We aren't just a representative republic. We are a federal republic, with rural and urban states, with large and small states, and the EC helps balance these competing interests. What Californians "lose" in terms of representative power in presidential elections, they more than make up in the legislature (53 seats in the House vs. Iowa's 4), never mind their influence on national economic policy by virtue of being the most populous state.
That the Electoral College defies the spirit of "one person, one vote" is a feature, not a bug. The EC forces presidential candidates to have broad national appeal. It's the difference between the Superbowl, where you win if you score the most points in one game, and the World Series, where you win only if you win the most games. The Superbowl is biased toward outliers---teams that have inconsistent overall performance but one really good day can win, but that doesn't mean they're the best team that year. The World Series mitigates that bias by forcing teams to win consistently---a team can have one really good day but still lose the series because they can't perform well all the time. Likewise, because of the EC presidential candidates aren't competing in just one election but in fifty-one, and that means appealing to more than just coastal states or urban population centers (cf. https://en.wikipedia.org/wiki/Electoral_College_(United_Stat...).
Conversely, our direct representatives at the federal level are members of the House (by design) and the Senate (as of the 17th Amendment). All of this focus on the EC and the Presidency is misplaced. While we need a President with broad appeal, we also need Representatives (and to a lesser degree, Senators) who represent our interests, and here's where I think federal election reformers should focus: on alternate voting systems (like in Massachusetts), on better voter enrollment and balloting mechanisms (like in one of the PNW states, maybe it was Washington's that caught my eye), on non-partisan redistricting, and on publicly funding candidates. These reforms can and should start at the state level.
The genius of western liberal democracy isn't just the allocation of political power to the people but also the careful balancing of competing interests: No one bloc should have too much political power. Eliminating the Electoral College would be a move away from this balance. The right place to drive nationwide political change is in the House of Representatives, not the White House.
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