The longtime mayor and a trustee in Dering Harbor, a tiny village on Shelter Island, are fighting to hold their seats in a rematch Tuesday after they tied with write-in candidates in last month's election.

It's a quirk of being New York State's tiniest incorporated village -- a 2-square-mile municipality near the northern tip of Shelter Island with roughly 35 secluded houses, most of them summer homes.

The candidates said Dering Harbor's size grants them the ultimate home rule: the power to control what homeowners build and craft rules such as a ban on street parking to maintain the community's charm and high property values.

The village, which incorporated in 1916, is home to 11 year-round residents, according to the 2010 U.S. Census.

Several dozen part-time residents live most of the year elsewhere, primarily in Manhattan, village officials said. All residents can register to vote in village elections, regardless of whether they live there year-round.

On June 17, 11-term Mayor Timothy Hogue tied 25-25 with Patrick Parcells, a resident who said he launched a write-in campaign after arguing with the mayor over government transparency and hedge trimming rules.

Incumbent trustee Mary Walker also tied 25-25, with Robert Ferris, a write-in candidate who ran with Parcells. Village Hall will be open for voting from noon to 9 p.m. Tuesday.

With about 60 registered voters, campaigning is simple.

Parcells said he's talking one-on-one with neighbors but avoiding those he knows support the mayor so as not to make them "uncomfortable."

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Hogue said he's not campaigning at all.

"I'm running on my record," he said. "I'm available to talk to people. I see people on the street, if they have questions. Everyone in the world has my cellphone number."

One election issue has been the small pool of potential volunteers to fill 15 seats on three land-use boards.

Parcells, 63, a retired Wall Street banker, said a small group of residents and their relatives dominate the village board and three appointed boards.

"It's a very closed system," he said. "The trustees control the boards. They know their wife or their mother, or they themselves are on the board."

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Hogue, 66, owns a financial consulting business and has served as mayor, an unpaid position, for 22 years. He attributed the limited board makeup to having only a few dozen residents, many of whom want to enjoy their summers boating or golfing, not participating in board meetings.

Parcells also said he wants to increase transparency in the village, which lacks a website.

Hogue said creating and maintaining a website would be too much work for the village's tiny staff, adding that it's not difficult to spread information among the village's three dozen homes.

The village has three part-time employees and one full-time "highway superintendent" who collects garbage and does odd jobs.

Dering Harbor's budget is $320,000 this year. A resident with a $3 million home pays $8,000 in village taxes alone.

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"Nobody comes to Dering Harbor because it's the cheapest place to live," Parcells said. "They come here because it's a beautiful place to live."