This stems mostly from the urban vs. rural composition of the country. Nationwide, there are about the same number of people living in big cities and rural areas. But in the Senate, rural areas get 2.5x more representation (!) than big cities.
And white voters are represented as though they're 68% of the country in the Senate, when they're actually 60%. It's basically as if you'd turned the clock back 20 years.
PS the Senate skew toward Republicans (6-7 points) is both bigger and more permanent than the Electoral College one (2-3 points) or the one in the House (a bit tricky to measure but probably amounts to 2-4 points in practice right now and possibly less after 2020 redistricting).
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