Well, let's compare the 3. Catarina was a prisoner in Impel Down who was broken out by Blackbeard, though she was noted as the strongest woman in the world before she went in. It's reasonable to think that she might still be, but unless she was a Yonko, it's unlikely she's as strong as Big Mom currently is. Then there's Boa, whose strength is certainly obvious and ample, yet her former bounty suggests that there's a difference between her and Big Mom.

Admittedly, these are all at least partially assumptions. We know only one Yonko's full strength, and that's Whitebeard, who was declared to be the biggest threat to the world in general. We know something about Shanks (at least, that his strength is somewhat comparable), and we have some idea that Blackbeard has likely become much stronger since the war at Marineford, but in reality, we know very little about the overall level of what constitutes a Yonko. Still, since that's the standard set for the strongest pirates in the show, I use that as my standard as well.

I have to agree with Whiteflame, for the most part. Before becoming a Shichibukai, Hancock was no Yonko. She's clearly strong, being one of the few to have left the War of the Best without a single wound, but I believe that her biggest asset is her undeniably charm and how nearly all weak willed men + Sanji become weak-kneed around her. She is, after all, reputedly the most beautiful woman (excluding Shirahoshi, who is not human) on earth, and the Shichibukai are chosen for their level of intimidation. Catarina was imprisoned in Impel Down for a long time. As we've seen the levels of power seem to change drastically in even a short time. No doubt, Teach was right in freeing her as a strong ally, but I wouldn't see it right to continue to call her strongest, since there are many who may have surpassed her

Linlin gets my vote because she is a Yonkou. She makes up one of the three great powers and his feared and known by all. The way the others panicked when Luffy stupidly challenged the woman for control of Fishman Island is a pretty big testament to her probable strength. And in terms of 'powerful influence', she wins hands down as Hancock isolates herself as a Shichibukai and Catarina was, well, out of commission. Besides that, there is something to be said about a character's size in relation to their strength, though we know it's not really a factor. Kuma, one of the strongest proven characters in One Piece, is a mammoth. Linlin is a freaking titan/giant/goliath hybrid, so I'm looking forward to seeing just how powerful she is, and how she fights.

Of course, I worry that he status is simply influential and she herself is not a powerful fighter. I doubt this possibility, though.

I agree with Whiteflame and Exorcist, but I haven't seen Big Mom yet, so I can't make my vote until I do. XD

Big Mom is a Yonko, the same level as Devon's CAPTAIN. And Hancock may be strong, but most of her power comes from her beauty, so I'm gonna say Big Mom.

Boa by far, at least on men, if it was these three in a battle against each other then Big Mom

ofcourse its big mom thats why she is one of the emperor of the sea..............he he he