The situation came up in a recent game where the Capo was wacked. The question that arises is who acts as Capo, breaks ties, etc. in the interim after the Capo is wacked and before a new Capo is appointed. Is it the player who controlled the Capo and has the ring, or would the Capo responsibilities fall to the next lowest rank?
It's not the Capo that breaks ties, etc. It's the player with the Capo ring. This is described in a couple sections of the rules, seen below.
Controlling the Capo
The player that controls the Capo immediately takes the Capo (First player) Ring. If no one controls the Capo, the player who currently has the Capo Ring retains it. The Capo Ring moves as soon as a new player has the most Influence markers on the current Capo – even if it is in the middle of a phase!
Also, later, in the Position Special Powers section:
Since the tie breaking power is tied to the Capo ring, not the position, it cannot be canceled.
In your case, the player who previously controlled the Capo (previous to the whackening) will retain the Capo ring and, thus, retains the affiliated tie-breaking power, etc.