In the Byzantine world of New York politics, the state Liberal Party's fall dinner is an annual ceremonial dance, a ritualistic gathering of the drumbeaters and breastbeaters of state politics, a place to see and be seen.

It is invariably a long and tedious affair. The speeches are long-winded, and seemingly unending. The food is mediocre and overpriced.

Yet it is an event few ambitious politicians dare miss. "No one else can put on a dais like we do," says Ray Harding, the party's chief strategic, with more than a little jusitification. "No other organization in this state can put together so many big-name Democrats and Republicans on the same platform."

In the past presidential election years, John F. Kennedy, Lyndon B. Johnson, Hubert H. Humphrey, George McGovern and Jimmy Carter have stopped by to join the political dance, and accept the endorsement of the small, but influential party.

But this year the party broke tradition and for the first time in 36 years refused to endorse the Democratic nominee for president. Instead, it endorsed John B. Anderson, the independent presidential candidate and Illinois congressman.

As result, never has the party had a head table quite like it did tonight. On one side were Anderson, his running mate, former Wisconsin governor Patrick J. Lucey, historian Arthur Schlesinger Jr., who has endorsed Anderson, Sen. Jacob K. Javits, who has endorsed Ronald Reagan, and New York Gov. Hugh Carey, who has endorsed Carter.

On the other side, were Lt. Gov. Mario Cuomo, Carter's state chairman, New York City Council Chairman Carol Bellamy, a supporter of Sen. Edward Kennedy before the Democratic National Convention, and Harding, who wore a campaign button boasting the party's fall ticket of Anderson, Lucey and Javits.

The matings were all marriages of convenience, not necessarily love. All of the officeholders need the liberal Party, and have been endorsed by it in the past. And the party, with a declining influence and membership, desperately needs them.

The party, founded in 1944 by garment industry union leaders and intellectuals disillusioned with the Democrats, has only about 100,000 members and attracted so few voters in the last election that it will appear fifth on the ballot this fall behind the Democratic, Republican, Conservative, and Right to Life parties.

But the party has been pivotal in past elections, drawing up to 850,000 voters. In 1976, the Liberals contributed 145,000 of the 280,000 votes Carter carried New York by, and there are those who believe its endorsement of Anderson will keep the president from carrying the nation's second-largest state on Nov. 4.

Anderson was obviously pleased to be invited to the dinner, which attracted more than 2,000 persons at $150 a plate. Never in his lonely independent campaign had he been surrounded by so many officeholders and would-be power brokers.

But his delivery was flat and the crowd's response lukewarm. Carey did not even mention Anderson by name. Javits called him a "Republican of my stripe" and said his campaign was an "extraordinary odyssey." Anderson accused Carter of waging a "mean and evasive" campaign and of attempting to "divide the nation for political gain."

"He is not a liberal, as he claimed to be four years ago," the Illinois congressman said. "But he is not a conservative either. His behavior is that of an opportunist."

Quoting freely from such liberal favorites as Franklin D. Roosevelt, Harry Truman, Adlai Stevenson and John Kennedy, Anderson said that under Carter's presidency "our economy has been mismanaged, our military preparedness has been reduced, and our foreign policy has been bungled. Trust in our political institutions has plunged. And our faith in the future has been dimmed.

"Mr. Carter's administration has been incompetent and incoherent," he added. "And, as Arthur Schlesinger has observed, he doesn't even learn from his mistakes: he gets worse every year."