Friday, October 26, 2007

A utility function is really a value function

Statistician Andrew Gelman argues that economists should use the term "value function" instead of utility function.

He has a point. The word value can mean an objective or subjective value. The word utility means the usefulness to somebody, but that is not necessarily what is important. The purpose of the function is to just capture consumer preferences. A consumer might prefer an item because it is more useful, or for other reasons. Whatever the reasons, preference for an item means that the item has more value to him.

My guess is that economists don't like the word "value" because it suggests a dollar value. Their utility functions are often ordinal-valued, meaning that the function can rank preferences, but not give numbers that be related to other contexts, such as the preferences of other consumers. Also, differences between preferences may not be quantifiable.

But an ordinal value is still a value.

I think that the economist concepts of ordinal utility and cardinal utility are also confusing. Ordinal numbers have the property that for any given ordinary, there a is next larger ordinal. But utility theory does not use that property. Economists are always assuming that given two choices, there is something else that is better than one but worse than the other.

Cardinal utility is for those economists who think that utility can be measured. But that doesn't make much sense either. Besides the problem of cardinal numbers not being divisible, as ordinals are not, cardinals are never negative. But measuring utility necessarily results in some things having negative utility. The utility functions are always real-valued.

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