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Decidability in complex social choices

Author

Listed:
  • Gennaro Amendola
  • Luigi Marengo
  • Davide Pirino
  • Simona Settepanella
  • Akimichi Takemura

Abstract

In this paper we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multi- dimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and proba- bilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima (called local and u-local) are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.

Suggested Citation

  • Gennaro Amendola & Luigi Marengo & Davide Pirino & Simona Settepanella & Akimichi Takemura, 2013. "Decidability in complex social choices," LEM Papers Series 2013/21, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2013/21
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    References listed on IDEAS

    as
    1. Callander, Steven & Wilson, Catherine H., 2006. "Context-dependent Voting," Quarterly Journal of Political Science, now publishers, vol. 1(3), pages 227-254, July.
    2. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    3. repec:cup:apsrev:v:77:y:1983:i:02:p:435-445_24 is not listed on IDEAS
    4. Sendhil Mullainathan & Joshua Schwartzstein & Andrei Shleifer, 2008. "Coarse Thinking and Persuasion," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 577-619.
    5. Bernholz, Peter, 1974. "Logrolling, Arrow-Paradox and Decision Rules-A Generalization," Kyklos, Wiley Blackwell, vol. 27(1), pages 49-62.
    6. Luigi Marengo & Simona Settepanella, 2010. "Social choice among complex objects," LEM Papers Series 2010/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    7. Luigi Maregno & Corrado Pasquali, 2008. "A computational voting model," LEM Papers Series 2008/24, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    8. Gennaro Amendola & Luigi Marengo & Simona Settepanella, 2012. "Decidability and manipulability in social choice," LEM Papers Series 2012/11, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
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    More about this item

    Keywords

    Social choice; object construction; hyperplane arrangement; probability; tournament; algorithm;

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