That may be true for small groups like clubs, gangs, and tribes, but I don't think you can generalize that to governments.

Or in other words, the more actively engaged the electorate is, the stronger the "public" lobby is vs. other private lobbies.

And the smaller and more local a government is, the more engaged the electorate is. Prime example, the smaller states have more independent senators, governors, etc. By independent I mean literally (I) and not (R) or (D), not just metaphorically independent.