Acting perhaps on the theory that 60,000 independent gasoline service station operators can't be wrong in an election year, President Carter has given qualified approval to their bill to protect them against price-cutting by the 16 largest oil companies.

The Carter-Mondale Re-Election Committee, at least, has endorsed the bill, even though the Energy Department hasn't made up its mind about the measure and the Justice Department has opposed its main provisions.

The bill, the top legislative priority of the Service Station Dealers of America, would compel the 16 largest oil refining companies to give up direct operation of service stations. The independent dealers say that at least some of the oil companies are using company-owned stations to undersell the independents and force them out of business.

Independent candidate John B. Anderson also has endorsed the bill, while Republican candidate Ronald Reagan said he is all for protecting independent dealers but feels existing antitrust laws give them enough protection, said Paul E. Pierce, the association's executive director.

It may be unusual for the administration's position on such an important, controversial energy bill to come from the campaign headquarters rather than the Department of Energy, but that is just another tribute to the lobby effort waged by Jack W. Houston, leader of the Service Station Dealers of America, and his colleagues.

A version of the bill passed this summer by the House Small Business Committee would put the 16 largest oil refiners out of direct service station operation and provide other forms of regulatory protection for the independent dealers. The antitrust subcommittee of the Senate Judiciary Committee has approved a similar bill.

The Service Station Dealers of America represents two kinds of independent service station operators -- those who own stations and buy brand-name gasoline from the oil-refining companies, and those who lease stations from the oil companies and sell their products.

Typically these "branded" independent dealers run the traditional gasoline stations that not only sell gasoline but also provide tires and other products and repair vehicles. Many of them are hard-pressed now by the "gas-and-go" stations that sell gasoline but offer no other services.

The independents also complain they are discriminated against by the refining companies who provide cheaper fuel to company-owned stations than to branded independents.

Critics in the industry say the independents are fearful of failing in today's world of high-priced gasoline and want a specially tailored congressional bailout which ultimately promises higher fuel prices for consumers.

The independent's bill -- The Small Business Motor Fuel Marketer Preservation Act -- is carefully designed to do just what its name says.

The prospects of getting it passed this year were considered slim even by some of its supporters, but that didn't deter Houston, a veteran service station dealer from Georgia, from trying to get the presidential candidates on record before the election.

He and Pierce wrote to Carter, Reagan and Anderson. The president's response came from Ronna Freiberg, deputy research director of the Carter-Mondale campaign committee, in an Oct. 21 letter hand-delivered to Houston at the association's Washington office.

The letter begins with a declaration that the administration supports the dealers' legislation. Freiberg then adds that the administration "supports the objectives" of the House and Senate bills. In a second sentence, she does put in a qualification, reflecting the Engergy Department's reservations about the bills, however. Further study is necessary, she said, to make certain that passage wouldn't harm competition or lessen the supply of gasoline.

Pierce and congressional supporters of the legislation take the statement as an endorsement and are delighted to have it. The independent dealers association has not backed a candidate for president, however, said Pierce.