Help, a politician I don’t like is in power! I should do something about it. But what? I know! I will join a protest – this is something. Now I can feel good about myself for having done something. And post on social media how I opposed evil so effectively. I am a socially conscious, altrustic person.
On a more serious note, one way to evaluate whether a given protest could change the situation is to put yourself in the position of the target audience. If your favourite politician was in power, would this protest change your support for said politician? If you were the politician in power, would you change your policy when many opponents use this protest against it?
Even if the answer is no, a protest may still have some effect, because it may change the preferences of the swing voters. The „no” may come from deeply ideological people, whereas more open-minded folks may conform to the herd. If they see many people opposed to something, they may start to oppose it too.
On the other hand, a protest may have the opposite effect to the one intended. It may harden ideological positions and increase polarisation. If the majority is weakly in favour of a policy, then protests against it may strengthen the support of the majority for it, leading to greater turnout and more yes-votes.
From an economic viewpoint, marching on the street with signs, chanting slogans or commenting on social media has no direct impact on politicians or most voters. The exception is those who are stuck in a traffic jam when a protest closes a street. Rational agents should not pay attention to protests which do not affect them (such activism is „cheap talk” in economic jargon, or at best „money burning”).
Real people may be swayed by the opinion of a large crowd. However, a form of protest that has an objective impact on people’s lives is likely to influence people more, because it affects them via both the opinion of the crowd and the direct impact. Both the belief shift and the hardening of the opposition are probably greater.
There are many illegal means of directly affecting the population, but also some legal forms of protest with objective impact. Economic protest is boycotting certain countries, firms or goods, refusing to work for the regime, and moving elsewhere („voting with one’s feet”), and is usually legal. The objective impact is that if enough intelligent and hardworking people shift their spending and taxpaying elsewhere, then the regime will be in fiscal trouble. If this does not change the policy of the leadership, then at least the lack of money will make the program harder to carry out.
There is a larger personal cost for economic protest than for cheap talk. One has to give up certain goods, or pay more, or experience the hassle of moving residence. This is why most people who threaten to boycott a firm or leave a country do not end up doing so. The threats are just another form of cheap talk, which can be posted on social media to impress other cheap talkers.