In this paper, we investigate the impact of algorithmic decision-making on social policy, focusing on ``algorithms of care" designed to enhance well-being and equitable access to services. We compare algorithmic prioritization (AP), which uses machine learning models, with categorical prioritization (CP), social policy’s current status quo method for decision-making in social policy.By establishing CP as a robust baseline, we provide a comparative analysis framework to evaluate AP against CP, using the Rashomon set to explore the spectrum of nearly optimal AP models. Our study investigates the efficacy and fairness of AP models relative to CP, utilizing a Rashomon set analysis to explore a spectrum of nearly optimal AP models. By conducting a detailed case study on student dropout prediction at the Polytechnic Institute of Portalegre (IPP) in Portugal, we demonstrate how well-designed CP rules serve not only as effective benchmarks but also potentially surpass AP in terms of fairness and operational simplicity. We emphasize the need for careful deliberation when choosing between AP and CP in social policy.