Reward design in reinforcement learning and optimal control is challenging. Preference-based alignment addresses this by enabling agents to learn rewards from ranked trajectory pairs provided by humans. However, existing methods often struggle from poor robustness to unknown false human preferences. In this work, we propose a robust and efficient reward alignment method based on a novel and geometrically interpretable perspective: hypothesis space batched cutting. Our method iteratively refines the reward hypothesis space through "cuts" based on batches of human preferences. Within each batch, human preferences, queried based on disagreement, are grouped using a voting function to determine the appropriate cut, ensuring a bounded human query complexity. To handle unknown erroneous preferences, we introduce a conservative cutting method within each batch, preventing erroneous human preferences from making overly aggressive cuts to the hypothesis space. This guarantees provable robustness against false preferences, while eliminating the need to explicitly identify them. We evaluate our method in a model predictive control setting across diverse tasks. The results demonstrate that our framework achieves comparable or superior performance to state-of-the-art methods in error-free settings while significantly outperforming existing methods when handling a high percentage of erroneous human preferences.