As cheerless as it is nearing the end of a dreary and uninspired presidential campaign, one of them - either George Bush or Michael Dukakis - is going to win. And then what?

Aside from the presidency, possession of the keys to the White House for the next four years, what will either of them claim in victory? What will the Americans who elect the next president expect from him?What is the Bush mandate? Or what is the Dukakis mandate?

Based on their campaigns, might we expect:

That President-elect Bush would take over supervision of all the state and federal prisons of the United States and, as national warden, order that no convicted murderer serving a life sentence be granted a furlough. And then he'll do something kind and gentle.

Or that President-elect Dukakis, his portrait freshly repainted and now showing a surprising resemblance to the late Franklin Truman-Kennedy, might order spankings all around for Republicans who lied about him. But he'll forgive those who said he was a liberal.

That's about it - what Vice President Bush and Governor Dukakis have been talking about in this most barren of presidential campaigns of recent history, this ordeal of misrepresentations, insults, lies and mind-numbing "sound bites" and television advertising.

Neither has fully explained himself and his intent on assuming the White House, except for the most obvious and superficial of arguments that would embarrass most political hacks:

- They'll both be tough on crime, especially tough on drug dealers, both ready to make the tough decisions on federal spending while both will demand a leaner, tougher military.

- World terrorists can count on tough treatment from Bush and Dukakis and, while they're both hopeful for a new era of peace and accommodation with the Soviet Union, they'll stay wary. And tough.

But the vexing prospect - and the threat - with the election of either Bush or Dukakis is that neither has asked for or can claim a more serious mandate, approval by a majority of the voters of the nation for specific programs and policies.

Federal debt in the eight years of the Reagan administration has more than doubled, to more than $2 trillion. More than $160 billion is now needed every year just to pay interest on that debt. The budget deficit in fiscal 1988, instead of decreasing, actually increased to $155.1 billion.

The presidential candidates dissemble and talk nonsense to avoid discussing the obvious - tax increases. Dukakis suggests the revenue problem can be cured by simply improving tax collections. He's spoken of some remote tax boosts "only as a last resort" while he says only the rich would be soaked.

Bush is worse with his "read my lips" palaver, promising no new taxes, even a round of new tax cuts for investors. Other Republicans know better. The two chief Senate GOP leaders, Kansas Sen. Robert Dole and Wyoming Sen. Alan Simpson, have acknowledged that, as president, Bush may have to ask for new taxes.

Dole, on weekend television, offered a grim joke on the subject. Just imagine, he suggested, the first meeting to discuss federal revenues between a newly inaugurated "President" Bush and the chairman of the Senate Finance Committee, Texas Sen. Lloyd Bentsen, the current Democratic vice presidential nominee.

The paradox of this lavishly financed and publicized presidential campaign is that the participants - the political parties, the campaign organizations, the media, the consuming voters - would allow the next president to be elected without discussing what he intends.

We won't know until much later what this was all about.