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### Strategy-proof cardinal decision schemes

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Dutta, Bhaskar, Peters, Hans, Dr. and Sen, Arunava.
(2007)
*Strategy-proof cardinal decision schemes.*
Social Choice and Welfare, Vol.28
(No.1).
pp. 163-179.
ISSN 0176-1714

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1007/s00355-006-0152-9

## Abstract

This paper analyses strategy-proof mechanisms or decision schemes which map profiles of cardinal utility functions to lotteries over a finite set of outcomes. We provide a new proof of Hylland's theorem which shows that the only strategy-proof cardinal decision scheme satisfying a weak unanimity property is the random dictatorship. Our proof technique assumes a framework where individuals can discern utility differences only if the difference is at least some fixed number which we call the grid size. We also prove a limit random dictatorship result which shows that any sequence of strategy-proof and unanimous decision schemes defined on a sequence of decreasing grid sizes approaching zero must converge to a random dictatorship.

[error in script] [error in script]Item Type: | Journal Article |
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Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics |

Divisions: | Faculty of Social Sciences > Economics |

Library of Congress Subject Headings (LCSH): | Utility theory -- Mathematical models, Decision making -- Mathematical models, Probabilities |

Journal or Publication Title: | Social Choice and Welfare |

Publisher: | Springer |

ISSN: | 0176-1714 |

Date: | January 2007 |

Volume: | Vol.28 |

Number: | No.1 |

Number of Pages: | 17 |

Page Range: | pp. 163-179 |

Identification Number: | 10.1007/s00355-006-0152-9 |

Status: | Peer Reviewed |

Publication Status: | Published |

Version or Related Resource: | Dutta, B., Peters, H. and Sen, A. (2008). Erratum : Strategy-proof cardinal decision schemes. Social Choice and Welfare, 30(4), pp. 701-702. http://wrap.warwick.ac.uk/id/eprint/30352. ; Dutta, B., Peters, H. and Sen, A. (2005). Strategy-proof cardinal decision schemes. [Coventry] : University of Warwick, Economics Department. (Warwick economic research papers, no.722). http://wrap.warwick.ac.uk/id/eprint/1469 |

Related URLs: | |

References: | Barberà S (1978) Nice decision schemes. In: Gottinger HW, LeinfellnerW(eds) Decision theory and social ethics: issues in social choice. D. Reidel. Dordrecht Barberà S (1979) Majority and positional voting in a probabilistic framework. Rev Econ Stud 46:379–389 Barberà S, Bogomolnaia A, van der Stel H (1998) Strategy-proof probabilistic rules for expected utility maximizers. Math Soc Sci 35:89–103 Duggan J (1996)Ageometric proof of Gibbard’s random dictatorship result. Econ Theory 7:365– 369 Dutta B, Peters H, Sen A (2002) Strategy-proof probabilistic mechanisms in economies with pure public goods. J Econ Theory 106:392–416 Ehlers L, Peters H, Storken T (2002) Probabilistic collective decision schemes. J Econ Theory 105:408–434 Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–601 Gibbard A (1977) Manipulation of schemes that mix voting with chance. Econometrica 45:665– 681 Gibbard A (1978) Straightforwardness of game forms with lotteries as outcomes. Econometrica 46:595–614 Hylland A (1980) Strategy proofness of voting procedures with lotteries as outcomes and infinite sets of strategies. University of Oslo, Institute of Economics Nandeibam S (1998) An alternative proof of Gibbard’s random dictatorship result. Soc Choice Welfare 15:509–519 Nandeibam S (2004) The structure of decision-schemes with von Neumann-Morgenstern preferences. Social Choice and Welfare Conference, Osaka Quirk JP, Saposnik R (1962) Admissibility and measurable utility functions. Rev Econ Stud 29:140–146 SatterthwaiteM(1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorem for voting procedures and social choice functions. J Econ Theory 10:187–217 Sen A (2001) Another direct proof of the Gibbard-Satterthwaite theorem. Econ Lett 70:381–385 |

URI: | http://wrap.warwick.ac.uk/id/eprint/32516 |

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