Preferential independence
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| - | In [[multiattribute utility theory]], | + | In [[multiattribute utility theory]], the last step is creating a multiattribute attribute utility function. There are several forms of this function, but the multiplicative and additive forms are easier to deal with because of its simplicity. However, certain conditions must hold in order to use these two forms. Besides preferential independence, two other conditions are relevant as well. These are the [[utility independence]] and [[additive independence]] conditions.<br /> |
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| + | An attribute is preferentially independent from all other attributes when changes in the rank ordering of preferences of other attributes does not change the preference order of the attribute. In general terms, the following must be true:<br /> | ||
| + | [[Image:Preferential_indep1.JPG]]<br /> | ||
| + | <br /> | ||
| + | For example, let's say the two attributes for a car are color (red/black) and style (sports car/SUV). Suppose the decision maker prefers a red sports car over a black sports car. If the decision maker also prefers a red SUV over a black SUV, then the color is preferentially independent of style: Red is preferred over black, regardless of style.<br /> | ||
| + | [[Image:Preferential_indep2.JPG]]<br /> | ||
| + | <br /> | ||
| + | However, style is not necessarily independent from color. It's possible that the decision maker prefers a red sports car over a red SUV, but prefers a black SUV over a black sports car. In this case, the preference on style is not independent of color. | ||
| - | + | == References == | |
| + | * Thurston, Deborah L. "Multi-attribute Utility Analysis of Conflicting Preferences." Decision Making in Engineering Design. Ed. Kemper E. Lewis, et al. New York, New York: ASME Press, 2006. 125-133. | ||
Current revision
In multiattribute utility theory, the last step is creating a multiattribute attribute utility function. There are several forms of this function, but the multiplicative and additive forms are easier to deal with because of its simplicity. However, certain conditions must hold in order to use these two forms. Besides preferential independence, two other conditions are relevant as well. These are the utility independence and additive independence conditions.
An attribute is preferentially independent from all other attributes when changes in the rank ordering of preferences of other attributes does not change the preference order of the attribute. In general terms, the following must be true:
For example, let's say the two attributes for a car are color (red/black) and style (sports car/SUV). Suppose the decision maker prefers a red sports car over a black sports car. If the decision maker also prefers a red SUV over a black SUV, then the color is preferentially independent of style: Red is preferred over black, regardless of style.
However, style is not necessarily independent from color. It's possible that the decision maker prefers a red sports car over a red SUV, but prefers a black SUV over a black sports car. In this case, the preference on style is not independent of color.
References
- Thurston, Deborah L. "Multi-attribute Utility Analysis of Conflicting Preferences." Decision Making in Engineering Design. Ed. Kemper E. Lewis, et al. New York, New York: ASME Press, 2006. 125-133.
