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Social Aggregation Rules and Continuity

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  • Graciela Chichilnisky

Abstract

It is shown that any continuous social aggregation rule for smooth preferences cannot simultaneously satisfy the properties of anonymity and respect of unanimity. This is true even when all individual preferences are linear. The relationship between the conditions on the social rule studied here and those of Arrow's paradox is discussed. The first result requires that the normalized gradient of the social choice rule be definable in the interior of the choice space, thus indicating a direction of increase of social preference. A second impossibility result extends the first to cases where the gradient of the social preference may vanish in the interior of the choice space.

Suggested Citation

  • Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(2), pages 337-352.
    • Handle: RePEc:oup:qjecon:v:97:y:1982:i:2:p:337-352.
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    File URL: http://hdl.handle.net/10.2307/1880762
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