2 political heavyweights say they wonât run for mayor of Cincinnati For the first time in months, the field for Cincinnatiâs top executive job got smaller. Former Cincinnati Mayor Mark Mallory (Source: The Enquirer/Adam Birkan) By Brian Planalp | January 26, 2021 at 4:36 PM EST - Updated January 26 at 4:58 PM CINCINNATI (FOX19/Enquirer) - Two well known Cincinnati politicians are bucking the trend in this yearâs mayoral contest â by keeping their hats out of the ring. Former Cincinnati Mayor Mark Mallory and former Ohio Democratic Party Chairman David Pepper will not seek Cincinnatiâs mayoralty in 2021, our media partners at the Enquirer report.