Normally, runs the conventional wisdom, the decision matters little. With the possible exceptions of Lyndon Johnson in 1960, widely credited with helping John Kennedy carry Texas, and of Dan Quayle who may have cost George Bush a couple of points in both 1988 and 1992, there is scant evidence that a Vice Presidential candidate has ever had much impact on the final outcome. This time, however, it could be different.
For one thing, Mr Dole at 73 would be the oldest man in history to enter the White House, should he win on 5 November. Never would the proverbial "heartbeat from the Presidency" factor - which perhaps weighed against Mr Quayle - have been so important. Second, this time a possible candidate does exist, apparently unavailable to be sure, but who every poll suggests would make a huge difference. That man is retired general Colin Powell.
If taken at his word, the former Joint Chiefs chairman has unequivocally ruled himself out of consideration. For weeks, associates have been insisting that nothing has changed since last November, when Gen Powell announced he would neither seek the White House, nor be Vice Presidential nominee on any other Republican ticket.
But speculation will not abate so easily - certainly not when every theoretical match-up shows Mr Dole and anyone else trounced by Clinton/Gore, but a Dole/Powell combination with a decent chance of victory. And as far as anyone knows, the commentators wistfully observe, Gen Powell has not been asked.
But if not Colin Powell then who? Until last week, the response might well have been Christine Todd Whitman, Governor of New Jersey, a state Mr Dole would love to win, perhaps has to win. And she has other advantages. She is young, personally and politically attractive, an economic conservative but social moderate who can appeal to both the new breed of "Contract with America" Republicans and the centrists and independents whose support is vital in a general election. Above all, by picking a woman, the hyper- cautious Kansan could show he is capable of the bold strike. The only problem is that on 27 March Mrs Whitman issued a pre-emptive "Thanks, but No Thanks".
At which point, the calculations revert to normal, dictated above all by the arithmetic of the electoral college. To win, Mr Dole must put together a coalition of the South and the Rockie Mountain and Plains states, plus the so-called "Rust belt" of the Midwest - the old industrial heartland of Illinois, Ohio, Michigan and Wisconsin where Mr Clinton currently leads by 10 to 20 per cent in the polls.
Scant co-incidence, therefore, that the Republican governors of all four of those states are plainly in the running. Undoubted favourite among them is John Engler of Michigan, followed by, in declining order of likelihood, George Voinovich of Ohio, Tommy Thompson of Wisconsin, and Jim Edgar of Illinois. Like another name sometimes mentioned, South Carolina's former Governor Carroll Campbell, all four are shrewd political operatives. But all lack the elan and stump appeal Mr Dole sorely needs.
So other names have emerged to fill the Easter political vacuum. One is John McCain, the respected Arizona senator, a military hero from the Vietnam war whose backing for a balanced budget and reform of Washington's financial ways might persuade Ross Perot not to run. Another is Congressman John Kasich, at 43 a political stripling but already chairman of the House Budget Committee and a pillar of the 1994 "Republican Revolution". Unlike most Gingrich revolutionaries, however, he is cheerful, smiling and also happens to come from Ohio, possessor of 21 electoral college votes.
John Engler: 47, elected Michigan Governor in 1990. Responsible for welfare and education reform in his home state; a devout Catholic
Jim Edgar: 49, Governor of Illinois. Welfare reformer, strong on law-and-order, has cut state government payroll sharply since taking office.
Christine Todd Whitman: 49, former US Senate candidate, elected Governor of New Jersey in 1993. Highly popular in her home state
Gen Colin Powell: 58, former national security adviser and chairman of the joint chiefs of staff. The most admired figure in US public lifeReuse content