Under simple majority voting an absolute majority of voters may choose policies that are harmful to minorities. It is the purpose of sub- and super-majority rules to protect legitimate minority interests. We study how voting rules are chosen under the veil of ignorance. In our experiment, individuals choose voting rules for given distributions of gains and losses that can arise from a policy, but before learning their own valuation of the policy. We find that subjects on average adjust the voting rule in line with the skewness of the distribution. As a result, a higher share of the achievable surplus can be extracted with the suggested rules than with exogenously given simple majority voting. The rule choices, however, imperfectly reflect the distributions of benefits and costs, in expectation leading to only 63% of the surplus being extracted. Both under-protection and over-protection of minorities contribute to the loss. Voting insincerely leads to a further surplus loss of 5-15%. We classify subjects according to their rule choices and show that most subjects' rule choices follow the incentives embedded in the distributions. For a few participants, however, this is not the case, which leads to a large part of the surplus loss.