No. There is a federal law preventing this (2 U.S. Code § 2c).
There’s nothing in the Constitution that prevents states from providing that representatives are chosen statewide. I’m not sure they could do it exactly the way you propose, but they could choose to have all of their representatives elected at large, meaning by everyone in the state, if not for this federal law.
Of course, doing it that way would be counterproductive to what you want to have happen, since probably the majority party would win all of the seats rather than only the seats corresponding to their total vote.
The reason I’m not sure that, if the particular federal law didn’t exist, the states could do what you suggested, is that the Constitution requires that the representatives be “chosen every second Year by the People of the several States”. One could make a pretty strong argument that, if the election is held at large, and the majority chose Democratic or Republican, that the minority party wasn’t actually chosen by the people. We don’t usually do proportional representation in this country, and we usually say that the majority rules, meaning the majority vote is what represents the will of the people. So if 51% of the people chose the Democratic slate in Nevada, if I were a Democrat I would argue that the will of the people is that the state be represented by Democrats. Basically, if you make the election statewide, it’s not obvious that it wouldn’t just end up the same way each individual district ends up, where the plurality winner gets all the votes.
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