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It seems as though there are myriad other voting schemes that do not require representatives to run for a "district". For example, representatives for the state could all be on the ballot for the entire state, and the top n in the state (where n is the number of available seats) get seats.
Do all multi-member states draw districts? If so, are they required to do so? If not, then why do they not adopt other voting schemes?
Q: Are states required to divide into congressional districts?
Yes.
2 U.S. Code § 2c - Number of Congressional Districts; number of Representatives from each District
In each State entitled in the Ninety-first Congress or in any subsequent Congress thereafter to more than one Representative under an apportionment made pursuant to the provisions of section 2a(a) of this title, there shall be established by law a number of districts equal to the number of Representatives to which such State is so entitled, and Representatives shall be elected only from districts so established, no district to elect more than one Representative (except that a State which is entitled to more than one Representative and which has in all previous elections elected its Representatives at Large may elect its Representatives at Large to the Ninety-first Congress).
Occasionally, a bill will be introduced to change to multi-member districts. However, the bills are never brought to the floor for a vote. One such example is H.R.3863 - Fair Representation Act from the 117th Congress. That bill would have allowed for some states to have districts with three to five members. And, others to have up to six at-large members. It would have also also required ranked choice voting for "all elections for Senators and Members of the House of Representatives".
