In order to say definitely what would happen, we need to make sure that
the light bulbs are the only items connected to the battery or power supply.
What I mean is: You can't start out with, say, a string of Christmas tree
lights, and at some point in the string, there's an extra little bulb in parallel
with one of the lights in the string. If that's the situation ... if there's anything else in the circuit besides the two light bulbs in parallel ... then we'd need
more information in order to predict what happens when we make changes
to that part of the circuit.
So the whole circuit consists of:
Two light bulbs in parallel, connected to a battery. That's all.
Now, we connect two MORE light bulbs in parallel with the first ones.
Now we have FOUR light bulbs, all in parallel, connected to the battery.
-- The battery would see the total resistance of the circuit DECREASE.
(An electron that leaves one terminal of the battery now has 4 ways to
reach the other side of the battery, instead of just two. It's easier for
electrons to get there, so more of them make the trip every second.)