Social Aggregation Rules and Continuity
证明，对于光滑偏好，任何连续的社会加总规则都无法同时满足匿名性和尊重一致性的要求，即使所有个体偏好都是线性的。
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.