Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes.

中文翻译：

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多属性权衡偏好的局部几何

多属性其他条件不变偏好陈述的现有表示为定性比较提供了有用的处理和清晰的语义，但没有为涉及定量权衡的比较提供类似的清晰表示或语义。我们使用初等微分几何中的方向导数和其他概念来解释条件多属性其他条件不变的偏好比较，这些比较说明了定量权衡比的界限。这种语义将熟悉的边际替代率的经济学概念扩展到多个连续或离散的属性。相同的几何概念也提供了解释有关不同属性的相对重要性的陈述的方法。