What are good voting rules if voting is costly? We analyze this question for the case that an electorate chooses among two alternatives. In a symmetric private value model of voting we show that majority voting with voluntary participation Pareto-dominates majority voting with compulsory participation as well as random decision-making.

For a mechanism designer with an objective such as welfare we propose a method for robustly ranking mechanisms. The method is based on eliminating weakly dominated strategies only, and thus does not require any assumptions about agents' beliefs about each other except full support. We illustrate the usefulness of this method in two examples: bilateral trading and voting. In both examples we show that there are mechanisms that are ranked by our method above dominant strategy mechanisms. These examples question the literature's focus on dominant strategy mechanisms in cases when such mechanisms yield undesirable outcomes.