Challenge: in any election, cause the Dems to win while losing the PV...

[SingingAnalyst]

...by flipping the fewest number of votes.

It is harder than it seems. Not only has every election since 1824 won without a PV plurality (1876, 1888, 2000, or 2016) been won by a Republican, but it is very easy to flip the following elections to the GOP with just a few thousand votes: 1916 (less than 2000 votes in CA), 1948 (4000 in OH, 9000 in CA, 17000 in IL), 1976 (5600 in OH, 3700 in HI). (Dems still would have won the PV in each case).

The smallest number I can come up with in any fairly recent election is 59,301. In 2004, if 59,301 Bush voters in OH had voted Kerry instead, we would have this:

Kerry/Edwards 48.31% / 272 EV
Bush/Cheney 50.68% / 266 EV

(Flipping IA, NV, NM, and SD requires 60,447 votes--slightly more).

If we go all the way back to 1884 and flip 28,790 Cleveland votes in PA to Blaine, we get the same map as IRL, but Blaine wins the national PV by 1 vote.

Can anyone do it with fewer than 28,790 votes (for any election)?

[Kingpoleon]

2,553 voters in New York in 1844. Also New York in 1880 - 10,517 Republicans to the Democrats. Another 11,000 third party voters to the Republicans in another state to maintain the PV loss. 20,517 votes flipped.

[SingingAnalyst]

2,553 voters in New York in 1844. Also New York in 1880 - 10,517 Republicans to the Democrats. Another 11,000 third party voters to the Republicans in another state to maintain the PV loss. 20,517 votes flipped.

Kingpoleon, thank you for accepting my challenge! I had forgotten about all the close elections from 1876 - 1892.

Based on your idea, I found two ways to do 1880 with fewer vote flips:

(1) Flip 10,517 NY votes from R to D as you said, giving the Dems a 190-179 EV majority and (unfortunately for this exercise) as you pointed out gives the Dems a PV plurailty of 11,964. So, simply flip 5,983 D votes to R in TX (a large, safe D state). This gives Hancock (D) the win and Garfield (R) a 2-vote national PV plurality-- by flipping 10,517 + 5,983 = 16,500 votes.

I found a way to do it with even fewer flips, however.

(2) Flip from R to D 3,322 votes in IN, 333 in OR, 1,331 in CT, 2,030 in NH, and 1,402 in CO. This gives Hancock (D) a 187-182 EV win, but also a 7,766 national PV plurality. So again flip 3,884 votes in TX from D to R. This again gives Hancock the win and Garfield a 2-vote PV plurality, by flipping just 3322 + 333 + 1331 + 2030 + 1402 + 3884 = 12,302 votes.

Have I ever got some great math problem ideas for my students! (Just kidding... sort of).

[Sir Mohamed]

Flip TX and IL in 1960, where accusions of voter fraud came up right after the election. I also just recognized that HI was decided by a little more than 100 votes in 1960.

✓ Vice President Richard Nixon (R-CA)/Ambassador Henry Cabot Ledge (R-MA): 274 EVs.; 49.6%
Senator John F. Kennedy (D-MA)/Senator Lyndon B. Johnson (D-TX): 255 EVs.; 49.7%

[Metalhead123]

Take the 2012 election and swing the vote 5% towards Mitt Romney. You will get Romney winning the popular vote while Obama wins the electoral vote.

[TheElectoralBoobyPrize]

...by flipping the fewest number of votes.

It is harder than it seems. Not only has every election since 1824 won without a PV plurality (1876, 1888, 2000, or 2016) been won by a Republican, but it is very easy to flip the following elections to the GOP with just a few thousand votes: 1916 (less than 2000 votes in CA), 1948 (4000 in OH, 9000 in CA, 17000 in IL), 1976 (5600 in OH, 3700 in HI). (Dems still would have won the PV in each case).

The smallest number I can come up with in any fairly recent election is 59,301. In 2004, if 59,301 Bush voters in OH had voted Kerry instead, we would have this:

Kerry/Edwards 48.31% / 272 EV
Bush/Cheney 50.68% / 266 EV

(Flipping IA, NV, NM, and SD requires 60,447 votes--slightly more).

If we go all the way back to 1884 and flip 28,790 Cleveland votes in PA to Blaine, we get the same map as IRL, but Blaine wins the national PV by 1 vote.

Can anyone do it with fewer than 28,790 votes (for any election)?

You can get a Kerry win while losing the PV in '04 with even fewer votes-57,787 in Colorado, New Mexico, and Iowa leads Kerry to win 273-265.