A higher voltage system enables the same energy at a lower amperage, so constrained to wanting to do a particular thing (loud stereo, bright headlights, ...), h

A higher voltage system enables the same energy at a lower amperage, so constrained to wanting to do a particular thing (loud stereo, bright headlights, ...), higher voltages result in lower amperages. I'll opt to not try to explain that intuitively, hoping that somebody else chimes in. For the other half, "why do amps determine wire size?" Amps are coulombs per second -- how much electrical stuff moves through a cross section in a second. The amount of heat produced is directly proportional to amperage (every bit of movement has a chance to whack into something and produce heat, and more movement per second or more seconds generates more heat). Wire size is ultimately constrained by being able to release that heat while still acting like a wire (not melting, not sublimating, still conducting, not setting anything else on fire, ...). The amount of heat released is proportional to surface area (proportional to the square root of diameter, but that difference doesn't matter a ton right now), and the amount of heat produced is proportional to amperage and approximately nothing else. The point where those two terms are equal is the limit for the system (engineers add in huge safety factors to account for conduit and insulation and other imperfections), above which your wire melts and below which it behaves reasonably. Higher amperages require higher surface area to release the extra heat (so much higher thicknesses), so a given amount of power (stuff you want your electrical system to do) requires lower amps or thicker wires to work appropriately, because you can achieve the same power by increasing the voltage on the same amperage, thereby solving your power problems without extra heat.