CONVENTIONAL WISDOM HAS it that the office of the vice president is not worth a bucket of warm something or other - there is some question about the word that former Vice President John Nance Garner actually used. But what he meant is clear enough. He meant that, apart from breaking the odd tie vote in the Senate, the nation's second highest office, as such, does not confer much in the way of responsibility or authority upon the incumbent, and that, accordingly, vice presidents over the years, having nothing much in particular to do, have not done much of anything. The problem has been compounded over the years by the fact that running mates have not usually been chosen for reasons that had much to do with their utility once in office. They have been picked for political balance but not necessarily for personal or intellectual compatibility with the president, or for unusual skills or special areas of expertise. Up to a point, that can be said of President-elect Carter's choice of Senator Mondale, whose northern liberlism plainly brought a measure of political balance to the ticket.

But only up to a point, judging from what both men have been saying consistently about their working relationship, and also from what one hears of the role Senator Mondale has actually been playing - in the transition phase as in the campaign itself. What the two men have been demonstrating, by what they have said and done so far, is that they like, trust and respect each other; that they are comfortable working together; that there may well be, in short, a genuine basis for believing that Mr. Mondale's vice presidency will defy the conventional wisdom - that he will, in fact, be functioning as an "equal partner" (Mr. Carter's words) or "almost as a co-equal" to the President (as press secretary-designate Jody Powell put in).

Now, reporters, political commentators and historians are not very good at believing things like that, in large part because too many presidents in the past have said precisely the same thing without meaning a word of it. So there had been a lot of snickering in print about the great things Mr. Carter has said he has in store for Mr. Mondale, and also a certain amount of self-inflicted confusion in the reporting of what the President-elect had in mind last week when he tried to spell out just how his collaboration with his Vice President would work in practice. "He's my chief staff person," Mr. Carter told his propective cabinet down at St. Simons Island, and this was quickly mis-translated into "chief of staff," which understandably shook up Mr. Carter's old Georgia hands. They had not exactly envisioned a White House in which it was going to be necessary for them to go through the Vice President to reach the President, and for good reason; it is a terrible idea. It is also an idea, it seems pretty safe to say, that neither Mr. Carter nor Senator Mondale ever had in mind.

And this, it seems to us, gets to the heart of the question of how a vice president can be useful in a way that would truly mark a historic departure from past practice. It won't happen if the arrangements are too rigid, or if the question is dealt with in tables-of-organization terms, for there is no organizational basis, and still less a constitutional basis, for making the Vice President a fixed and formal part of the executive structure. If there is no prohibition against it. And there is a lot of precedent for presidents assigning importance and authority to figures in and out of government whose counsel and assistance they value. In moments of high crisis, Lyndon Johnson turned to Dean Acheson and others for advice and even gave them an informal role in decision-making because he trusted their judgment. John F. Kennedy assigned special missions to a number of retired former statesmen. Similarly, Jimmy Carter's old friend and counsellor, Charles Kirbo, could remain in his Atlanta law firm, as it has been indicated he may well do, and quite probably continue to exercise more influence on Mr. Carter on certain policy questions, than, let us say, a particular member of the Carter cabinet.

In the case of a vice president occupying an adjacent office, Mr. Carter can go a lot farther than that. He can invest him with full authority to act in the President's name. He can assign specific missions. He can delegate just about anything to Mr. Mondale except ultimate presidential responsibility. But he can do none of these things effectively unless he is as prepared as he professes to be to surrender some part of his power and his authority; to trust another man to speak for him: to back him up in adversity; and to accept the possiblity that he may have to share with him the credit for successes as well. It will not be enough for him to tell Mr. Mondale to speak or act for him. He will have to make that unmistakably clear to those Mr. Mondale will be dealing with.

In theory, it's an idea whose time came a long time ago, as the real and serious - as distinct from the merely ceremonial - burdens of the presidency expanded beyond the capacity of one man to deal with them effectively. In practice, it has never worked, largely for lack of a mutual readiness on the part of past presidents and vice presidents to make it work. Maybe it won't work this time - or won't work for long, as Jimmy Carter learns his own way around the government and the world. But we have a hunch that it will, or at least that the chances of its working are better in this instance than they've ever been. Perhaps it is the advent of a brand new administration that encourages us to fly in the face of conventional wisdom. But that's not the whole basis for our hunch; it rests at least as heavily on what we perceive to be the quality and the character of the two men most directly involved.