Nov 09 '16 at 22:40
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    @JonathanReez: It does change the result, because the districts will almost certainly have different people-per-electoral-vote ratios than the state. It might be optimal to include some districts but not others to get the lowest percentage. – BlueRaja - Danny Pflughoeft Nov 09 '16 at 23:39
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    I stumbled across some data for the estimated numbers of people who are eligible to vote in each state, which would make this more accurate – David Richerby Nov 10 '16 at 12:06
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    You don't need to win 50.1% of the population or even registered voters. You just need to win 50.1% of the votes cast. – paparazzo Nov 10 '16 at 14:29
  • @paparazzo: yeah, that's why this answer gets the same percentage as in Federico's (CGP Grey's actually). – the gods from engineering May 04 '19 at 19:02
  • Have you taken into account that some states divide their EVs proportionally according to the poll within that state? – komodosp Nov 07 '19 at 09:44
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84,572 votes

Assuming you're a third party longshot candidate and there are no other longshot candidates.

You only need to win one state to get elected. The easiest state to win in terms of votes is Wyoming. Assuming you're a third party candidate and you win Wyoming with 34% of the vote, you can win with only (248,742 * .34 = 84,572) votes. I got the 248k number by adding up the results for the 2016 election of the top candidates from a quick Google search.

You then need a map that makes the two main candidates not sweep the electoral college, such as this one:

enter image description here

Then, once the electoral college fails to vote someone in, the top three scoring members are decided on by the House as detailed by FiveThirtyEight's Benjamin Morris

Now, if for example both mainstream candidates were incredibly hated by everyone in the House (hypothetically of course, since that could never possibly happen) if you got enough of them to vote for you, well, you're the new president! Hip hip! Hurray!!

In theory you only need 1 electoral vote, but the only way to get a single vote without a faithless elector is to win a district of Nebraska or Maine, both of which require more popular votes than Wyoming.

corsiKa
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    This is like code golf for Politics.SE! – Golden Cuy Nov 10 '16 at 01:48
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    Some thought this might happen if Evan McMullin won Utah in the 2016 US Presidential election. FiveThirtyEight had an article on how he could win the Presidency via Utah at http://fivethirtyeight.com/features/how-evan-mcmullin-could-win-utah-and-the-presidency/ – WBT Nov 10 '16 at 23:23
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    While this is clever, I don't think it meets the request of winning the electoral college. It does win the presidency, but only in the House of Representatives. – Ross Millikan Nov 11 '16 at 01:59
  • That's a surprisingly realistic electoral map! The unrealistic part of it is the person who only got enough votes to win one state (and only 34% of the vote in that state) being the person chosen by the house. – Daniel Nov 11 '16 at 21:09
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    @Daniel You didn't read my penultimate paragraph. – corsiKa Nov 12 '16 at 06:06
  • @RossMillikan Stack Exchange reminded me of this (which has obviously gained some attention due to current events) and it occurs to me that "winning" the electoral college couldn't possibly mean anything but winning the presidency! If you emerge from the electoral college on the same footing as all the other candidates to go through to the House, I fail to see how that isn't "won"! – corsiKa Jan 20 '21 at 05:18
  • @corsiKa: It appears you meant this comment in response to my comment on another answer (the one with a title that begins 1 vote). I stand by my comment that the question was winning the electoral college, regardless of the final result of the presidency. Of course, in 2016 we thought those were the same thing unless the electoral college was a tie. Emerging from the electoral college on the same standing as the others is a tie there. It is a good point that if nobody wins a clear majority in the electoral college, it is a tie between the top three. – Ross Millikan Jan 20 '21 at 05:43
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1 vote (0.000000685367% of the popular vote)

Maine and Nebraska both award their electoral college votes according to the winner of each of their congressional districts. Therefore, a candidate could win a single electoral college vote by winning one district in either state.

Of course 270 or more elector votes are needed to win the presidency but there are scenarios that exist where one candidate could win 269, another 268, and then a third candidate win one of the districts above and be awarded a single elector. When no candidate candidate achieves the 270 threshold, the 50 state delegations in the House are to choose between the top three electoral vote winners which would include the winner of the single district.

The smallest of those districts is Nebraska's 3rd district with 608,438 people, with an estimated 403,803 registered voters (calculated as 1/3 of the total registered voters in the Nebraska). Since there are approximately 146,311,000 registered voters in the U.S., winning this district with the single vote cast would give a popular vote percentage of 1 / (146,311,000 - 403,802) = 0.000000685367%

Jaquez
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    While this is clever, I don't think it meets the request of winning the electoral college. It does win the presidency, but only in the House of Representatives. – Ross Millikan Nov 11 '16 at 01:59
  • Fair enough, although I suspect that winning the presidency was what the question was really about, on the premise that winning the electoral college is (typically) how that is done. – Jaquez Nov 11 '16 at 11:58
  • How do you win Maine or Nebraska's loner-districts with just a single vote? There's not two other people voting in the entire state? – corsiKa Nov 12 '16 at 06:08
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    It's certainly not as realistic as the scenario in your answer. It is really just the logical extreme extrapolated from your comment about getting one electoral vote. I assumed every registered voter in the US voted except NE3 where only 1 person voted. The percentage would have been smaller if I had used WY but you did an excellent job of exploring that possibility so I took a different approach. I really felt the premise of the question indicated that we were looking for possibilities, not plausibilities. – Jaquez Nov 12 '16 at 07:19
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    With faithless electors, you could win with 0 popular votes. – endolith Apr 01 '17 at 14:22
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A related question is: How many electors can you get with a minority of the public vote? Answer: All but three electors. You can win 49 states with a 1 vote majority each, and then lose the 50th state with 3 electors with a huge majority for the opponent.

And you can win without shenanigans with only 11 votes by getting one single vote in the 11 largest states (with the most electors), if nobody else votes in these states at all. If everyone votes and 100% for the opponent in the other 39 states, that would give the smallest possible percentage of the public vote to become president.

gnasher729
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100%

In principle the electors can completely ignore the popular results and vote for anyone they like, even people not in the party that selected them.

klojj
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If there were numerous parties (instead of two) and the vote was almost evenly split, then one party slightly ahead in every state could win. There is no lower limit, it just depends on the number of parties. (Of course the system is rigged in favour of two parties so this would never happen.)

Keith McClary
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Obtain the minimum points to win by 1 vote on each state (51%), then lose every other point with 0 votes (0%). So about 25% of the popular vote.

gia
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You can win the electoral college and thus the presidency without accruing a single popular vote. It could still happen in the current election.

If Trump were to die before the electoral college casts their votes, then I am not sure of the elector's voting obligations. Maybe they would be obligated to vote for Pence. Just to be sure, hypothesize that Pence also dies. Then I am pretty sure that the electors are no longer obligated and could vote for whomever they wish.

They probably would not vote for Clinton or any of the other candidates listed on the ballot. So in that situation, the winner would be someone who did not receive a single electoral vote.

emory
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