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We analyse and empirically examine a multi-level common-pool resource (CPR) game consisting of a collective-choice level game and an operational-level game. In the collective-choice game, participants anonymously propose allocation rules to be used in the operational game and vote anonymously on the proposed rules. Majority and unanimity rules are investigated. Our major finding is that both types of voting rules substantially increase efficiency relative to a baseline with no opportunity for collective choice, but the distributional consequences of the rules differ. To understand the process by which efficiency is improved better, we examine four predictive theories related to proposals, votes, and outcomes.