(a) If a majority of those voting at the election vote in favor of the measure, the requirement that dogs be registered takes effect in the county on the 10th day after the date on which the result of the election is declared.
(b) The county judge shall issue a proclamation declaring the result of the election if the vote is in favor of the measure. The proclamation shall be published at least once in an English language newspaper of general circulation in the county or, if there is no English language newspaper of general circulation in the county, the proclamation shall be posted at the courthouse door.