I think nothing in the US Constitution prohibits states from electing their members to the federal House of Representatives by a proportional representation method. For example, California has 53 representatives, and these could be elected not in 53 separate districts, but instead in a single state-wide election.
Making this change would require action by a state's legislature, and likely changes to federal law as well, but no federal constitutional amendment is needed.
I think it's highly germane to discuss alternative election systems in a discussion on fighting gerrymandering.
If people are concerned about the geographic link that too can be solved.
E.g. Norway uses proportionality within regions, and counts votes per party list and then keeps track of how many "wasted" votes each party has.
Then a small fixed number of seats are allocated in descending order of remaining wasted votes (each allocation removes an equivalent number of votes from that party-lists pool) from the region where that party had the most wasted votes.
There's also a 5% threshold in the national vote to be able to receive seats from that pool.
It both gets relatively close to proportional, still makes it possible for very popular independent candidates to get elected directly, and the seats used to even out are also linked to regions. The areas are just a bit larger.
Even 2-3 seats per district plus a few seats used to even out representation would give dramatic improvements in proportionality.
Correct, not constitutional, but by federal statute.
This was done variously by allowing and disallowing multi member districts, after reapportionment via a decenial census.
Multi-member districts were un-regulated in the early 1800s, then disallowed in the 1842 statute, but had a number of states with multi-member districts were in the subsequent election allowed to have their multi-member-district representatives seated. Then allowed again by silence in the statutes in 1850, then disallowed by statute again in 1862, and generally not allowed in subsequent reapportionment statutes through 1911, allowed by absence of regulation in 1929 (via Supreme Court ruling in 1932, Wood v. Broom, that the provisions of each apportionment act affected only the apportionment for which they were written).
Then disallowed most recently in 1967 by statute (as part of a civil rights concerns, after the 1965 Voting Rights Act, that southern states might resort to winner-take-all at-large elections to eliminate voting strength of recently-enfranchised blacks in the South).
See:
The History of Single Member Districts for Congress:
Seeking Fair Representation Before Full Representation - by Tory Mast
Making this change would require action by a state's legislature, and likely changes to federal law as well, but no federal constitutional amendment is needed.
I think it's highly germane to discuss alternative election systems in a discussion on fighting gerrymandering.