If, as we suspect, Rudy faces off with Fred Thompson in the Republican primary and Hillary takes on Obama in the Democratic contest, it'll important to see the primaries not as separate and distinct, but as one combined battle.

At least half the states, including California, allow independents to vote in either party's primary. With more people identifying as independents than as either Democrats or Republicans, their presence in the primaries is crucial.

So the fact is that each of these four final candidates is running, not against his or her party opponent, but against all three other potential nominees. In 2000, for example, Bill Bradley, running for the Democratic nomination, and John McCainJohn Sidney McCainJuan Williams: Biden's promises on women are a big deal Ernst calls for public presidential campaign funds to go to masks, protective equipment President Trump is right — Now's the time for 'all hands on deck' MORE, fighting for the Republican nod, both out-polled Gore and Bush among independents. In fact, the only reason McCain was able to win in New Hampshire was his overwhelming support among independents. Bush beat him handily among Republicans.

In 2000, in a sense, McCain beat Bradley in their unspoken and informal independent primary and attracted more independents into the Republican primary to vote for him than Bradley could attract into the Democratic contest where he was a candidate.

But next year, it may be a question not of which candidate independents like the most but of who they like the least. The primaries may break down into a pro-Hillary and an anti-Hillary contest in which independents are more concerned with stopping the former first lady in the Democratic primary than they are with Giuliani or Fred Thompson being the Republican nominee. Since neither of the Republicans incites much antipathy, and since Hillary does just that, it is very likely that lots of independents will choose to vote in the Democratic primary for Obama so as to stop their bête noire from getting elected.

In some states, even Republicans can vote in the Democratic primaries (and vice versa). Even dedicated GOP voters might switch into the Democratic primary to stop Hillary.

So each candidate in the semi-finals has to pay attention to the entire field, not just to his or her specific primary. That will make strategizing this race very, very interesting.