Argument #1
The Court should rule in favor of Ohio. The evidence obtained by the police against Mapp should be allowed in court. The Fourth Amendment does not apply to non-federal cases like this one.
Argument #2
The Court should rule in favor of Mapp. ANy evidence that is obtained illegally (without a valid search warrant) should not be allowed in court. The Fourth Amendment should apply to the state authorities as well as the federal ones.