When Republican Thomas M. Davis was campaigning for the Fairfax Board of Supervisors for the first time four years ago, a woman told him that she knew his in-laws from church, his wife from school and his brother from the Boy Scouts.

"Great, then you'll vote for me," he said. No, she explained, because she came from a long line of Democrats.

"If your grandfather was a crook, and your father was a crook, would that make you a crook?" Davis said he jokingly asked her.

"No, a Republican," she replied.

Davis, 34, who has lived in the area for more than 10 years, likes to tell the story to emphasize his personal ties in the community, ties that he believes clearly distinguish him from his Democratic challenger, Mason District newcomer John W. Purdy. Although those ties failed to convince one woman, Davis believes that in most cases both Republicans and Democrats prefer a hometown boy in local elections.

Davis, an attorney with Advanced Technology, hopes that on Nov. 8, when he is up for reelection to a second term as Mason District supervisor, the voters will prove him correct.

But Purdy, 53, who served on the Arlington County board from 1973 to 1980 and was chairman of the board for two of those years, says he is enormously familiar with the problems that face Mason District.

"Arlington is very similar to Mason District . . . the mix of commercial and residential . . . of foreign born, black, poor and wealth," said Purdy, who established a commission in Arlington on the status of women.

Purdy, whose campaign slogan is "Purdy Please," has been an attorney for 29 years, with the Navy, the IRS, the National Education Association and in private practice. He is currently the managing attorney of the Hyatt Legal Services office in Falls Church.

While on the Arlington County board, Purdy was active in the Arlingtonians for a Better County, a nonpartisan organization, and served in 1975 and 1979 as the chairman of Northern Virginia Transportation Commission. In 1979, he ran unsuccessfully for the Democratic nomination for commonwealth's attorney in Arlington.

Purdy first moved to Fairfax from Arlington in 1981, then moved back to Arlington briefly and then bought a house in Mason District a year ago.

Purdy has raised about $800. Davis has raised about $20,000. While the latter figure is in line with what most other supervisors who are running have raised, Purdy finds it excessive. "I wonder how much more he Davis needs to campaign for a job that only pays about $21,000 per year," Purdy said.

Purdy also bitterly criticized an August fundraising letter by Davis that accused Purdy of a "longtime association with special-interest groups who would like to make our district supervisor a sure vote for their special-interest projects."

"If Davis is referring to my service to minorities, to women, the disabled, elderly, downtrodden, unemployed and to causes like housing, hospice, public employes and the foreign-born, then I . . . plead guilty to that," said Purdy.

Mason District is less than 16 square miles, making it the smallest and most densely populated of the eight supervisor districts in Fairfax County. It borders Arlington and Alexandria and includes the highly developed Bailey's Crossroads area, Seven Corners Shopping Center, Columbia Pike and the Lake Barcroft area.

There is a high concentration of moderately priced apartments in the Mason district and 48 percent of its residents are renters--the largest percentage in Fairfax. Mason District also has the highest percentage of minorities, elderly and poor.

While much of the rest of Fairfax grapples with plans for future developments, Mason District concentrates on the need to rehabilitate older, rundown areas. Davis has been one of the board advocates for an aggressive rehabilitation and redevelopment policy for Fairfax.

Purdy argues that his eight years of experience on the Arlington board can easily be put to work effectively in the Mason District.

Asked why he would be a better supervisor for Mason District than Davis, Purdy replied, "I'm not running a campaign that offers comparisons between me and him. I'm offering the people an alternative. His voting record is that of a conservative Republican, although he tries to appear moderate."

When asked for specific examples of such votes by Davis, Purdy said, "Well, I have not researched his record and I don't intend to."

While Davis often votes with his three other Republican counterparts on the board, he also sides with Democratic Supervisor Audrey Moore, whose Annandale district borders his. Davis says he respects and personally likes Moore. Likewise, if he makes biting, sarcastic remarks at board meetings, they seemed aimed more often at Republican Chairman John F. Herrity than at Democrats.

Rumors float constantly that Davis has his eye on Herrity's post or on the U.S. Congress. Davis, the youngest member on the Fairfax board, says that, right now, he's only interested in Mason District.

Davis says he has tailored his activities as a supervisor to the needs of each area in his district--for instance, an exemption for residents of the Skyline complex, a high-rise development of condominiums and apartments, from the leaf collection tax.

He points to the settlement of a potentially explosive dispute over the development of the Pinecrest golf club as an example of how he defuses controversial situations by bringing opposing groups together to thrash things out in private. Davis also noted that when he incorrectly disputed the arguments of a constituent on a certain issue, he apologized to the man and appointed him to head a task force on that subject.

One conservative Republican groused that Davis took that philosophy to the extreme by appointing Democrats to represent him on some important boards and commissions, like the Park Authority and the county planning commission. A joke floating around before Purdy declared his candidacy was that no one would run against Davis because he had given an appointment to every potential opponent.