Additive utility
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In economics, additive utility is a cardinal utility function with the sigma additivity property.[1]: 287–288
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apple | 5 |
hat | 7 |
apple and hat | 12 |
Additivity (also called linearity or modularity) means that "the whole is equal to the sum of its parts." That is, the utility of a set of items is the sum of the utilities of each item separately. Let be a finite set of items. A cardinal utility function , where is the power set of , is additive if for any ,
It follows that for any ,
An additive utility function is characteristic of independent goods. For example, an apple and a hat are considered independent: the utility a person receives from having an apple is the same whether or not he has a hat, and vice versa. A typical utility function for this case is given at the right.
Notes
- As mentioned above, additivity is a property of cardinal utility functions. An analogous property of ordinal utility functions is weakly additive.
- A utility function is additive if and only if it is both submodular and supermodular.
See also
- Utility functions on indivisible goods
- Independent goods
- Submodular set function
- Supermodular set function
References
- ^ Brandt, Felix; Conitzer, Vincent; Endriss, Ulle; Lang, Jérôme; Procaccia, Ariel D. (2016). Handbook of Computational Social Choice. Cambridge University Press. ISBN 9781107060432. (free online version)
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