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Elements of Utility Theory
Published in Craig Friedman, Sven Sandow, Utility-Based Learning from Data, 2016
The cardinal utility function of this theorem is called a von Neumann-Morgenstern utility function. For a cardinal utility function, the numerical value of the utility has a precise meaning (up to a linear transformation). Thus, unlike an ordinal utility function (which, when composed with any monotone function, produces another ordinal utility function), a cardinal utility function encodes information on preferences beyond rank. Two different cardinal utility functions can be consistent with the same ordinal utility function. Thus, two consumers who make the same choices under certainty may choose different lotteries.
Multicriteria Decision Making
Published in Albert G. Holzman, Mathematical Programming, 2020
James S. Dyer, Rakesh K. Sarin
The function v is commonly called an ordinal utility function. However, we shall refer to it as a value function in order to distinguish it more clearly from the parallel development for the utility function in the risky case. v is unique up to a monotone increasing transformation; that is, if a value function v satisfies (1), any other value function constructed by a monotone increasing transformation of v will also represent the same preferences.
On the incremental investment in residential energy efficiency: a Saudi perspective
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2021
It would help to first provide an example of how the graphs are read in the following discussion. For each energy efficiency measure already installed (the bottom row), the utility values for all additional measures (the data points) are compared3Although the closeness of the results is insightful to gauge potential sensitivities to assumed parameters such as the discount rate, the analysis focuses on the qualitative notion of the differences. The presented comparison focuses on if the efficiency measures result in higher or lower utility values (ordinal utility) as opposed to the numerical values of the differences (cardinal utility). Microeconomics has trended toward ordinal utility over the last century (Köbberling 2006). to the same measure without initial energy efficiency purchase. For instance, the utility value of additionally installing more efficient air conditioners when a household already purchased low-e windows is compared to the utility when the household installs the air conditioners without any measure already installed. Let us take Figures 4 and 5, which show the utility results for both electricity pricing cases in the eastern region. With base electricity pricing, the households that reduce air infiltration in their homes do not experience any other measure that improves their welfare state. However, under ToU pricing, further installing more efficient air conditioners would raise their welfare.