It's the core of the case Hillary Rodham Clinton is making to the undeclared superdelegates:

I should be the Democratic presidential nominee because I've won more popular votes in the primaries and caucuses than Barack Obama.

So has she actually won more votes than her rival?

You would think that would be easy to answer. You would be wrong.

There are at least four ways to count the overall popular vote, which is close by any reckoning.

And Obama leads Clinton in three of them.

Only if you give her every benefit of the doubt does she come out ahead in one.

The outcomes range from Obama being ahead by 449,034 votes, which is 1.3 percent of the nearly 35 million votes cast, to Clinton by 174,047.

In counting the popular vote, the main sources of consternation are, as ever, the problem states of Michigan and Florida. They held their primaries earlier than party rules allowed, throwing the results into limbo.

Further muddying the waters is the fact that in four caucus states - Iowa, Maine, Nevada and Washington - no one bothered to count how many people showed up and whom they supported.

Obama won three of those caucuses, and estimates place his cumulative, popular-vote advantage from them somewhere between 23,000 and 113,000. But no one knows for sure, and no one ever will.

Speaking in Florida yesterday, Clinton pressed her case for the primacy of the popular vote, telling supporters that it's "the truest expression of your will." In Kentucky on Tuesday night, she declared: "We're winning the popular vote."

Obama's aides say that their candidate is winning the popular vote but that it hardly matters. Party rules state that the nomination is determined by delegates, not votes, and Obama has won an absolute majority of the delegates available in the full slate of primaries and caucuses.

Keep in mind that the cumulative popular vote has no official standing under Democratic rules. So there's no right or wrong way to count it.

The most widely accepted count - the one seen most often - excludes both Michigan and Florida, since the national party has not recognized either primary.

In that count, Obama is ahead by about 449,034 votes, according to the nonpartisan Web site Real Clear Politics.

His margin is a lot smaller than it was two weeks ago, before Clinton's landslide victories in West Virginia and Kentucky. A big win by Clinton in Puerto Rico on June 1 could make it smaller still but not wipe it out.

So much for Method No. 1.

Method No. 2 takes into account the results from Florida, a primary in which both were on the ballot but neither campaigned. Clinton beat Obama by 295,000.

Add the Florida numbers to the mix and Obama's overall lead dwindles to 154,262. But he is still ahead.

The dicier questions concern what to do with the votes from Michigan.

As was the case in Florida, neither candidate campaigned in Michigan, and voters were warned in advance that the results probably would not count.

The added complication is that Obama removed his name from the Michigan ballot after the national Democratic Party ruled the primary a nonevent. As it turned out, Michigan supporters of both Obama and John Edwards were urged to vote "uncommitted."

So the question is whether Obama should get credit in the popular-vote calculation for the 238,168 uncommitted votes cast in Michigan.

If you give those votes to Obama - and the DNC appears likely to use them as a basis for awarding him some delegates when it considers the Michigan/Florida mess on May 31 - then you have Method No. 3, in which Obama leads by 64,121.

But if you credit him with no votes at all in Michigan, then Clinton leads by 174,047. This is Method No. 4, which, understandably, is the one favored by the Clinton campaign. It is the source of her oft-repeated claim that she is outpolling Obama.

In the end, though, the nomination will be won or lost in terms of who has the most delegates. And Obama's advantage there is clear-cut.

Contact senior writer Larry Eichel at 215-854-2415 or leichel@phillynews.com.