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Ordinal utility
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{{Short description|Preference ranking}} In [[economics]], an '''ordinal utility''' function is a function representing the [[Preference (economics)|preferences]] of an agent on an [[ordinal scale]]. Ordinal [[utility theory]] claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask ''how much'' better it is or how good it is. All of the theory of [[consumer choice|consumer decision-making]] under conditions of [[certainty]] can be, and typically is, expressed in terms of ordinal utility. For example, suppose George tells us that "I prefer A to B and B to C". George's preferences can be represented by a function ''u'' such that: :<math>u(A)=9, u(B)=8, u(C)=1</math> But critics of [[cardinal utility]] claim the only meaningful message of this function is the order <math>u(A)>u(B)>u(C)</math>; the actual numbers are meaningless. Hence, George's preferences can also be represented by the following function ''v'': :<math>v(A)=9, v(B)=2, v(C)=1</math> The functions ''u'' and ''v'' are ordinally equivalent β they represent George's preferences equally well. Ordinal utility contrasts with [[cardinal utility]] theory: the latter assumes that the differences between preferences are also important. In ''u'' the difference between A and B is much smaller than between B and C, while in ''v'' the opposite is true. Hence, ''u'' and ''v'' are ''not'' cardinally equivalent. The ordinal utility concept was first introduced by [[Vilfredo Pareto|Pareto]] in 1906.<ref>{{cite journal|last=Pareto|first=Vilfredo|title=Manuale di economia politica, con una introduzione alla scienza sociale|journal=Societa Editrice Libraria|year=1906}}</ref>
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