Council members did not see who received votes on the contested ballots. They checked to make sure the names could not be found in the polling books, then voted unanimously to reject the ballots.
Angela Dorsey, 22, of 106 Ranson Estates Circle, said she cannot understand why her ballot was rejected.
"That's like taking my right as a citizen away," Dorsey said.
When she went to vote, she was told she lived outside Ranson town limits and that her ballot would be contested.
Dorsey said she believes she lives well within the town limits. She said Ranson provides her with police protection, street service and garbage pickups.
Dorsey said she plans to lodge a protest at the next council meeting.
Dorsey declined to comment on which candidate she had voted for.
"I don't care who got in," Dorsey said. "But whoever got in, I have to follow the rules they make because they set the town ordinances and I live in the town."
James M. Jackson, another voter whose ballot was rejected, said he believes that when he registered for the 1996 general election he mistakenly was put into the wrong precinct.
Jackson said he was not too upset about it. He also declined to say for whom he voted, "but it wasn't Hamill. I voted for the only candidate who bothered to come down and talk to me."
Hamill, 52, celebrated his victory Monday night in North Myrtle Beach, S.C., where he was vacationing with his family.
Hamill said in a telephone interview he was surprised by the closeness of the vote.
"I have to say I wasn't nearly as nervous as I expected I would be (waiting for the outcome)," Hamill said. "You have to wonder sometimes if it's worth it because of the strain."
The post, with a four-year term, pays $2,700 a year.
Watson could not be reached for comment Monday night.
In the other races, Elizabeth T. Lloyd easily won re-election to her Ward 3 council seat and at-large councilman Keith "Duke" Piersen held on to his seat. Council members also serve for four years.
The mayor and council members will be sworn in June 17.
Slusher said that 40 years ago, the mayoral race also was won by four votes. In the last election, Councilman Howard Shade won his seat by one vote.