Humans are increasingly making decisions with the aid of algorithms. In some cases, people have exhibited algorithmic aversion, or a tendency to disregard potentially accurate advice from an algorithm. In other cases, the reverse is true, and humans display algorithmic appreciation. Prior work has focused on the role of task type in determining aversion or appreciation, or has considered an individual's agency in the decision making process. In this paper, we posit that certain latent preferences can explain these decisions. We introduce two constructs related to individuals' tolerance for uncertainty and sensitivity to the source of uncertainty and measure them across three different preregistered experimental tasks (N = 451 participants total). We find an overall robust tendency towards algorithmic appreciation and find that the measures we introduced significantly moderate the propensity to accept algorithmic advice. We find some heterogeneity across task types and identify circumstances where individuals express aversion instead of appreciation.