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We show how this trade-off is encoded into the logic of T cell responses by hierarchical sensitivity to different immune signals. Notably, we find the designs that balance harm from acute infections and autoimmunity produce immune responses consistent with the experimentally observed patterns of T cell effector expansion in mice. Extending our model to immune-based T cell therapies for cancer tumors, we quantify the trade-off between the affinity for tumor antigens (\u201cquality\u201d) and the abundance (\u201cquantity\u201d) of infused T cells necessary for effective treatment. Finally, we show how therapeutic efficacy can be improved by targeted genetic perturbations to T cells. 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