The League of Women Voters, hoping to avoid controversy that marred the presidential debate in Louisville, yesterday settled on a panel of four journalists for Thursday's vice presidential debate in Philadelphia.

Sources said the four are John Mashek of U.S. News & World Report magazine, Robert S. Boyd of Knight Ridder Newspapers, Jack White of Time magazine and syndicated columnist Georgie Anne Geyer.

White and Geyer were chosen yesterday after a meeting among representatives of the Reagan-Bush and Mondale-Ferraro campaigns and the league. Mashek and Boyd had been selected earlier.

Sources said last night that White had accepted the invitation to help question Vice President Bush and Rep. Geraldine A. Ferraro (D-N.Y.). League officials were trying to reach Geyer.

More than 100 reporters proposed by the league for last Sunday's debate in Louisville were rejected by representatives of the two candidates. As a result, the panel had three reporters.

Yesterday's discussions were described as congenial. Among the considerations were inclusion of women and minorities on the panel.

White is the first black panelist for this year's debates. Gerald Boyd, a black reporter for The New York Times, turned down an invitation to join the Louisville panel in protest over the selection process.