Protests are events where people openly reject and denounce the presidente's rule.
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Tropico 3 and 4Edit
Protests happen when a citizen is unhappy and lacks respect for the government, but not to the degree of becoming a rebel. The protesting citizen (symbolized by an icon of a picket sign with "Pendejos muerte!" ("Die, idiots!) written on it above their heads) will stop what they're doing and begin rallying other people around them with a speech. Depending on their own happiness with the government, audience members will either agree with the protest and start losing respect or will be unmoved by the protest.
Protests can be stopped by having the presidente interact with the protestor. If the presidente is too far away, the protest can be stopped by arresting or eliminating the protestor, though this will almost assuredly cause at least one witness to become a rebel. Protests can also be prevented outright; buying the Presidente Statues upgrade for the palace keeps citizens from protesting near the building and citizens with low liberty satisfaction will often be too afraid of the government to protest against it.
In Tropico 5, protests happen when many citizens are unhappy. The protesters (marked by a wooden icon of a picket sign with a 'no' symbol on it) will stop what they're doing and begin rallying other people around them. Depending on their own happiness, passing citizens will either join the protest or ignore it.
There are three ways of dealing with protesters; they can be dispersed violently by the army, they can simply be paid to leave, or they can be negotiated with, initiating a task to quell their discontent.
In Tropico 5: Espionage, protests can be prevented outright by building a Police Blimp with the "Watchful Eye" upgrade. (Because protests happen near residential buildings, the Police Blimp with the upgrade should be put near those buildings).