A lack of political legitimacy undermines the ability of the European Union to resolve major crises and threatens the stability of the system as a whole. By integrating digital data into political processes, the EU seeks to base decision-making increasingly on sound empirical evidence. In particular, artificial intelligence systems have the potential to increase political legitimacy by identifying pressing societal issues, forecasting potential policy outcomes, informing the policy process, and evaluating policy effectiveness. This paper investigates how citizens perceptions of EU input, throughput, and output legitimacy are influenced by three distinct decision-making arrangements. First, independent human decision-making, HDM, Second, independent algorithmic decision-making, ADM, and, third, hybrid decision-making by EU politicians and AI-based systems together. The results of a pre-registered online experiment with 572 respondents suggest that existing EU decision-making arrangements are still perceived as the most democratic - input legitimacy. However, regarding the decision-making process itself - throughput legitimacy - and its policy outcomes - output legitimacy, no difference was observed between the status quo and hybrid decision-making involving both ADM and democratically elected EU institutions. Where ADM systems are the sole decision-maker, respondents tend to perceive these as illegitimate. The paper discusses the implications of these findings for EU legitimacy and data-driven policy-making.