Some people cobbled together what they thought were optimal structural components from a few different governments, tweaked it, and trotted it out as a country.
Maybe de Tocqueville coined the term.
I’m not sure you can cite one government, established by men, that’s not accurately described as an experiment, but I see that accuracy isn’t an interest among current participants.
There's not a government left from classical times anywhere in the world. Indeed very few last more than about five hundred years. With that in mind they can all be considered experimental.
There have been numerous attempts to create governmental "systems" that sought to both protect the security of those governed and also perfect the workings of society from the many contradictions inherent in human nature. All have failed as a result of their own internal contradictions and, in some cases, failed attempts to change human nature (think of Lenin's "socialist man").
The 16th century Italian Philosopher, Niccolo Machiavelli, wrote an interesting work, entitled "Discourses on Livy" , an examination of the history of Rome as described by Livy, its eminent historian. He also included observations from other sources including histories of the Greek Republics. His self described goal was to determine what form of government would best ensure the long term stability of a city or republic.
He concluded that there is no ideal form of government for such purpose: all have their excesses, limitations and failings - all arising from the contradictions in human nature. His formula for the best that can be achieved is a system with build in limits on the excesses driven by competing classes of citizens, and a means for compensating for them when they occur.
The real foundation for the, so far, enduring American experiment at representative democracy, is , in my view, the checks and balances the founders deliberately put in the structure of the government. These limit the powers, both of the legislature and the Executive, and the Judiciary limits both. In our history we have already seen excesses by all three branches, but the system was able to contain them all. I have often suspected that some of the framers might have been inspired by old Niccolo.
Walter Hinteler wrote:
Iceland, btw, has the longest running parliament in the world (since 930 AD, the Althing).
A relatively successful experiment.