Paul Gann, co-author of Proposition 13, which ignited a nationwide taxpayer revolt in 1978, now has another voter initiative in the works that could cause state legislative leaders to look back on Prop 13 with nostalgia.

Gann's new proposal, planned for the June, 1984, ballot, would reduce the budget of both the state Senate and the Assembly by 30 percent, restructure legislative procedure to increase the power of the minority party, and greatly reduce the power of the speaker of the Assembly, who is second only to the governor in the state's political power structure. Democrats hold the majority in both California houses.

The incumbent speaker, Willie L. Brown Jr., a Democrat, has on occasion likened his power to that of "the ayatollah."

Gann's Proposition 13 significantly reduced the taxes paid by California property owners, and touched off similar movements across the country. His "Victim's Bill of Rights," which won an easy victory as Proposition 8 last November, radically overhauled the state's criminal justice system. Now, observers are wondering if Gann's skill at mobilizing voter resentment against politicians may again take on national significance.

Gann said the new initiative would "simply take away the speaker's right to control the finances of the Assembly." But much of the power of the speakership comes from control of the Assembly's $48 million annual budget.

Maxine Waters, chairman of the Elections and Reapportionment Committee, said her committee has hired an attorney to analyze the initiative, which is awaiting a title and summary from the state attorney general's office.

Waters, who characterized the proposal as "a plot by some Republicans to undermine the speakership," expressed concern that its passage would leave the legislature without leadership and unable to make compromises. "This would set up a scenario of chaos in which you would never be able to pass a bill out of the legislature," Waters said.

Many Democratic legislators said the driving force behind Gann's proposal is a group of conservative Republican legislators sometimes called "the Cavemen" by Democrats in Sacramento. One of the "Cavemen," Dennis Brown, said he had been involved in planning the initiative in an "attempt to change the way things are run up there in Sacramento . . . . The speaker is a dictator in California; he has total control. Willie Brown is elected to office by just one-eightieth of the people of California, as am I, and he is second in power to the governor. I just don't think that's proper." There are 80 Assembly districts in California.