The structure of coalitional power under probabilistic group decision rules

The paper extends the work of S. Barbera and H. Sonnenschein on probabilistic social welfare functions by permitting quasi-transitive and/or acyclic probabilistic social preferences. Allowing for quasi-transitivity it is shown that the social decision rule is characterized by a subadditive veto power structure. Gibbard's result on oligarchy is shown to be a special case. Similarly, Sen's theorem on Paretian Liberals is shown to be implied by the power structure in the acyclic case.