Do fuse blow on ampere or effect?
The 180W reasoning is wrong. You don't have the full 12V across the fuse, only a fraction of it. Say the fuse has a 0.1\$\Omega\$ resistance, then 15A will cause a power dissipation of  


  \$ P = I^2 \cdot R = (15A)^2 \cdot 0.1 \Omega = 22.5W \$.


And that 22.5W in the thin wire is just too much, and the fuse will blow.
Note that the 12V doesn't appear anywhere in this, and you could do the same calculation for 15A at 230V AC. There's a "but", however. Fuses do have a rated voltage. Not for the blowing, as we've seen, but to make sure the remains of the fuse won't cause sparks when at a high voltage. So you can't use a 12V car fuse in a mains appliance, but the other way around should be safe.  

Automatic fuses also react on current only. They have a coil which releases a latch if the number of coil-windings exceeds the rated value. Also here it's independent of voltage.