There was a really good conversation about the Republican presidential nomination on Tuesday's Special Report panel. I want to tease an insight out from it, so I'll quote a longer-than-usual portion of it:

BRIT HUME, HOST: Our colleague Mr. Barnes here wrote an article in The Weekly Standard just the other day that said that when you get down to it and look at it with care, the Republican race is now a two man affair between Mitt Romney and Rudy Giuliani.

And the next thing you know, Mitt Romney is moving up in South Carolina, which means that he now leads, or is close to leading, in all three of the early states. Fred, what about this?

FRED BARNES, EXECUTIVE EDITOR, WEEKLY STANDARD: It's the impact of my piece.

HUME: Yes, exactly.

BARNES: Romney is scooting up.

These two, Giuliani and Romney, are the only ones that have realistic scenarios for actually winning the nomination. You have to do well in the early primaries, in Iowa and New Hampshire. And then what is after New Hampshire?

HUME: Super Tuesday.

FRED BARNES, EXECUTIVE EDITOR, WEEKLY STANDARD: Well, you have Michigan, South Carolina, Florida, and then Super Tuesday. They're the only ones that I think realistically have a scenario--

HUME: And the reason is that if somebody else were to win one of those early states that, that person, whoever it is among the rest of the field, whether it be Thompson or anybody else, lacks the organization to capitalize?

BARNES: They lack the organization, they lack the money, in particular, because you wouldn't have time to raise a bundle before getting to Florida on January 29, and then all those primaries on February 5. They really would lack that serious base.

What would happen is what happened to John McCain in 2000 running against George W. Bush. He won in New Hampshire, and then couldn't do much with it. He won in Michigan, where independents could also vote, but after that he petered out. He didn't have the money, didn't have the base of support, didn't have, among Republicans, the organization. [Snip]

BILL KRISTOL, EDITOR OF THE WEEKLY STANDARD: I totally disagree. I think it is a genuine five-way race.

Fred says you can't write a credible scenario for McCain, Huckabee, or Thompson. I think I could write a credible scenario for any of them.

Let's just take New Hampshire. Say McCain went to Iowa and gave an anti-ethanol subsidy speech. I think he is going to write off Iowa, hope that Iowa fragments off into a four-way, 22, 20, 18, 15 result, which is entirely possible -- no big winner.

He is in New Hampshire, that's where he has won before. If McCain wins New Hampshire, how much is it worth? How much paid money do you need if John McCain comes back, wins New Hampshire? The next primary is Michigan. McCain beat Bush in Michigan last time.

McCain could win. Fred Thompson could win or run second in Iowa. And Huckabee, if wins Iowa, is competitive.

I wanted to quote this because I think that Fred Barnes and Bill Kristol are thinking exactly the same way about the Republican nomination contest, even if their conclusions are different. I think this is the correct way to think about it - and I want to take some time to amplify this method because it is of general applicability.

This method is one that I have been using, though I have not been as explicit about it. What they are doing here is working backwards. They are assuming a result, and trying to argue for a way that this result could happen. This is the appropriate way to examine a "game" like the Republican nomination contest because it is one that occurs over time. It is not an all-at-once process. This line of thinking has a bit in common with the method of backwards induction.

Let's take an example, a seemingly unlikely one: Mike Huckabee wins the presidential nomination. Let's start at the end and work backwards, crafting a scenario by which Huckabee could win.

(5) Huckabee wins more delegates than Giuliani
(4) Thompson and Romney drop out of the race
(3) Huckabee wins South Carolina outright, and beats Thompson and Romney in Florida
(2) Huckabee does surprisingly well in New Hampshire
(1) Huckabee wins Iowa outright

This is the first step. You outline a way in which Huckabee arrives at the nomination. Because each event is predicated upon the one immediately preceding it - it is fairly easy to work out whether this whole process can happen. You take the probability of event 1 occurring, multiply by the probability of event 2 occurring given that event 1 has occurred, multiply by the probability of event 3 occurring given that event 2 has occurred...and so on.

So - by this method - we can begin to see whether Huckabee stands a chance of winning the nomination. Let's assign some hypothetical numbers here - just to give us a sense. First off, let's assume that this is Huckabee's only path to the nomination. There may be other ways, but they would be so unlikely that they are not worth mentioning (their final effect would be to increase whatever number we uncover, but probably only by a little bit)

What are the chances that Huckabee wins Iowa? As of right now, he is trading on InTrade at 25.0. That's as good a place as any to start. Let's say that the chances of him winning Iowa are thus 25%.

What are the chances that, given the Iowa win, he does surprisingly well in New Hampshire (e.g. he finishes a close second to Romney, thus taking the luster off the latter's win ala Clinton v. Tsongas in 1992)? Let's put that at 50%. That seems reasonable to me. Romney has a firewall he has built for himself in New Hampshire. It might hold in this scenario. It might not.

So, given an outright win in Iowa and a strong second in New Hampshire - Huckabee looks like the Southern son on the triumphant march back home. I'd expect him to win South Carolina and beat the other cultural conservatives in Florida. Let's put that one at 75%.

Thompson and Romney would assuredly drop out at that point, so step (4) gets 100%.

That would leave Huckabee versus Giuliani. Let's put the odds of Huckabee winning more delegates than Rudy at 50%.

So, the final number comes pretty simply: 25% X 50% X 75% X 100% X 50% = 4.69%.

Now, I don't think that Fred Barnes would agree with the numbers I have assigned here. In his article on the subject as well as during Tuesday's conversation, Fred seems to place a higher premium on money than I do - so he might think that Huckabee breaking through Romney's firewall in New Hampshire is less likely, say only 25%. This would move Huckabeee from about 4.5% to 2.25%. And money might be an impediment to Huckabee in South Carolina and Florida, which would reduce the number even further. Personally, I am more in line with Bill Kristol on the importance of money. I do not think it matters as much after the race actually gets going.

But we should not get caught up on the specific numbers. Don't be beguiled by the two decimal points of that figure I quoted. The numbers that informed it are far too imprecise to put much stock in it. There is just too much cloudiness in all of this to enable us to assign any number.

The point here is the general method - how it works, and how it helps us understand the race. By working backwards, we have done a great deal to clarify disagreements about the Republican race. We've isolated the various steps, and now we can discuss and disagree over the various steps along the way. We've moved from "Huckabee can't win" versus "Yes he can" to "Huckabee won't have the money to break through Romney's firewall" versus "He won't need money to do that." We also appreciate that, since only a few steps (if any) are assured, there is a multiplicative effect in any multi-stage scenario. It's not just a matter of the likelihood of Huckabee winning Iowa. It's a matter of that likelihood multiplied by several other likelihoods.

This is a process that could be repeated for all five Republican candidates - and thus it can serve as a good framework for analyzing this race. This is why I think the conversation on Tuesday's panel was so illuminating. They were talking about the contest in the correct terms.