The opportunity of law enforcement officers to exercise their own judgment in choice in their daily activities (deciding which offenses to punish or ignore) is known as:

Police discretion 

Police discretion is defined as the decision-making powers police officers have that enable them to decide whether they will pursue policing procedures or drop a case with a warning to the offender. Police discretion is more commonly used in incidents involving mentally ill perpetrators, issues of domestic violence or hate crimes (if evidence does not back up allegations), and speeding or driving violations.