Hallum pleaded guilty in September to bribing absentee voters, in a previous election, with chicken dinners, vodka and cash.
He resigned and is ineligible for the seat because of the felony conviction.
His name remains on the ballot, because the Crittenden County Election Commission hasn't received an order to remove it.
A spokesman for the Arkansas Secretary of State's office says that if Hallum receives the most votes in November, it would create a vacancy in office that would trigger a special election.