I think they serve two purposes:

1. Name recognition for down ballot candidates.
2. For ones on private property: signaling to other people how you feel.

I don't think they really change people's votes per se, or are even really about that. I think the statement it makes to others can make a difference in the mood of a place, even if the effect on the vote count in a given election is minimal.

For example, I was supporting Mills and didn't like LePage very much, and the Republicans were very early in getting their signs up. Seeing a few LePage signs and nothing else around the neighborhood felt kind of meh, like maybe my neighbors really don't agree with me on this. But over time, a few more people (including myself) put Mills signs up. It felt more like an even split at that point, like I wasn't really out on a limb in the neighborhood. If it was only LePage signs the whole time, it wouldn't have changed my vote, but I would have felt like the Dems really didn't have any momentum or local presence, which could change my feeling about them over time.

So yeah, I don't think they swing many voters, but I don't think they're worthless either.

I will say there was a senate candidate in Lewiston who absolutely blanketed the city in his signs because he's a big landlord and some other big landlords were supporting him, so they had plenty of free real estate to cover. It gave me great satisfaction that he lost by a lot.