We consider the problem of extending a (complete) order over a set to its power set. The extension axioms we consider generate orderings over sets according to their expected utilities induced by some assignment of utilities over alternatives and probability distributions over sets. The model we propose gives a general and unified exposition of expected utility consistent extensions whilst it allows to emphasize various subtleties, the effects of which seem to be underestimated – particularly in the literature on strategy-proof social (...) choice correspondences. (shrink)

A Collective Identity Function (CIF) is a rule which aggregates personal opinions on whether an individual belongs to a certain identity into a social decision. A simple CIF is one which can be expressed in terms of winning coalitions. We characterize simple CIFs and explore various CIFs of the literature by exploiting their ability of being expressed in terms of winning coalitions. We also use our setting to introduce conditions that ensure the equal treatment of individuals as voters or as (...) outcomes. (shrink)

We consider the problem of producing an impure public good in various jurisdictions formed through the strategic decisions of agents. Our environment inherits two well-known problems: Under individual decisions, there is a tension between stability and efficiency; Under coalitional decisions, stable jurisdiction structures may fail to exist. The solution, we propose is the use of membership property rights: When a move among jurisdictions is subject to the approval of the agents whom it affects, coalitionally stable jurisdiction structures coincide with those (...) which are efficient. (shrink)

We consider the extension of a (strict) preference over a set to its power set. Elements of the power set are non-resolute outcomes. The final outcome is determined by an “(external) chooser” which is a resolute choice function. The individual whose preference is under consideration confronts a set of resolute choice functions which reflects the possible behaviors of the chooser. Every such set naturally induces an extension axiom (i.e., a rule that determines how an individual with a given preference over (...) alternatives is required to rank certain sets). Our model allows to revisit various extension axioms of the literature. Interestingly, the Gärdenfors (1976) and Kelly (1977) principles are singled-out as the only two extension axioms compatible with the non-resolute outcome interpretation. (shrink)

We identify a new monotonicity condition (called cover monotonicity) for tournament solutions which allows a discrimination among main tournament solutions: The top-cycle, the iterated uncovered set, the minimal covering set, and the bipartisan set are cover monotonic while the uncovered set, Banks set, the Copeland rule, and the Slater rule fail to be so. As cover monotonic tournament solutions induce social choice rules which are Nash implementable in certain non-standard frameworks (such as those set by Bochet and Maniquet (CORE Discussion (...) Paper No. 2006/84, 2006) or Özkal-Sanver and Sanver (Social Choice and Welfare, 26(3), 607–623, 2006), the discrimination generated by cover monotonicity becomes particularly notable when implementability is a concern. (shrink)