Hellas: Worlds of Sun and Stone
Stymphalos is a democratic monarchy, with the position of King being an elected one. The governmental structure is heirarchal, but flows both ways: the Ecumenopolis can initiate a vote, which is then voted upon by the Planetary Forum (an elected, representative council) and then ratified by the King. Or, the King can initiate a law by issuing a decree, which is then voted on by the Planetary Forum, and finally the Ecumenopolis.
There are exceptions, and in times of great turmoil, the King may issue an emergence decree, which can be enforced and can be carried out before the voting is completed. Voting may even be suspended until an immediate crisis has passed.
The king, once elected, never has to run for office again, and serves a term “for life”. However, if one has cause to challenge the King, they may bring their case before the Forum, and if agreed there is cause, the King must be re-elected, running against the challenged.
The Stymphalean Forum is historically reluctant to agree to accept such a challenge, as it’s believed to be disruptive to the government, so it’s usually only in time of extreme public dissatisfaction or evidence of misconduct by the King that such elections are permitted.
After the King’s death, a new King is elected. While a King’s heirs are permitted to run, their status as the offspring of the former king carries little weight.