Newt Gingrich seems to be making decent sense, in terms of apparent logic, in saying that by staying in the race he can help rack up enough delegates to keep Mitt Romney from winning on the first ballot at the GOP national convention. Sometimes, though, that which seems to make sense does not actually work in practice. Nomination arithmetic is different from normal arithmetic. And no, I am not talking about how he alters the “impressions game” by splitting the conservative vote and thus either handing pluralities to Romney or narrowing the margins of victory for Santorum. That is a very good argument, but that’s not at issue here. What I’m talking about here is exactly the sort of “delegate math” to which Gingrich claims to be appealing.

Here’s how it works: By staying in the race, Gingrich actually helps the second-place candidate in many states (which we will assume will be Romney, for purposes of illustration) gain more delegates, even with a lower total percentage of the vote. This is counterintuitive, but it is 100%, incontrovertibly accurate. Why?

Because a number of states award a huge bloc of delegates “at-large” statewide according to the proportion of the vote each candidate wins statewide — except in a case where one candidate wins an absolute majority of the statewide vote. In that case, the candidate would be awarded every single one of the at-large delegates in a “winner-take-all” system rather than proportionally. 

Consider the rules in Alabama on Tuesday, which are similar to those in a number of other states (with my emphases bolded):

All delegates from the State at Large shall be awarded to a presidential candidate
who receives a majority of the votes in the Republican presidential preference primary election in the state. If no presidential candidate receives a majority of the votes in the state, then the allocation shall be as follows: Based on the relationship that the number of votes received by each presidential candidate bears to the total number of votes cast for candidates receiving at least 20 percent of the vote cast in the Republican presidential primary election in the entire State, the Steering Committee of the Alabama Republican Executive Committee shall apportion pro rata the number of delegates from the State at Large.

If there are only two major candidates (or, in this case, even with Ron Paul pulling something like a minor 5% of the vote), then the likelihood is very high that the “winning” candidate will actually earn a majority, rather than a mere plurality, of the statewide vote. So if Gingrich were not in the race, then the winner (in this case Santorum) would win not 35-30 (or whatever the final numbers were), but, say, 50.5 to 45.5. (And that is assuming that the Gingrich vote would split precisely evenly. Nobody, of course, makes such an assumption in real life; the more likely outcome, backed by several polls (one had it at 57-27), is that Santorum would earn two “Gingrich” voters for every one “Gingrich voter” that goes to Romney.

So how would this have played out in Alabama? Well, with Gingrich in the race, Santorum looks like he will win 10 of the at-large delegates, with Gingrich and Romney each winning eight. Romney would get those eight delegates for earning about 29% or 30% of the vote. But if Gingrich were not in the race and Santorum won the state over Romney 51-42-7 (a very reasonable assumption, actually rather generous to Romney, with Santorum getting 16 of Gingrich’s 30 percent, Romney getting 12 of it, and Paul getting a two percent boost), then Santorum would get all 26 at-large delegates and Romney would get zero.

Yes, read that again: Romney’s percentage of the vote would go from 30 to 42, but his delegate count would drop from 8 to zero. (And Santorum would move up from 10 delegates to 26, at-large.) 

The simple arithmetic is that the way to deny Romney a first-ballot win is not to concentrate on how many delegates other people win; the way to deny him is to keep Romney himself from winning more delegates. What matters in this game is Romney’s delegate count in relation to the target majority of 1,144. The only way to slow him down is to give a conservative challenger a chance not just to win more proportional delegates, but to win more via “winner-take-all” rules which deny any new delegates at all to Romney.

(Granted, the risk is that if Romney comes out ahead in a certain state, this math would work in reverse, in his favor — but since he’s already ahead anyway, the only way to stop him is to at least have the chance to make up the gap in larger chunks.)

In short, for all those states with rules like Alabama’s, a Gingrich candidacy enables Romney to move inexorably closer to a first-ballot nomination victory. Only a Gingrich withdrawal can stop that march.

Now this is not to say whether Romney ought to be stopped or not. This is just to say that if Gingrich’s goal is stopping Romney, Gingrich’s continuation in the race is directly counterproductive.