In this position paper, we advocate for the use of value sensitive design (VSD) as a framework fordeveloping fair AI recruitment tools. As a starting point, we assert that the current paradigm in AI fairnessin the hiring context is severely limiting. We then document an ongoing process within the EU-horizonproject BIAS, seeking to escape this paradigm by applying VSD to the development of AI applicationsfor candidate selection with diversity and fairness as focal points. In particular, we present case-basedreasoning as a case study in the intentional operationalization of stakeholder positions on fairness anddetail how such an approach can be further expanded, drawing from the concept of agonistic machinelearning. In this endeavor, we hope to contribute to the discourse on the ethical design and use of AIwithin the labor market and in general.