In a basement room on the sunny campus of Claremont Men's College, a dozen students sit patiently tracing precinct lines into U.S. Geological Survey maps of the state of Washington.

Nearby, a computer hums and video terminals display outlines of hypothetical new legislative districts for Los Angeles County.

It is all part of a typical day's activities at the Rose Institute of State and Local Government -- and a huge worry to Democrats from Sacramento to Washington, D.C.

The work going on here and in the Detroit offices of Market Opinion Research Co. and in the Capitol Hill headquarters of the Republican National Committee represents a multimillion-dollar investment by businesses and GOP groups in the redistricting of state legislatures and the U.S. House of Representatives.

Through these organizations, sophisticated computer technology and the most complete demographic and political data will be cranked into the districting fights that will begin in legislative halls this spring. The battle will continue for a year -- with control of a decade's worth of legislation at stake.

The Democrats are worried because frankly they have nothing to match the expertise or investment that big business and the Republicans are massing.

An effort by House Democrats to launch a similar project with public funds was quietly killed by Republican opposition last week. The AFL-CIO and the Democratic National Committee are just getting organized to match the business-GOP effort.

"We're playing catch-up," concedes Dan Lucas, the only person at the DNC currently working on redistriction projects. "In terms of having a developed data base and advanced technology, the Republicans are way ahead of us."

The stakes in the battle are large. Maxine Fernstrom, the head of the Republican National Committee's 14-member redistricting staff, likes to point out that in 1980, Republican candidates for the House of Representatives won 50.2 percent of the two-party popular vote, but only 41 percent of the House seats.

In individual states, the disparities were even greater. The Republicans won 45 percent of the popular vote in Texas, but only five of 24 seats; 49.2 percent of the popular vote but only two of seven seats in Washington; 40 percent of the popular vote but only one of four seats in Oregon.

With population trends shifting seats from the old Democratic bastions in the center cities of the Northeast and Great Lakes states to the more independent and Republican-oriented suburbs and Sun Belt, GOP officials claim that a "fair" redistricting would put Republicans in position to gain a majority in the House of Representatives.

The fact that they have won fewer seats than votes in the last decade is not an accident. These disparities, and similar cases of Republican "underrepresentation" in the state legislatures, stem from the fact that Democrats had the upper hand in most states when the existing lines were drawn after the 1970 census.

Despite what happened to them in the 1980 election, the Democrats still have most of the political leverage in the redistricting battles now beginning.

In 14 of the 30 largest states, for example, Democrats control both houses of the legislature and the governorship, giving them effective control of the process. Republicans enjoy a similar advantage in only four states, with the other 12 split.

But redistricting is not a purely partisan exercise. Incumbents of both parties often get together on plans to protect their own seats. Ethnic and minority groups jockey to increase their representation. And the whole process often ends up in the courts, which can intervene to protect the standards of population equality, compactness, fairness -- and, not infrequently, the political interests of the party that controls the state supreme court.

That is why even in a state like California, where Democrats exercise complete control of the capitol, bit business, through the California Roundtable, has found it worthwhile to invest $600,000 in the "nonpartisan" but strongly GOP-oriented redistricting project of the Rose Institute.

The project's origins go back 10 years, when Dixon Arnett, now vice president of the college, was a Republican assemblyman, and Alan Heslop and Thomas B. Hofeller, now the director and associate director of the institute, were consultants on redistricting to the assembly Republicans.

Arnett recalls that as a member of the legislative minority, he was given about a 30-second glance at the makeup of his proposed district before the Democrats brought the plan to a vote. "There was no chance for us to analyze what they were doing to us," he says.

Forewarned is forearmed in redistricting fights, and part of what the Rose Institute is doing is building a capacity that will permit almost-instant computer analysis of the demographic and political consequences of the districting plan the Democrats are sure to develop on their own.

But the business-backed group is doing more than that. It is promoting and propagandizing for the cause of "fair" districting and showing, through its own designs, how it might be done.

"We believe," said Hofeller, "that the more competitive districts there are, the more representative and responsive the legislature will be. The Democrats think that's just a plot to increase the influence of business contributions and lobbying, but there is a risk for business, too, in making the legislature more responsive."

Assembly Speaker Willie Brown, a Democrat whose district is cited by the Rose Institute as one of the most gerrymandered in the state, has labeled the Rose Institute "a pure Republican front."

But Arnett, who saw Brown's handiwork in the last redistricting, says: "If anyone stole in any other way the number of districts you can steal in a gerrymander, there'd be a huge outcry. In Sacramento, they just regard this as part of the game."

Plainly, the game will be different this time in California. A prominent Democratic lawyer observes, "it's obvious as anything that the Rose plan will be the basis for challenging the legislature's redistricting plan in the courts. That's why business is putting up the money."

But Heslop and his colleagues are playing the game straight, briefing all inquiring reports on their plans and offering their tools to such "good government" groups as Common Cause and such minority organizations as the Mexican-American Legal Defense and Education Fund (MALDEF).

That last action may not be entirely altruistic. Heslop has written that, "Especially in states where Democratic legislature majorities have been based on the loyal voting behavior of ethnic minorities, the creation of ethnic seats may endanger Democratic control of neighboring districts."

As Fernstrom, the RNC official, puts it, "We see a real opportunity in redistricting to make a substantive and not just a cosmetic alliance with the minorities."

The Rose Institute group has sold its services in Illinois, Washington, Mississippi, Texas, New Mexico and Pennsylvania, with discussions under way in Maryland, North Carolina and Florida.

Market Opinion Research of Detroit, whose president, Robert Teeter, is a well-known pollster for Republican candidates, has sold a similar service in Connecticut, Michigan, Indiana, Ohio, Minnesota and Wisconsin, with Colorado and Missouri possible early additions to the list.

In some cases the clients are bipartisan state agencies, but in most they are Republican or business groups. The RNC will spend about $1 million in the next year developing a data base and computer readiness for use in the states.

Fernstrom is assembling three teams of traveling consultants, each with a lawyer, a computer specialist and an experienced political operative, who will move from state to state "to help our Republicans protect their interests."

"The contrast between the Republicans and the Democrats is just phenomenal," says Kimball Brace, whose Washington firm, Election Data Services, is a Democratic-oriented rival of Heslop's and Teeter's operations. "The Republicans have been working on this for about 2 1/2 years; the Democrats are just not finding out there is such an animal as redistricting."

The House Post Office and Civil Service Committee, still under Democratic control, put a $200,000 item in its budget this year to finance a computerized analysis of the economic, population and demographic characteristic of proposed congressional districts as a "bipartisan" service for members of the House.

An informed Democratic staff member said, "We weren't going to include the political data -- the registration or election results -- but with what we gave them, it would have been easy enough to crank in." But Republicans caught wind of the move and killed the appropriation last week.

The AFL-CIO Committee on Political Education is launching a redistricting research project under Elizabeth Smith of the Amalgamated Clothing and Textile Workers, and new DNC Chairman Charles T. Manatt is holding a meeting on the problem next week.

But for now, if there is a computerized redistricting revolution in 1981, it looks like Republicans and business will be at its controls.