Welfare-maximizing algorithms offer new insights in experimental economics. During an experiment, they identify the most beneficial treatment for the subjects and thus maximize the experiment's overall welfare impact. However, for experimentalists or policy implementers, this implies transferring decision-making power to an algorithm. Allocating individuals to treatment arms using an algorithm exposes us to contemporary criticisms of artificial intelligence, such as discrimination or exacerbation of inequalities. Can we meet the requirements of fairness in these automated designs? I will present preliminary work implementing strategies to control inequalities generated by basic algorithms using recent results on inference in this experimental setup.