In the D&D next manual it states: "Dual Wielding: When you wield two weapons at the same time, you can attack using both of them using a single action, provided that one of them is a light weapon. You take a -2 Penalty to both attack rolls, and you use only the light weapon's damage dice to determine its damage, you add no bonuses to it. If both weapons are light, only one of them is limited in this way (you choose)." This is what it means, in the most LITERAL way possible. - You need to have at least 1 light weapon equipped to make a dual wielding attack. - Only the light weapon doesn't add the bonus - If both weapons are light, 1 of them does not have the -2 to attack rolls. - If both weapons are not light, then you add your strength modifier to both, because there is no light weapon. What other peoples interpretations are: Even with having two light weapons, you take -2 to both. If you wield 1 regular weapon and 1 light, you use the light weapons damage for both with no strength modifier. Dual wielding two non light weapons means you only get the regular damage, not the strength modifier. That interpretation means that the dual wielding feat is useless, and the only way to effectively dual wield is with two light weapons. Im just trying to look at what it means literally in the manual, right there.
It seems that we've come to a consensus about what the ruling should actually say. The Text should be rewritten to:
Dual wielding: You may declare a dual wielding attack as an action when you wield a light or medium weapon in your mainhand and a light weapon in your offhand. You take a -2 attack penalty to both attack rolls when you attack with both weapons while dual wielding. When you attack, your offhand weapon does not apply its ability modifier during damage.
Dual Wielding Feat: You may wield a medium sized weapon in your offhand as if it was light.