707 research outputs found

    Complexity of Strong Implementability

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    We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated towards a social choice. This is one of the central questions in mechanism design. If the concept of weak implementation is considered, the Revelation Principle states that one can restrict attention to truthful implementations and direct revelation mechanisms, which implies that implementability of a social choice function is easy to check. For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open so far. In this paper, we show by using methods from polyhedral theory that strong implementability of a social choice function can be decided in polynomial space and that each of the payments needed for strong implementation can always be chosen to be of polynomial encoding length. Moreover, we show that strong implementability of a social choice function involving only a single selfish individual can be decided in polynomial time via linear programming

    Low-temperature behaviour of ammonium ion in buddingtonite [N(D/H) 4 AlSi 3 O 8 ] from neutron powder diffraction

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    The structural response of buddingtonite [N(D/H) 4 AlSi 3 O 8 ] on cooling has been studied by neutron diffraction. Data have been collected from 280 K down to 11 K, and the crystal structure refined using the Rietveld method. Rigid-body constraints were applied to the ammonium ion to explore the structural properties of ammonium in the M-site cavities at low-temperature. Low-temperature saturation is observed for almost all the lattice parameters. From the present in situ low-temperature neutron diffraction studies, there is no strong evidence of orientational order–disorder of the ammonium ions in buddingtonite.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46909/1/269_2004_Article_425.pd

    Taking the detour

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115976/1/jhm2424.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/115976/2/jhm2424-sup-0001-suppinfo.pd
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