(SPOILER: This isn't so much of an academic treatise, but an interesting footnote and fun thought experiment, so stop reading if you might be doing something more productive instead.)
The initiative system, or allowing voters to directly affect public policy, has a long history stretching back to ancient Greece. Its history in the United States, on the other hand, is a bit more recent. In the 19th century, some states had been experimenting with allowances for local initiatives, it wasn't until 1898 that a state -- South Dakota -- adopted a system of direct democracy. Oregon followed 4 years later with our Initiative and Referendum system (recall powers were added in 1908). Because Oregon is awesome, the system was nationally known as the Oregon System (and not the South Dakota System).
But it almost wasn't so!
In 1859, Oregon became a State with the passage of the Statehood Act, which held Oregon to certain commitments as a State, among them " conformity with the Constitution of the United States."
Fast-forward to 1906, when Oregon's newly-minted initiative system produced Measure 11, which imposed a 2% revenue tax on telegraph companies, including a company called "Pacific States Telephone & Telegraph." Here's a snippet from the Rogue River Courier:
Well, the measure -- a business tax increase -- passed by a pretty solid margin of 92% to 8%. That didn't sit very well with the folks at Pacific States Telephone & Telegraph, who sued and took their case to the U.S. Supreme Court. Their beef (aside from initially arguing about defects in the initiative text itself) was largely based upon this little bit of the U.S. Constitution:
"The United States shall guarantee to every State in this Union a Republican Form of Government" (Article IV section 4)
Despite the capital "R" in Republican, the phrase refers to the type of government characterized by legislative power being exercised by elected representatives, in contrast to the kind of "direct democracy" exhibited by the Oregon System (take that, South Dakota!).
We know how this ends, given that Oregon still has an initiative system. The Court ruled unanimously in Oregon's favor. But it wasn't all that cut-and-dry.
The Court neatly pivoted the question away from whether this was a violation of the Constitution's Article IV, but rather on whose role it would be to enforce such a question:
"It is important, since it calls upon us to decide whether it is the duty of the courts or the province of Congress to determine when a state has ceased to be republican in form"
Seizing upon an obscure precedent from Rhode Island (gone into more detail in the opinion linked above), the Supreme Court determined that it was not, in this case, supreme... and dismissed the case on a lack of jurisdiction. Saying that the determination "rests with Congress," the Court implied that Congress might make whatever determinations it likes with respect to recognizing what constitutes a legitimate State:
"And when the senators and representatives of a state are admitted into the councils of the Union, the authority of the government under which they are appointed, as well as its republican character, is recognized by [Congress]."
Here's where it gets fun and current:
Over the years, the popularity of the initiative system had grown, and 24 states now have some version of the initiative (and two -- Maryland and New Mexico -- dabbling in veto referenda, but lacking a method of initiating policy).
You'll notice, of course, that despite the inclusion of Oregon, Washington, and California, a lot of the initiative states are rural and midwestern states that often tilt capital-R Republican in their State Legislatures... and Congressional delegations. This brings me to an interesting question:
What would happen if the Congressional delegations from initiative states weren't seated, either by Congressional decree or by the Supreme Court?
Right now [EDIT: As of June 2019], the makeup is the Democrats controlling the House and the Republicans holding a slim edge in the Senate:
... but if the delegations from the initiative states are not seated, the Democrats maintain control of the House and handily pick up the Senate.
Of course, even if the 1912 Supreme Court was fine with it, this would be a terrible Constitutional crisis, and should never happen. The precedent of the Supreme Court or Congressional leadership being able to determine the makeup of Congress based on unappealable "political" determinations would be a staggering way to throw our system of checks and balances out of whack for a long time. (Plus, Oregon would lose out!)
But, remember there was a time just over 100 years ago when Oregon went to the Supreme Court for something that the Court determined was out of its jurisdiction... and the Court seemingly gave Congress the ability to make itself smaller.
