PHILADELPHIA—The five Democrats best positioned to win their party’s nomination for Philadelphia mayor have each landed on a central pitch to voters: The city needs a bigger role for police. In response to historically high crime, the top Democratic candidates have called for measures such as more patrol officers, bolstered detective ranks and faster 911 response, and they are debating the merits of police investigative stops—often called “stop-and-frisk”—as a tool for getting illicit guns off the streets. They have also called for expanded violence-prevention efforts, increased youth employment and other steps that don’t involve law enforcement, but the role of police has dominated the debate.

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