Sparta:
The five "Eforoi," who were actually in charge at Sparta, were chosen and merely need to justify their decisions to and be subject to the authority of the following "Eforoi." The choice was approved by "Apella". The body of adult Spartans known as "Apella" had little actual political influence other than via voice ratification of officials and vocal acceptance of legislation (easily manipulated). If not restrained, the two monarchs were little more than hereditary leaders of the army. They created the laws and ensured that they were followed by "Gerousia". The person who inspired this system was Lykourgos, who may have been an imaginary being.
In Athens, the "Ecclesia of Dhmos," which was composed of all adult males and cast a vote with a psifos (really a stone), was in charge of making important decisions. There was also the "Vouli of the 500," which was composed of voters and used to pass legislation. For more serious offenses, the legal system was the "Iliea" and "Areios Pagos." Additionally, the "10 Arxontes" were redirected and mostly made donations to their individual offices. Clesthenes was the latest to update and implement the system via significant adjustments.