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? Are adaptive experiments more fair by virtue of their objective? In this paper, I propose a comprehensive examination of fairness by considering multiple dimensions that can influence the researchers' preference for one design over the other. By summarizing and analyzing these distinct dimensions through a utility model, I aim to discuss the relative fairness of adaptive experiments and standard randomized controlled trials. Specifically, I show that these different designs align with extreme versions of the fairness utility model, reflecting the pursuit of distinct fairness objectives within experimental settings. My model highlights the presence of intermediate solutions that can be pursued to reconcile and balance different fairness objectives in experimental designs.