The claim is that if you have 4 smaller cores but don't need the processing power of more than one of them the other 3 are idle thereby saving the battery.
3 are idle saving the battery i.e. it is a single core in action.
So what's wrong with current single core Windows Phone, where the (non-existant) other 3 are always idle saving the battery!
Before anyone jumps on and says yeah but games and yeah but videos and yeah but graphics... say if I was doing what I do generally, communicate - text, emails, phone, whatsapp, skype, tango, facebook, twitter, linkedin, viber, current games - then I don't really need the second core to make it any faster do I? i.e. battery isn't going to be any better than what it is right now for the mass that don't play those core intensive games or use those graphic hungry video recordings.
However, a scenario when the whole mass market wants to and will use those games everyday and record everything in their life - they will make all the other 3 cores come into action or at least 1 or 2 of them, right? Will they have a better battery than the single cores or worse?
If the theory is that the battery is "better" because we have 3 cores sitting idle - how is it different than single core running all the time on current phones or quad-core Windows Phone?
If the theory is that the battery is "better" because s2 with dual core had both cores working all the time whereas s3 with 4 cores, will have only 1 core working all the time, then it makes sense. But even if with dual cores, the second core is just there if the phone demands for it, then the effect of saving battery won't be noted my the user ever!
In summary, if your tasks are small enough for a single core, it doesnt matter how many cores your phone has, you will never see your battery being better. May be worse, but not better.
But if you tasks are larger than what a single core can handle, for obvious reason, firing up more than 1 core, will drain more battery every time you do that.
However, this is my understanding and will love to discuss this and understand it from someone well-versed with how these cores and battery life work!