The terminology of the American Mafia is taken from that of the Sicilian Mafia, and suggests that an analogy is intended to imitate the court of a medieval Italian principality. For example, Venice was led by a doge ("duke") and a consigliere ducale (advisor to the doge).

https://en.m.wikipedia.org/wiki/Doge_(title)

Doge, along with the related English word duke and the Italian duce, duca (masculine) and duchessa (feminine) all descend from the Latin dux, meaning either "spiritual leader" or "military commander".

Who’s the top military contractor, again?

New regulations for the elections of the doge introduced in 1268 remained in force until the end of the republic in 1797. Their object was to minimize as far as possible the influence of individual great families, and this was effected by complex elective machinery. Thirty members of the Great Council, chosen by lot, were reduced by lot to nine; the nine chose forty and the forty were reduced by lot to twelve, who chose twenty-five. The twenty-five were reduced by lot to nine and the nine elected forty-five. Then the forty-five were once more reduced by lot to eleven, and the eleven finally chose the forty-one who elected the doge.