Congressman-elect Stanford E. Parris (R-Va.) will attempt to gain on the powerful and prestigious House Ways and Means Committee when the 97th Congress organizes this week, staking claim to a tradition -- extending nearly unbroken back to James Madison -- of having a Virginian involved in writing the nation's tax laws.

If Parris fails -- and he says his chances of success are "not even money" -- Virginia will be without a representative on the committee for the first time in a quarter of a century. The Old Dominion's most recent representative, Democrat Joseph L. Fisher of Arlington, was defeated last month by another Republican, Frank Wolf.

Parris, who will succeed Democrat Herbert E. Harris II as the 8th District memeber of Congress next month, faces an uphill fight, however, as there is no Republican vacancy on the committee.

The solution to Parris' dilemma is to change the 2-to-1 ratio of Democrats to Republicans on the 24-member committee to 3-to-2, or some other ratio that would more nearly approximate the 243-to-192 Democratic margin in the new house.

In deference to Republican election gains, House Speaker Thomas P.(Tip) O'Neill has agreed to give the GOP a bigger slice of the pie on all but the most sought-after committees -- Rules, Appropriations and Ways and Means. The speaker is believed to be adamant on retaining the 2-to-1 ratio on Rules, although the ratio of Democrats to Republicans on the other two major committees may be subject to negotiations.

Parris, who attended a seminar for freshman Republicans at the Dulles Marriott last week, warned that the new minority members are going to "raise havoc if Tip tries to thwart the results of the election." The hyperbolic Parris said that if the Democrats don't compromise, "we'll have to give them R-squared," which Parris defined as "rape, ravage and destroy the system" until reason is served. Parris said R-squared might take such forms as "constant quorum calls, reading the journal, unplugging the elevators or setting fire to the Capitol."

House Democrats will take up the question of revised ratios when they caucus on Monday. An aide was asked if O'Neill would give ground on the two contested committees.

"It's not his decision," the aide insisted. Then, lapsing into political reality, he explained, "The caucus instructs Tip, and he hasn't decided what to instruct the caucus to instruct him."

The Ways and Means committee's power derives from its responsibility for tax legislation, which must originate in the House. Its jurisdiction extends to matters that take up more than half the federal budget, such as tariffs, Social Security, Medicare and Medicaid, unemployment compensation, welfare and many energy-related bills, including windfall profits, oil import fees and energy-tax credits.

The committee will have a new chairman, Rep. Dan Rostenkowski (D-Ill.), because incumbent chairman Al Ullman of Oregon was defeated last month. But the ranking minority member, Rep. Barber B. Conable Jr. of New York, will be back, and he is prepared to press the issue of greater GOP representation, although there is no indication the Republican leadership has its eye on Parris for any vacancy that might be created on Ways and Means.

"A 3-2 split is only fair, especially when the numerical relationship is actually 5-4," said an aide to Conable. "He feels very strongly about this," the aide continued, indicating that if O'Neill and the Democratic majority don't offer a comprise, the Republicans are prepared to make a floor fight of the ratio as the first business of the new Congress when it convenes next month.

There are no formal qualifications for membership on Ways and Means, or any other committee, but among factors considered, Parris would qualify on two -- his seniority as a former member (he served one term in Congress before he was beaten by Harris in 1974), and the absence of any other Virginian on the committee. Those considerations might be outweighed by members who have a background in tax law, or who would contribute better to a balance between conservatives and liberals.

Service on the committee is deemed so important and time consuming that most of its members accept no other regular committee assignments.

Parris, however, said he might also seek permission to serve on the District Committee, for which there is "some lack of enthusiasm" among other members. Combining Ways and Means with D.C. is "not totally without precedent," Parris noted. In the 96th Congress, Rep. Fortney H. (Pete Stark (D-Calif.) drew that combination.

If Ways and Means don't open up, Parris said he will seek assignments to Foreign Affairs and D.C. He said he and Wolf, the other representative from Northern Virginia, have agreed to divide responsibilities on committees that are of special significance to the Washington area.

Wolf will seek membership on the Post Office and Civil Service committee, which is the Hill's closest link with federal workers. Wolf's other committee preferences are Energy and Commerce, "because energy affects everyone," and Public Works and Transportation, whose duties include overseeing the Federal Aviation Administration, which runs Dulles International and Washington National airports.

The last time Virginia did not have a member on Ways and Means was during the 83rd Congress, 1953-1954. Democrat Burr Harrison joined the committee in 1955 and he was followed in 1963 by Democrat W. Pat Jennings. The following year Jennings was joined by Republican Joel Broyhill.