Artificial intelligence algorithms are ubiquitous in daily life, and this is motivating the development of some institutional initiatives to ensure trustworthiness in Artificial Intelligence (AI). However, there is not enough research on how these algorithms can influence people's decisions and attitudes. The present research examines whether algorithms can persuade people, explicitly or covertly, on whom to vote and date, or whether, by contrast, people would reject their influence in an attempt to confirm their personal freedom and independence. In four experiments, we found that persuasion was possible and that different styles of persuasion (e.g., explicit, covert) were more effective depending on the decision context (e.g., political and dating). We conclude that it is important to educate people against trusting and following the advice of algorithms blindly. A discussion on who owns and can use the data that makes these algorithms work efficiently is also necessary.