Abstract
We introduce semi-flexible majority rules for public good provision with private valuations. Such rules take the form of a two-stage, multiple-round voting mechanism where the output of the first stage is the default alternative for the second stage and the vote-share thresholds used in every round of binary voting (a) vary with the alternative on the table for a public-good level and (b) require a qualified majority for approving the alternative on the table by stopping the procedure. We show that these mechanisms implement the ex post utilitarian optimal public-good level, provided valuations can only be high or low. This public-good level is chosen after all potential socially optimal alternatives have been picked for a voting round. We explore ways to reduce the number of voting rounds and develop a compound mechanism when there are three or more valuation types.