When some voters have nonseparable preferences across multiple binary issues, majority rule may not select a Condorcet winning set of outcomes when one exists, and the social choice may be a Condorcet loser or Pareto-dominated by every other set of outcomes. We present an empirical example of one such paradox from voting on the Internet. We evaluate potential solutions to the problem of nonseparable preferences in referendums, including set-wise voting, sequential voting, and vote-trading. Sequential voting and vote-trading prevent the selection of Condorcet losers and universally Pareto-dominated outcomes. Legislatures facilitate sequential voting and vote-trading better than referendums, suggesting that referendums increase the quantity of participants in democratic decision-making but decrease the quality of participation.