Inequalities and injustices are thorny issues in liberal societies, manifesting in forms such as the gender pay gap; sentencing discrepancies among Black, Hispanic, and White defendants; and unequal medical resource distribution across ethnicities. One cause of these inequalities is implicit social bias: unconsciously formed associations between social groups and attributions such as "nurturing," "lazy," or "uneducated." One strategy to counteract implicit and explicit human biases is delegating crucial decisions, such as how to allocate benefits, resources, or opportunities, to algorithms. Algorithms, however, are not necessarily impartial and objective. Although they can detect and mitigate human biases, they can also perpetuate and even amplify existing inequalities and injustices. We explore how a philosophical thought experiment, Rawls's veil of ignorance, and a psychological phenomenon, deliberate ignorance, can help shield individuals, institutions, and algorithms from biases. We discuss the benefits and drawbacks of methods for shielding human and artificial decision-makers from potentially biasing information. We then broaden our discussion beyond the issues of bias and fairness and turn to a research agenda aimed at improving human judgment accuracy with the assistance of algorithms that conceal information that has the potential to undermine performance. Finally, we propose interdisciplinary research questions.