It's a Single Party Autocrasy / Constitutional Monarchy. The Monarchy does not lead anyone around.
I told you. We're an anarcho-syndicalist commune. We take it in
turns to act as a sort of executive officer for the week.
Listen, strange women lying in ponds distributing swords is no basis
for a system of government. Supreme executive power derives from a mandate
from the masses, not from some farcical aquatic ceremony.
You can't expect to wield supreme executive power just
'cause some watery tart threw a sword at you!
I mean, if I went 'round saying I was an emperor just because some
moistened bint had lobbed a scimitar at me, they'd put me away!