In democracies, an absolute majority of voters may choose policies that are harmful to others, even when the harm is larger than the benefit to the majority. We study how individuals choose threshold rules in voting situations, including where sub- or super-majority thresholds are optimal. In our experiment individuals choose thresholds knowing distributions of possible valuations of alternatives but not knowing their own valuation (veil of ignorance). As is optimal, subjects do propose more extreme thresholds for more skewed distributions. However, threshold choices are biased towards simple majority rule, leading to substantial welfare losses. We also identify systematic changes in subjects’ decisions in response to variations in distributions of valuations, even when these variations do not change the optimal threshold choice.