Is Calling The Police An Act of Delegation of Authority?

[allodial]

It is well established that a citizen in whose presence a misdemeanor has been attempted or committed may effect a citizen’s arrest and in so doing may both summon the police to his aid and delegate to police the physical act of taking the offender into custody. People v. Johnson(1981) 123 Cal.App.3d 495, 499

..the delegation of the physical act of arrest need not be express, but may be implied from the citizen’s act of summoning an officer, reporting the offense,and pointing out the suspect.” Padillav. Meese (1986) 184 Cal.App.3d 1022, 1030

...a citizen’s arrest “may be implied from the citizen’s act of summoning an officer, reporting the offense, and pointing out the suspect. Arpinv. Santa Clara Valley Transportation Agency (9th Cir. 2001) 261 F.3d 912, 920

In view of the above California cases, is calling the police an act of delegation of authority? If so what does that tell you? Is the message in the above anything short of loud as clear as to from whence police derive their powers? Is it then true that when a police officer makes an arrest even without being called, he is merely a delegate of the people and nothing more? Does it follow that all arrests are citizens arrests? If the police officer isn't a citizen then what is he?