The United States Constitution apportions representation by states. Many other republics apportion representation by political parties.
The misconception here is the implication that it must be one or the otherâ€”states or political parties.
In fact, there are very few proportional representation systems that do not apportion their seats by state or province (or whatever their subunits might be). Almost all PR systems have district lines that coincide with existing subnational units. In that sense, they are just like the US, where states are allocated House representation in proportion to their share of the national population.
The apportionment to subnational units is a separate dimension from what the districting arrangements are, and how seats are won within those districts.
It would not be necessary (though it would be possible, even under federalism) for a hypothetical PR-USA system to allocate seats by national proportion of the vote. Supposing no such national party allocation, PR simply would mean that a state’s seats (for those states with more than one) would be allocated by party share of the vote cast within that state. Districts would be multi-seat, whether statewide or, in larger states, with intra-state districting.
PR without national calculation of party shares would be easier to manage in a larger House (so fewer states would have small numbers of seats to divide among the parties), but the question of increasing the size of the House is a separate question and would be a good idea regardless of whether we ever jump on the PR train or not.
The bottom line is that in no sense would proportional representation by party compromise the principle of apportioning representation in the House by state. I find that this point is often not well understood (and thus I am by no means picking on Stephen!)