The Polearm Master feat says:

You can keep your enemies at bay with reach weapons. You gain the following benefits:

• When you take the Attack action and attack with only a glaive, halberd, quarterstaff, or spear, you can use a bonus action to make a melee attack with the opposite end of the weapon. This attack uses the same ability modifier as the primary attack. The weapon’s damage die for this attack is a d4, and it deals bludgeoning damage.
• While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter your reach.

The Duelling fighting style says:

When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon.

So if you were using a spear or a quarterstaff one handed, as I am reading this, you should get a +2 to both the primary attack and to the BA attack.  Is that correct?  The character builder doesn't seem to support that, but it's also not a definitive rules source.  It looks to be a kind of cheesy interpretation of the rules, but seems to be legit.

That appears to be correct RAW. The DDB character sheet couldn’t possibly show it though because of the way the feats are coded. The one feat creates an action, the other modifies a weapon attack. The software has no way of figuring it out.

Thanks, I just wanted to make sure I was reading it right.  I'm not quite sure I'd call it overpowered, but it seems strong at low levels at least, and definitely cheesy.

Legal and a good strategy,  Note, to get that +2 to both attacks, you are converting a 1d10 into a 1d6 and a 1d4.   Damage gain of 0.5 total, excluding increased chances for critical and similar  benefits. 

You're theoretically gaining a shield too, which is why I was thinking about it.  Someone had posted something recently about a hoplite, and spear/shield is the definitive answer for how to make a hoplite.  I thought, well Duelling at least brings the spear up to rapier levels...then I thought, and maybe the secondary would benefit too.  That would give a level 5 ranger three attacks/turn also, with hunter's mark in play and better bonuses than DW alone.

Quote from crzyhawk >>

You're theoretically gaining a shield too, which is why I was thinking about it.  Someone had posted something recently about a hoplite, and spear/shield is the definitive answer for how to make a hoplite.  I thought, well Duelling at least brings the spear up to rapier levels...then I thought, and maybe the secondary would benefit too.  That would give a level 5 ranger three attacks/turn also, with hunter's mark in play and better bonuses than DW alone.

 It would also bring it closer in line with dual wielding. The bonus attack has a smaller die than two weapon fighting (daggers excluded) but does benefit from the attack modifier while also being able to benefit from dueling. If you bring the comparison of dual wielder feat into play (1 feat each), you gain +1 AC, potentially lose 3 average damage from d8s vs the d6 and the d4, but gain +4 from dueling fighting style versus two weapon fighting style. Then it's just the comparison between the OA vs being able to draw two weapons in one turn. Go figure, PAM wins again even here. 

PAM gives you the free OA when something moves into melee range too.  Poor dual wield :(

Quote from crzyhawk >>

PAM gives you the free OA when something moves into melee range too.  Poor dual wield :(

 Yeah, that's what I was comparing to being able to draw two weapons. Chances are, that's not going to matter to the hoplite or anyone else that doesn't dual wield or use thrown weapons. I'm kind of sad that my half-orc barbarian is married to his great axe. I'll have to settle for GWM.

yeah, I re-read your post and understood better what you were trying to say.  DWer should be a half-feat at the very least. If it allowed you to add 1 to your str or dex, it would be a lot better.  DW in general just kind of sucks unfortunately.  I've been playing DW characters since the 2e days, and the 5e implementation is just kind of depressing.  I understand /why/ the came to the conclusions that they did, but I don't like it.  DW would be much better imo, if the offhand weapon scaled kind of like the monk's martial arts rather than on the actual weapon damage.

GWM has it's own benefits, particularly with reckless attack.  I'm generally not a fan of GWM because I don't like missing, but with reckless attack it looks much more attractive to me.  I do like +10 static damage mods though lol.  I'd be lying if I hadn't admitted to kicking around an idea of a warcleric ranger MC with sharpshooter.  Bless + archery fighting style pretty much takes care of the -5 to hit penalty and lets me just throw +10 bombs from the backline.

PAM is truly the spiked chain of 5E.