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.
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We are most grateful to an Associate Editor and two referees for very helpful comments on an earlier version of the paper.
An erratum to this article can be found at http://dx.doi.org/10.1007/s00355-008-0299-7
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Dutta, B., Peters, H. & Sen, A. Strategy-proof Cardinal Decision Schemes. Soc Choice Welfare 28, 163–179 (2007). https://doi.org/10.1007/s00355-006-0152-9
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DOI: https://doi.org/10.1007/s00355-006-0152-9