lt 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.