Some do. Others have the position of municipal council president be popularly elected along with the other municipal councillors. Just depends on the municipality. Yes, but being the presiding officer of a legislature is a very different thing from being the executive of an entire sovereign state. It is not impossible that the Federation President is elected by the Council, but you don't usually hear the term "run for" used in the contexts of such offices. "Run for" carries connotations of making campaign stops to raise one's support among the general population. It is, however, possible that the elections are like those of the Republic of South Africa, in which it is understood that the legislature will not elect as head of government a candidate who is not supported by a majority of the populace. ETA: There is, however, no canonical reference whatsoever to the Federation President being elected by the Council, only to him being "democratically elected." I find it highly implausible to imagine they meant indirectly elected. There is also no canonical evidence that the Federation President routinely serves as the presiding officer of the Federation Council, though he seemed to be doing so in the exceptional circumstances that constituted Kirk's court-martial in TVH. The novels have firmly established the Federation President to be popularly elected, and that the Federation President does routinely serve as the Council's presiding officer. End edit. Of course, as the Republic of South Africa proves, having a legislatively-elected head of state and head of government does not mean that it's an alliance rather than a sovereign state.