The blackout rule has impacted the Cincinnati Bengals and the Cleveland Browns since its inception the 1970s.
The Federal Communications Commission has considered putting an end to the NFL's blackout rules, allowing every game to be broadcast locally regardless of ticket sales.
The FCC is crafting a proposal that would require the NFL to show each team's games in its home market, arguing that those who cannot afford tickets should not be punished.
Brown's proposal is the latest push in an effort to overturn the blackout rule.
Last month, a bill was introduced in the Ohio House by Democrat Robert Hagan of Youngstown. It is designed prohibit any team playing in publicly financed stadiums or arenas from blacking out games. A violation would result in the team repaying its public funding.
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