Are they effective in anyway or are they just as pointless as voting?
Effective for whom?
They are generally a very effective way of getting people to believe that they have done something tangible for a cause. This pressure relief, often means that they will not go on to other more effective forms of protest or action. The petitions are then almost invariably ignored.
Effective for whom?
Who ever is making the petitions for their cause.
Then no. Petitions are not really effective. Look at the UK gov most signed petitions (as of 2017) all of them were basically ignored. I’m sure this is true across the world.
We had several petitions that were succesful in the past years. We had one for the energy crisis for which we managed to raise hundreds of thousands of petitions. It led to a price decrease of the energy bill.
We had a petition against a tax reform for which we raised over 300 thousand petitions. It led to the government abandoning the reform.
Petitions are not going to save the world but it is a useful tool for getting a lot of people to see what your party could do. Hundreds of thousands of people have filled in our petitions, have spoken to our members and have seen that we as a party want to help them.
They are perfectly effective for what they are designed for, the circus part of bread and circuses
I would hesitate to generalize the whole world over, but if we're talking about a dictatorship of capital, where the powers have no reason to listen to you unless 1) what you're saying aligns with their goals or 2) they want to do a PR thing so they pick it out as a show of them being magnanimous, consider Frederick Douglass's words, "Power concedes nothing without a demand."
Is a petition a challenge to power with substance behind it that pressures them to listen? Or is it a suggestion in a suggestion box that can be dumped in the trash?
Especially in the digital age, a petition can be easily ignored entirely. You can't fill someone's office with digital signatures and make them sort through it or find where to put it in a dumpster. In this way, cases where phone calls can be made or emails can be sent is probably more of a realistic pressure, since you're flooding their communication channels. Though with how spam filters are now, emails may also be easily ignored if they share much of the same elements.
I would say pressure needs to either overwhelm with immediacy in order to force a response (which will not necessarily force a wanted change) or be organized enough to have sustained pressure (and then you will face efforts to attack and dismantle it). As petitions don't seem to fall under either, the only value I can see in it is if you are using it as part of a larger strategy to get people energized and gauge how committed they are and see if you can bring some of them into further organizing. But in a place like the US, being increasingly surveillance state and high funding for cops and so on, I would hesitate to imply anyone should be encouraging use of petitions, since that makes a public list that can be used to target people.