This badge is a symbolic representation of a police officer. Police officers often the traits of a hero; they are brave, the protect the public often with cost to themselves. Police officers risk their lives for the safety of the public.
This is a photo of a real police badge. This has to do with the book I read because Bill Hodges is a police officer who ends up retiring at the beginning of the book. At the same time he goes through a divorce which affects him emotionally because he feels alone. It gets so serious sometimes that he occasionally contemplated suicide. That is until he found some sort of purpose in his life by deciding to investigate the Mercedes Massacre.
Ch.12 Legitimate power is based on social agreement. Society as a whole has agreed to respect the power of a policemen because he has been appointed the position through the correct training and commitment.This badge for the Los Angeles policemen represents this legitimate power, the same way the uniform would.