The constitution calls for a "republican form of government," however the conventional understanding at the time was that such a government is one in which the people choose their rulers. We could use the term "democratic republic" if that term hadn't been co-opted by states that are the exact opposite.

In contrast, states in which the rulers are elected from among a limited set of candidates chosen by the government, do not qualify. For instance, some states curate the selection of candidates by jailing or murdering opposition candidates. Others vet their candidates through a separate body of religious leaders.

In the US, gerrymandering probably does not pass a basic constitutional sniff test, but getting governments to relinquish powers that they enjoy is no small feat.