Additive utility
In economics, additive utility is a cardinal utility function with the sigma additivity property.[1]:287-288
| 0 | |
| 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". I.e, the utility of a set of items is the sum of the utilities of each item separately. It says that for every bundle :
An equivalent definition is: for all sets and :
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.
See also
- 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 subadditive and superadditive.
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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