- Abstract: Ensuring the privacy of sensitive data used to train modern machine learning models is of paramount importance in many areas of practice. One approach to study these concerns is through the lens of differential privacy. In this framework, privacy guarantees are generally obtained by perturbing models in such a way that specifics of data used to train the model are made ambiguous. A particular instance of this approach is through a ``teacher-student'' model, wherein the teacher, who owns the sensitive data, provides the student with useful, but noisy, information, hopefully allowing the student model to perform well on a given task without access to particular features of the sensitive data. Because stronger privacy guarantees generally involve more significant noising on the part of the teacher, deploying existing frameworks fundamentally involves a trade-off between utility and privacy guarantee. One of the most important techniques used in previous work involves an ensemble of teacher models, which return information to a student based on a noisy voting procedure. In this work, we propose a novel voting mechanism, which we call an Immutable Noisy ArgMax, that, under certain conditions, can bear very large random noising from the teacher without affecting the useful information transferred to the student. Our mechanisms improve over the state-of-the-art methods on all measures, and scale to larger tasks with both higher utility and stronger privacy ($\epsilon \approx 0$).