You double the voltage and halve the resistance. With longer cables you can invest more in more expensive stuff at the ends to deal with the high voltage.
Edit: Basic power loss formula is P=I^2R, so yes power loss is divided by 4 for a 2x increase in voltage assuming the target power delivered is held constant.
At a given power, double voltage means half current. If the resistance is kept the same, that means 4 times lower losses. If the resistance is doubled by using a thinner cable, that still results in two times lower losses.