Comment by Amadou

When did you agree to let the police protect you if they encounter you being mugged?

That's a particularly poor example.

Supreme Court Justices Rule Police Do Not Have a Constitutional Duty to Protect

http://www.nytimes.com/2005/06/28/politics/28scotus.html

In case you can't get past the paywall (try googling the title and going from there), the summary is that a woman got a protective court order and then she called police and told them her husband had violated the court order. They did not act, and he killed her three kids.

If a court order with explicit instructions to arrest should it be violated isn't enough to move the police into action, simply encountering you isn't worth a hill of beans.