Symbolism, Imagery, Allegory
We here at Shmoop believe in equal opportunity, so there's no way we're going to leave the men folk out of symbolic interpretation. Boccaccio sends three men along on the trip with the troop of seven ladies, to provide governance and protection. We know how that sounds to modern ears, but try to get yourself into a 14th-century headspace.
As Elissa points out in the Introduction to the First Day, man was considered the "head" of woman, not just in terms of rational thought but also in terms of governance. The analogue runs something like this: the head governs and directs the body, turning it in the direction it should go. Just so, a man has the superior moral sense to direct women in all things.
Okay, shake it off. Because McWilliam has another theory behind what the men of the brigata represent. Just as the women stand for theological and cardinal virtues, the men represent the tripartite (three-fold) division of the soul, as described by Plato in the Republic. So we have Reason (Panfilo), Spirit (Filostrato) and Appetite/Lust (Dioneo). We might also be able to link these designations to the meaning of their names: Panfilo ("all-loving"), Filostrato ("one destroyed by love") and Dioneo (a reference to Dione, mother of Aphrodite, or Dionysus, the party god).
This may seem like a stretch, but remember that these "characters" are not well defined and do not possess the kind of distinctive personalities that you might expect in a work of fiction. We aren't focusing on their "inner lives" or their individuality, so don't feel too squeamish about working at the symbolic or allegorical levels. It's going to allow you to expand the possibilities for understanding the work as a whole.