The last time a presidential nominating convention went beyond the first ballot was in 1952; the next time it happens may be in 1984.

That intriguing possibility was raised last weekend when the Democrats' latest commission on presidential nominations began getting down to cases.

There is a fervent desire on the part of the commission chairman, North Carolina Gov. James B. Hunt Jr., and many other party leaders to bring more elected officials--especially members of Congress--into the convention hall.

It has struck them forcibly, in thinking about what went wrong in the government their party ran from 1977 through 1980, that some of the divisions might have been avoided had there not been such a gulf between the "presidential party" headed by Jimmy Carter and the congressional party on Capitol Hill.

Only 15 percent of the House Democrats and 18 percent of the Democratic senators were delegates to the 1976 convention that nominated Carter. It was hardly surprising, then, that a Democratic Congress blithely ignored many of the recommendations of that Democratic president.

In 1980, when Carter was renominated over Ted Kennedy, congressional participation declined further. Many elected officials shunned the Madison Square Garden civil war and did their best to distance themselves from Carter in the subsequent campaign.

With this in mind, many Democrats see that a practical way to build unity in both the campaign and the government would be to involve members of Congress and other elected officials more fully in the presidential selection process.

The AFL-CIO and the party's state chairmen have formally endorsed setting aside 30 percent of the 1984 seats for elected and party officials. That means about 1,000 of the 3,330 delegates, if the Democrats have the same size convention they did in 1980.

But here is the catch: the House Democratic caucus, through its chairman, Rep. Gillis Long of Louisiana, advised the Hunt commission that House Democrats would participate en masse only if they were allowed to come as uncommitted delegates.

If they have to identify themselves, in advance, with one contender and against others, Long said, forget it. That kind of political trouble they don't need, when all of them will be on the ballot in the fall of the presidential year.

If the House members are allowed to come uncommitted, then obviously the governors, mayors and party officers who would fill the rest of the 1,000 reserved seats would demand the same privilege for themselves. The AFL-CIO and the state chairmen, recognizing that reality, said they would allow all the big shots to come uncommitted, if they wished.

Now, 1,000 uncommitted votes is a lot of votes--enough to make it very hard for anyone to "lock up" the nomination by sweeping the primaries. In 1980, about 80 percent of the delegates were committed, directly or indirectly, by the results of the primaries, with the other 20 percent coming out of caucuses and conventions.

But if 30 percent of the seats are held by uncommitted elected and party officials, then only 56 percent of the convention delegates will be mandated by the primaries. To guarantee a victory from the primaries, a candidate would have to win about 9 out of 10 of the available primary-election delegates. That is a tall order.

Some dismiss the idea that the uncommitted elected and party officials would vote as a bloc. They argue, plausibly, that the candidate who captured the primaries would surely be nominated, if only because most of the uncommitted delegates would not be heroic enough to defy the sentiments of the popularly chosen delegates from their states.

Some say that even if the uncommitted swung the convention to another candidate, it might not be a bad idea. The politicians and elected officials may know more about the presidential candidates than those primary-election voters do and be better equipped to make the choice.

The last brokered convention produced Adlai Stevenson, whose candidacy was a lot less embarrassing to most Democrats than some of the recent "people's choices."

But for the last 12 years, ever since the bitter Chicago convention of 1968, the prevailing belief in the Democratic Party has been that the voice of the people, as expressed in the primaries, should be reflected in the convention decisions.

You could see the Hunt commission members gulp at the enormousness of reexamining that principle. As they realized that might well be the price they would have to pay for bringing the congressional party into convention hall, they clearly were hesitant.

They meet again in January to make the decision. You can believe there will be a lot of head-scratching and heart-searching between now and then.