It requires 20 inches of wire in both cases. When connected in parallel, each socket acts as a pass-through to connect the hot and grounded wires to the next s

It requires 20 inches of wire in both cases. When connected in parallel, each socket acts as a pass-through to connect the hot and grounded wires to the next socket in the set, in addition to providing power to the bulb. Thus, the sockets are in series but the bulbs are in parallel. This is how electrical wall outlets are wired. The problem is that a parallel connection requires bulbs that can take 120VAC directly. This is not a problem with C7 and C9 light sets (the small Edison base bulbs). The minis, though, can only take a few volts. Thus, they need to be series-connected to get the voltage drops across the individual bulbs to the level a single bulb can handle.