Former Illinois congressman John B. Anderson, who bolted the Republican Party is 1980 to make an independent run for the Presidency, said last night that he hopes the GOP will broaden its voter base, stressing the need for a "pragmatic coalition-building effort."

In a Democratic Club sponsored speech to about 50 people in Science Center E. Anderson said he doubts "this Administration [has] any interest in people on the lower end of the income scale."

He urged the GOP to move away from the embrace of the Moral Majority and its call for prayer in the schools, which he said alienate yuppies and other groups needed to forge a successful majority coalition. Anderson is currently a guest lecturer at Brandeis University in Waltham.

As far as the Democratic Party, Anderson said it must "reeducate people to the desirability of a posit and redeeming role of government. However, he said he thinks. Democrats should not concentrate winning back middle-class vote because they will inevitably lose the GOP.

Anderson said he voted for wall F.Mondale in November. He said that he hopes that instead of letting special interest groups draw up its platform, the Democratic Party will come up with an "overarching vision" and then "do brokerage politics within a framework of a clear and consistent policy.