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Larry J Sabato, professor of politics at the University of Virginia, takes a close look at Hillary Clinton"s arguments that she deserves the Democratic Party"s presidential nomination.

Give Hillary Clinton credit. She has shown toughness, stamina, and persistence in one of the longest presidential campaigns in American history.

She has fought hard and come back time and again in the 2008 primary season, defying the pundits who insisted on writing her political obituary prematurely. She has held the charismatic phenomenon named Barack Obama almost to a draw in the fight for votes and delegates in the Democratic party"s nominating battle.

As some of Obama"s weaknesses become more apparent, her arguments are drawing new attention, and at least a few Democratic leaders are considering them.

All that being true, it"s still very unlikely she will overcome Obama"s lead. With just seven states (plus Puerto Rico and Guam) remaining on the primary schedule, Obama is ahead by close to 160 elected (or pledged) delegates and, overall, by about 130 delegates, once the super-delegates are included.

This may not sound like many in a convention that will host more than 4,000 delegates, but party rules make it difficult to gain a sizeable number of delegates quickly. (Incredibly, you can win a big state and net a mere handful of delegates. The Democrats have developed a system so fair it is unfair.)

Changing the maths

Here"s the basic dilemma for Hillary Clinton: How can she convince senior Democrats to turn their backs on the most loyal party constituency, African-Americans, who regularly give 90% of their votes to party candidates?

For the first time, one of their own has a real chance to become the presidential nominee and the occupant of the White House. The anger in the black community would be palpable and long-lasting if Obama is sent packing.

Democratic women appear unlikely to respond in the same fashion if the first serious woman candidate is turned aside.

Worry among super-delegates about Obama"s viability in the fall is not enough. The only conceivable scenarios that might change the present nominating math are:

How can it be that Clinton is so unlikely to prevail, especially close on the heels of her solid, impressive 9.2% victory in Pennsylvania on 22 April?

Why wouldn"t that victory generate significant momentum for Clinton, just at the moment when the remaining super-delegates prepare to make their decisive choice? Didn"t her 214,000-vote plurality in the Keystone State vault her into the popular-vote lead nationally, as she claimed?

The size and breadth of Clinton"s triumph in Pennsylvania certainly demonstrated the emerging limitations of Obama"s appeal, not least the disaffection of many whites, blue-collar workers, and low-income Democrats.

But it almost certainly will be Obama, not Clinton, who is on the November ballot under the Democratic label.

Michigan and Florida

Take Clinton"s claim about the popular vote. On the morning after Pennsylvania, she insisted that she had taken a narrow popular-vote lead, about 15.12 million to nearly 15 million for Obama. But this is classic "new math", where the numerical answer obtained is often less important than the agile mental gymnastics used to get there.

Clinton"s total relies on two very dubious assumptions. First, one must incorporate the primary results from Florida and Michigan, two January contests excluded by the Democratic National Committee for violating the scheduling rules set by the party. This is no minor sum of votes - 2,344,318, to be exact.

But no even-handed person would contend that Michigan, whose primary occurred on 15 January, should be part of the equation. Barack Obama"s name was not even on the ballot.

The vote total cited by Clinton conveniently excludes three caucus states won by Obama, in Iowa, Maine, and Washington. (Nevada, won by Clinton, is also left out of the tally.) No-one knows the exact number of votes cast for each candidate in these four states since the state parties, by tradition, refuse to release the data.

Eliminating Michigan, the Obama-Clinton match-up shows an Obama edge of a couple hundred thousand votes. Striking Florida brings it to about a half-million-vote Obama plurality. And the unknown caucus results would add at least 100,000 to his lead.

Comparing like with unlike

This discussion of caucus states raises another interesting subject. How can one compare primary and caucus states at all? By their very nature, primaries attract a large electorate in most states. A caucus is a very different political animal, requiring hours of commitment from each participating individual.

The caucus also is inflexible, beginning at a set, mandatory time. There are no absentee ballots and no excuses for troops abroad, medical personnel who must attend to the sick, or elderly individuals who cannot brave a lengthy, stressful outing. Caucus participation is usually just a fraction of the turnout that would have occurred had the state held a primary.

Therefore, the national vote total is heavily skewed to the states holding primaries, and this total mixes primary apples and caucus oranges in an unenlightening way.

The concept of the national popular vote is borrowed from the general election, when it makes more sense. However, in the nominating season the idea is dubious, and it is not a particularly useful measure for the undecided super-delegates. Nevertheless, it has been bandied about so much by the campaigns and news media that it has now become an inescapable yardstick of electoral validity for Clinton and Obama.

Key states

Other questions about the vote mathematics are also compelling. Should the voting results in November"s likely competitive states-the ones we often call purple - a mixture of Republican red and Democratic blue - be given special weight in the popular-vote formula? After all, the purpose of the nominating contest is to pick a candidate who can win the general election.

Hillary Clinton has pushed this interpretation, but only up to a point. She wants her wins in competitive, significant states such as Ohio and Pennsylvania to be determinants for the super-delegates, yet she ignores Barack Obama"s victories in medium-sized toss-up states such as Colorado and Virginia.

With apologies to George Orwell, all states are equal, but some are more equal than others.

Overall, though, this game is pointless since both Clinton and Obama have won states critically important to a Democratic electoral college majority in November.

Different voters

The flaw in the state-based argument is also fundamental. Party primary electorates do not resemble the November electorates in the vast majority of states, so primary results tell us surprisingly little in most states about how a party presidential nominee will fare in the general election.

Think of it this way - perhaps 35 million Americans will have voted in all the Democratic primaries and caucuses by June, but the November voter turnout could reach 135 million people-and those extra 100 million voters are different, both in ideological and partisan terms, than the 35 million early-birds.

US territories

An ancillary issue is whether the U.S. territories, none of which has electoral college votes in November, should even be included in the party nominating system.

In an extremely close race, their delegates could decide the outcome of a presidential nomination, and potentially the Presidency itself. Should Puerto Rico, voting on 1 June, have more delegates than half the American states, as the Democrats have assigned?

Neither Clinton nor Obama will raise this concern, of course, but unbiased observers ought to do so. In most conventions, the territorial votes are a harmless matter, but every now and then, the unintended consequences of their inclusion could become enormous.

The long and short of the debate over the popular vote is this - no-one is likely to agree on exactly what it is, or how it should be counted.

There are considerable flaws inherent in the concept. The popular-vote notion ought to be shelved - but naturally, in this endlessly contentious campaign season, it will not be.

Professor Larry J. Sabato is director of the University of Virginia"s Center for Politics and author of A More Perfect Constitution.