Electoral votes by congressional district?

Which party would benefit on net if this idea was implemented in most states?

The hypothetical is that most states switch to a new scheme of awarding electoral votes for the president where 2 EVs go to the statewide winner & 1 EV is awarded to the winner of each congressional district in that state. It seems to me that this would help the GOP on average. Increasing voter turn-out is easier in urban districts than in rural ones, and on net this helps the Democrats in contests for state-wide majorities/pluralities. This new EV scheme would make state-wide vote totals much less important.

Nate Silver suggests that public disgust with gerrymandering influencing presidential elections leads to the abolishment of the electoral college in favor of an direct national vote for the president (e.g., national plurality, national majority with possible run-off election, or some other scheme that treats votes from different states equally). Unlikely! It only takes 13 states to prevent a constitutional amendment, but there are 33 states with below-average adult population. (I computed 33 from here.)

Also, states don't have to gerrymander forever. Several states already have independent redistricting commissions. EV-by-district could push more states towards this solution. Or maybe some big states would just keep gerrymandering, leading to a constitutional amendment that somehow restores the de facto status quo of awarding most EVs to the winners of state-wide pluralities. (The de jure status quo is that states can award choose their electors however and whenever they want, and electors vote however they want on the Monday after the second Wednesday in December.) Both of these seem more likely than the less populous states giving up their disproportionate power in selecting the president.

Let us also consider the robustness of election results. For example, Minnesota is typical in requiring a recount of a state-wide vote if the margin is less than half a percent. 2 out of the last 47 presidential elections had a national popular vote margin less than half a percent (1880, 1960). (1 out of 47 had a margin less than a quarter of a percent (1880); 6 out of 47 had a margin of less than one percent (1880, 1884, 1888, 1960, 1968, 2000).) If those had been direct elections, would expensive national recounts have been required? You might invoke the law of large numbers to argue for a lower threshold than 0.5% at the national level, but the law of large numbers is about random, uncorrelated errors. What recounts are really about is the fear of election fraud. Think about how the incentives of election officials in deep red Idaho and deep blue Massachusetts would change if presidential elections became direct.

In actuality, 2 of 56 presidential elections were disputed, but, thanks to the electoral college, the disputes were limited to a few states (FL in 2000; FL, LA, SC, and OR in 1876). If EVs were awarded by congressional district, disputed presidential elections would still be rare, and within this small set of disputed elections, most disputes would not require any state-wide recounts.

P.S. I dismiss purely moral arguments for "one man, one vote" because government should be a mere means to ends like life, liberty, and the pursuit of happiness. Having my vote and your vote weighted equally either promotes these ends or does not promote them.