Let’s get back to the question in the OP and my objection to Polycarp’s statement in post #3.
My statement was: “With respect, while the state itself must have a republican form of government, the city is not the state. So the analysis is faulty.”
Let’s examine this to see what it is NOT, which may help us out.
It is NOT a statement that a city is not a political subdivision of a state. It is, as are school districts, counties, water districts, mosquito abatement districts, etc. Such subdivisions are subject to the provisions of the U. S. Constitution which regulate “state” action, just as the states themselves are. But a subdivision of a state is not a state.
It is NOT a statement that there are not aspects of city and or county government that are dealt with under similar concepts as state government itself. For example, the equal protection clause can be applied to a scheme for electing representatives to a city government just as it can to a scheme for electing representatives to a state legislature. But just because there are similar aspects, this itself does not make the assertion that the guarantee of Article IV regarding republican forms of government is applicable to subdivisions of a state.
In short, what I was doing was challenging Polycarp’s rather over-general assertion. To make the assertion contained in his post, it is imperative to establish that the rules applicable under Article IV to a state itself are applicable to its subdivisions, which he had not done. Simply asserting that they are “legal creations of the state” is not enough. After all, there are many “legal creations of the state” whose members are not elected at all; the assertion in Polycarp’s post would appear to mandate that, for example, a Department of Education could not have a governing board that wasn’t directly elected by the people. The same would be true, for example, of the California Workers’ Compensation Appeals Board, the members of which are not elected at all, and which exercise a considerable power over the lives of workers in the state.
In a subsequent post, I will address the question of the OP more fully. I will, however, suggest that the rather heated debate over what cities are and aren’t misses the point of my post, for which we can, perhaps, thank ascenray, who needlessly, perhaps, blurred the lines with a somewhat less than detailed assertion that “[a]s arms of the state government, they are subject to the same constitutional provisions as state governments.” Without debating the actual point contained in that statement, I will simply point out that it doesn’t address the language of the Constitution, which I will reiterate, since everyone seems willing to ignore it: