There are several forms of PR, and several options for vote-counting mechanisms. However, our present system is seemingly simple while operating with truly obscure rules. PR counting procedures are mathematical, but math can be learned by the ordinary citizen. The masses of rule and regulations governing candidacies and elections in our present system require legal training to interpret. The constitutional barriers to changing the electoral system - The most consistent argument against PR in the United States has a constitutional basis.
Opponents often confuse a voting system with a system of government.
PR is not a parliamentary system, but a system of election. The Constitution is silent on methods of election for US Congress. In the early decades of American democracy, proportional representation was simply unknown and political viewpoint was often consistent with geography. Reformers began discussing more representative, less geographically based electoral systems in the latter half of the 19th century. US House seats could be chosen through proportional representation simply by repeal of a 1967 federal law mandating one-seat districts.