One possibility is analogous to the way running for Parliament works in the UK. If I am not mistaken, you are required to submit a large number of signatures or pay a deposit of £500 which is refunded if you get more than a rather small amount of votes.
So, for instance, a petition might have to pay the Commission for the ex-ante legal advice, with the cost of the advice (1000 euros, give or take ?) being refunded if the petition obtains more than (say) 100,000 signatures. En un viejo país ineficiente, algo así como España entre dos guerras civiles, poseer una casa y poca hacienda y memoria ninguna. -- Gil de Biedma