To be frank, you are likely to see a pattern in the pundits populating the APF. Though 'pundit' is broadly defined as a 'learned person who makes commentary or judgements', I am narrowing the definition for acceptance into the APF.
1) The pundit must have a fanbase, or at the least a credible means for achieving one. Having listenership via a Radio show, viewership via TV show, readership via blogs, columns and books etc...
2) The pundit must engage the other pundits. To truly be a part of the APF they need to interact, they may contribute or debate on each other's shows. They might also reference, deconstruct or ridicule other pundits.
3) Be interesting or popular.
Below is an example of pundits that are relevant but most likely will never appear on the APF: from Jedediah Reed's piece on Radar Mag:
The Iraq Gamble; At the pundits' table, the losing bet still takes the pot
More specifically, since political pundits like Brooks play such a central role in our national decision-making process, maybe something is amiss in the world of punditry. Are the incentives well-aligned? Surely those who warned us not to invade Iraq have been recognized and rewarded, and those who pushed for this disaster face tattered credibility and waning career prospects. Could it be any other way in America?
The pundits mentioned in the article are no doubt influential but don't satisfy certain criteria (most likely 1 and 2). It is is highly probable that these pundits appeared as guests on some of the APF members shows. What is interesting about the article is that it supports the contention I had which started this whole federation: That punditry is a lot like wrestling. In Punditry, your ability to connect and draw in viewers is valued over honesty and accuracy.
Don't misunderstand the wrestling analogy however. It is not to discount or disparage pundits or punditry as a whole, it is truly valuable in providing insight on issues. Rather it is to dispell any notion that it is a meritocracy, just because you are the most seen, heard and paid doesn't mean you are the most accurate or should be the most trusted.