In the Bible story that has given the English language the phrase "Solomonic Choice," King Solomon is asked to mediate a dispute between two women--in fact, between two prostitutes. Each of the two claims to be the mother of the same baby. Solomon announces that he will settle the dispute between them by cutting the baby in half. One woman is prepared to see this happen rather than give in to her rival. The other woman, dismayed, says that her rival should be given the baby. The wise king then gives the baby to the woman who was prepared to give the baby up, for it was she who showed herself truly and unmistakably maternal. As the real mother and her baby were safely united, "all Israel came to hear of the judgment which the king had pronounced and held the king in awe, recognizing that he possessed divine wisdom for dispensing justice" (1 Kings 3:28).

If King Solomon were awarding the presidency of the United States, he would presumably award it to the first of the two rival candidates to concede for the good of the country, for the conceding candidate would be the one who showed himself truly and unmistakably presidential. But since neither is prepared to concede, perhaps the election baby--being twins (baby and vice baby)--can be divided after all. This suggestion is not as frivolous as it might sound, given the special circumstances that affect each of the two vice-presidential candidates.

If Vice President Al Gore and Sen. Joseph I. Lieberman win, Senator Lieberman will have been elected to two offices: vice president of the United States and senator from Connecticut. Which will he choose to accept? The assumption has been that he would accept the office of vice president and allow the Republican governor of Connecticut to name a (presumably) Republican senator to succeed him. But does that assumption remain valid?

If Senator Lieberman chooses to accept the office of senator, the Senate will be divided 50-50, with ties to be broken by a new vice president to be named by the president-elect. If Senator Lieberman renounces the vice presidency, in other words, the Democrats gain a technical majority in the Senate.

This clever maneuver might go down quite badly with the American people, however, not to speak of the Republican Party. A Democrat would cast the tie-breaking vote on those few occasions when the vote was 50-50 in the Senate, but the Gore administration would take office having further exacerbated partisan rancor.

Unless, of course, President-elect Gore chose a Republican vice president. If President-elect Gore did this, he would make a dramatic and truly unprecedented move in American politics at a time when nothing less dramatic or more conventional has any chance of succeeding. Who would this Republican be? Whoever he or she would be, we can be sure that in announcing his choice, the Democratic president-elect would say that he had chosen the most respected Republican in the country, someone sure to place the national interest of the country above party interests.

And a good many Republicans might believe him, if only because a good many Democrats would be so appalled. Most proposals for a "national unity" government are borrowed from systems too unlike the American to work. Here would be a solution squarely within the American system.

And there is a Republican as well as a Democratic version of it. Former Secretary of Defense Richard Cheney has just suffered his fourth heart attack. He is 12 years past the kind of surgery (coronary artery bypass graft) that is typically trouble-free for only about 10 years. (I quote the rule of thumb given me after my own bypass surgery less than a year ago.) Mr. Cheney's heart attack provides a President-elect Bush the same opportunity that Senator Lieberman's re-election to the Senate provides a President-elect Gore and at exactly the same cost in political power.

National unity requires sacrifice. At this juncture in American history, the man called on to make the sacrifice that unifies the nation may yet be the vice president-elect. All it will take, beyond that, is a bit of semi-Solomonic wisdom on the part of the next president, whoever he turns out to be.