Once they made rules that political ads had to specify who was sponsoring them, we started seeing a lot of ads that would say they were sponsored by some unknown organization with a good sounding name. You see this from all sides of the equation; everybody picks a name that sounds like they are for truth, justice and the American Way, and anybody against them is against those things.
But what does a name like the “League of Concerned Citizens” (I made this up) mean? Very little. So what if we extended the requirement that, at least in the political ads, the name had to talk about how many concerned citizens they represented. You might pay more attention to the “League of 84,000 concerned citizens” than a league of 25 of them.
The number would have to represent paying or contributing members, not just people who put their name on a petition. And even so, special interests would try to game it. But still, “The Sierra Club of 750,000” would hold more weight than “The union of 84 homeowners.”