I read recently that the earth can be used as a wire to save wiring costs. My understanding of how this works is that a power source, say a battery, separates charge, creating electrons on one side and the absence of electrons on the other, or negative and positive voltage. So a 3V battery would produce -1.5V and 1.5V. Then if we hooked either side of this battery to a ground which has 0V, electrons would flow from the -1.5V to the ground and from the ground to the 1.5V.
However if this were true it seems that if we put a resistor on either side of the battery it would only enjoy half the voltage, i.e 1.5V, that the battery an produce since that is the difference between either side of the battery terminal and ground.
Thus Single Wire Earth Return solutions sacrifice 50% voltage for saving 50% wire cost. However, I cannot find any information stating my analysis is true. Thus I suspect there's something wrong with my reasoning and understanding of electricity.
Thanks for the help!