Governments are increasingly turning to algorithmic risk assessments when making important decisions, such as whether to release criminal defendants before trial. Policymakers assert that providing public servants with algorithmic advice will improve human risk predictions and thereby lead to better (e.g., fairer) decisions. Yet because many policy decisions require balancing risk-reduction with competing goals, improving the accuracy of predictions may not necessarily improve the quality of decisions. If risk assessments make people more attentive to reducing risk at the expense of other values, these algorithms would diminish the implementation of public policy even as they lead to more accurate predictions. Through an experiment with 2,140 lay participants simulating two high-stakes government contexts, we provide the first direct evidence that risk assessments can systematically alter how people factor risk into their decisions. These shifts counteracted the potential benefits of improved prediction accuracy. In the pretrial setting of our experiment, the risk assessment made participants more sensitive to increases in perceived risk; this shift increased the racial disparity in pretrial detention by 1.9%. In the government loans setting of our experiment, the risk assessment made participants more risk-averse; this shift reduced government aid by 8.3%. These results demonstrate the potential limits and harms of attempts to improve public policy by incorporating predictive algorithms into multifaceted policy decisions. If these observed behaviors occur in practice, presenting risk assessments to public servants would generate unexpected and unjust shifts in public policy without being subject to democratic deliberation or oversight.