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Symmetric (3, 2) simple games serve as models for anonymous voting systems in which each voter may vote "yes," abstain, or vote "no," the outcome is "yes" or "no," and all voters play interchangeable roles. The extension to symmetric (j,2) simple games, in which each voter chooses from among j ordered levels of approval, also models some natural decision rules, such as pass-fail grading systems. Each such game is determined by the set of (anonymous) minimal winning profiles. This makes itdoi:10.1016/j.geb.2008.09.035 fatcat:wfnykigqdbdrdkjcpflsqo5pje