Final answer:
The style of police discretion where some deviance is allowed while focusing on more serious crimes is known as the watchman style. It contrasts with other styles like the legalistic and service styles and is influenced by the prevailing political culture.
Step-by-step explanation:
When police allow some deviance to occur while they prioritize pursuing more serious criminals who pose a greater threat to the peace of a given area, they are employing a particular style of law enforcement discretion. This approach is characterized by the police making strategic choices about which laws to enforce strictly and which minor violations to overlook in favor of maintaining overall public order. The style that best fits this description is known as the watchman style of discretion.
In making these decisions, officers operating under the watchman style may consider the context and severity of the offense, as well as community norms and expectations. This style contrasts with other styles such as the legalistic style, which emphasizes strict enforcement of laws without regard to the severity of the offense, and the service style, which focuses on helping the community and problem-solving over strict law enforcement.
Policies like these are shaped by various factors including moralistic and traditionalistic political cultures, which may influence how government views its role in society, such as maintaining the status quo or bettering society. Police discretion, therefore, becomes a tool for law enforcement to balance the preservation of public peace and the regulation of social order through the selective enforcement of laws.