First off, I hope you have actually spoken to the neighbour about the noise, rather than just coming up with the massively technological solution, which though

First off, I hope you have actually spoken to the neighbour about the noise, rather than just coming up with the massively technological solution, which though possibly fun, could also be quickly used against you. If your stereo matched the decibel level of your neighbours stereo in your apartment, that means your apartment would be as loud as your neighbours apartment, in your apartment, but the neighbour isn't in your apartment, so he would still hear his stereo over yours, you'd just annoy yourself. So you would have to match the decibel level in their apartment, which would make your apartment even louder, and if your neighbour had the same stereo decibel sensor, it would sense your apartments noise, and raise it's volume, and you'd be in this loop of apartments raising the volume until one or all of the stereo's maxed out.