Mmm…it depends. So, one particular example I recall calling for UBI without giving any details and urging people on /r/Europe to sign up for it was at an international level in Europe, and I don’t know what, exactly, the implications of that petition were.
But there are definitely systems of government where petitions do make a difference. The popular initiative exists, and there it’s explicitly part of the process.
I’m not really a huge fan of the popular initiative and referendum – I live in California, which uses both, and I think that some of the policy that I think is most ill-considered in California has gone through via that process. However, it certainly can – and has, on a number of occasions, has – had dramatic impact on the state’s policy, as with California’s unusual property tax situation.
Initiative Statute: Petitions proposing initiative statutes must be signed by registered voters. The number of signatures must be equal to at least 5% of the total votes cast for the office of Governor at the last gubernatorial election. (Cal. Const., art. II, § 8(b); Elec. Code, § 9035.)
The total number of signatures required for initiative statutes is 546,651.
Initiative Constitutional Amendment: Petitions proposing initiative constitutional amendments must be signed by registered voters. The number of signatures must be equal to at least 8% of the total votes cast for the office of Governor at the last gubernatorial election. (Cal. Const., art. II, § 8(b); Elec. Code, § 9035.)
The total number of signatures required for such petitions is 874,641.