American democracy works on the theory that rational calculation drives two parties competing for a huge electorate toward the center, where the mass of voters congregates. When the Republicans nominated Barry Goldwater in 1964, and the Democrats George McGovern in 1972, the elections were considered deviant.

But this year, the Republicans and Democrats both start the campaign from extreme positions. There is a huge void at the center, and the election turns on the question of which of three candidates will move most effectively to fill it.

Ronald Reagan came to the nomination from the right wing of his party. He tried at the Republican convention to move to the middle. Hence his effort to get Gerald Ford as a running mate, and his final acceptance of a man he didn't much like -- the progressive Republican, George Bush. Hence, too, a remarkable acceptance speech that made no reference to such talismans of the right wing as "nuclear superiority" and the "right to life."

But earlier the party activists had held Reagan to the letter of his past loyalties. In the platform, they committed the party against an arms control treaty with Russia and to a quick and dirty tax cut. They went beyond Reagan in forcing into the platform language that opposed women's rights and any acceptance of abortion and even energy conservation.

Jimmy Carter came to the Democratic convention from a centrist position. But he was challenged on the floor by the liberal wing of his party. He held his ground in fighting demands for wage and price controls, and a unilateral freeze on missile development. However, he was obliged to accept language that virtually supported abortion on demand. He was also forced to give fuller employment a higher priority than fighting inflation. He was jeered when he spoke, in his acceptance speech, of measures taken against the Soviet invasion of Afghanistan, including a draft registration.

Inevitably, perhaps, each candidate has assailed the far-out crowd on the other side. Thus Reagan is stigmatizing the Democratic spenders and the failure to respond to challenges. President Carter, by the same token, represents Reagan as a "threat to world peace."

One certain consequence is that neither party is getting at the country's true problems. Chronic inflation is not going to be conquered by the Democratic stress on jobs or the Republican lust to cut taxes. The energy shortage is not going to yield to Reagan's emphasis on turning business loose or Carter's fine words about new sources. The Republican distaste for arms control and the Democratic inclination to such half-measures as boycotting the Olympics have absolutely no bearing on the vortex of world power around the Persian Gulf.

Positions so far removed from reality seem certain to turn off the great mass of voters who do not throb to shrieks against the welfare state or cries of Armageddon. While fragmentary, the best evidence suggests that neither major candidate is tilting the center in a decisive way. Carter's low rating in the polls continues, and he appears now to be running behind in the must state of New York. The television ratings show that interest in even the high points of the Democratic convention ran well below interest in old movies.

But Reagan is not setting the prairies on fire either. A poll of California by Marvin D. Field showed that even in his home state, Reagan was winning only 51 percent of the vote.

In other words, there is a gaping hole in the electorate. The huge vacuum at the center, expressed by the 75 million eligible voters who didn't bother to cast ballots in 1976, appears to be widening.

Perhaps the void will be filled by the independent candidate, John Anderson. Anderson has money and ballot access and is probably superior in powers of analysis and articulation to the other candidates. If he can begin to show political skills equal to his qualities as an individual, he has a golden opportunity.

Almost certainly the two main candidates will leave the sidelines and push toward the center. But they have to travel a long distance in a short time. The guess here is that nobody will command the center, and that the elections of 1980 will provide one more example of America in political mid-passage, marking time until fresh conditions will at last call forth a working national majority.