This article is from the Car Audio FAQ, by Ian D. Bjorhovde (email@example.com) with numerous contributions by others.
A common myth in the car audio community is that upgrading the power or
ground wire to the amplifier will result in the amplifier drawing less
current and therefore decreasing the voltage fluctuation. While the
logic is sound, the premise is not. Most amplifiers on the market have
semi-regulated supplies which don't maintain a steady power output at a
range of supply voltages. This is reflected in the power ratings
provided by many manufacturers; some provide ratings for their
amplifiers at two different voltages, and the lower voltage almost
always causes the amp to deliver less power. In general, the
difference in power output tends to correspond well with the supply
voltage such that the current draw remains roughly constant (assuming
somewhat similar efficiency). Consequently, upgrading the power/ground
wiring, which serves to increase the voltage at the amplifier's
terminals, will not reduce headlight dimming.